First Results from a 20-Liter Prototype Dark
Matter Detector with Directional Sensitivity
MASSACHUSETTS WInT'rE,
OF TECHNOLOGY
by
Jeremy Paul Lopez
JUL 0 1 2014
B.A., Columbia University (2008)
LIBRARIES
Submitted to the Department of Physics
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Physics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2014
@ Massachusetts Institute of Technology 2014. All rights reserved.
A uthor ...............
Signature redacted
'
6
.. . . . .
Department of Physics
November 13, 2013
Signature redacted
.......
Peter Fisher
Professor
T esis Supervisor
Certified by..............
Signature redacted
............
Krishna Rajagopal
Associate Department Head for Education
Accepted by................................
2
First Results from a 20-Liter Prototype Dark Matter
Detector with Directional Sensitivity
by
Jeremy Paul Lopez
Submitted to the Department of Physics
on November 13, 2013, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Physics
Abstract
Astronomical and cosmological evidence suggests that 27% of the energy content
of the universe is in the form of non-baryonic matter referred to as "dark matter."
Weakly interacting massive particles have long been considered attractive candidates
for this dark matter and can be found in a wide variety of models of physics beyond
the Standard Model.
The Dark Matter Time Projection Chamber experiment uses low-pressure gas time
projection chambers to search for nuclear recoils caused by interactions between nuclei
inside a detector and weakly interacting massive particles in the dark matter halo of
the Milky Way galaxy. These detectors are also able to reconstruct the directions of
these nuclear recoils, allowing for better rejection of possible background events.
This thesis describes the design of a small prototype detector and the strategies
used by the DMTPC collaboration to reconstruct events, reject backgrounds, and
identify nuclear recoil candidate events. It presents the results of several studies
aimed at understanding background events in DMTPC detectors. Finally, this work
will present the first results from a nuclear recoil search taken with this detector in a
surface laboratory at MIT.
Thesis Supervisor: Peter Fisher
Title: Professor
3
4
Acknowledgments
There are many people who deserve to be acknowledged for their contributions to my
work in graduate school. I would first like to thank my advisor, Peter Fisher, for his
support and advice throughout my time at MIT. I would also like to acknowledge
Wati Taylor and Richard Milner for their work as my other connittee members.
It has been a privilege to work closely with James Battat, Cosinin Deaconu, and
Shawn Henderson for the past few years on the prototype detector described in my
thesis. This work has been a collaborative effort and could not have been possible
without their contributions. I would like to thank the other members of our group
(both past and present), including Asher Kaboth, Gabriella Sciolla, Denis Dujmic.
Hidefnii Tomita. Jocelyn Monroe, and everyone else who I've worked as part of
the DMTPC collaboration. I also enjoyed collaborating with Denis, Kazuhiro Terao,
Lindley Winslow, and Janet Conrad on a neutron detection project spun off from our
dark matter work.
The staff of the MIT Department of Physics and the Laboratory for Nuclear
Science deserve recognition for tirelessly working to make life easier for all of us.
I would also like to thank both the staff at WIPP and the members of the EXO
collaboration for helping us learn how to work and stay safe in an underground
environment.
Finally, I would like to thank my friends andl fatmnilv for their love and support
throughout my time as a graduate stuident.
5
6
Contents
List of Figures
11
List of Tables
25
1
Introduction
29
1.1
Observational Evidence For Dark Matter
29
1.2
The Density of Dark Matter . . . . . . .
33
1.3
Particle Dark Matter . . . . . . . . . . .
38
1.3.1
Thermal Relics of the Big Bang .
38
1.3.2
Supersymmetry . . . . . . . . . .
40
1.3.3
Universal Extra Dimensions
. . .
44
1.3.4
Non-WIMP Dark Matter . . . . .
45
2
WIMP Dark Matter Searches
47
2.1
Collhder an(I In(lirect Searches .................
2.2
D irect D etection
2.3
. . . . .
47
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
2.2.1
WIMP-Nucleus Scattering . . . . . . . . . . . . . . . . . . . .
49
2.2.2
Recoil Energy Spectrum. . . . . . . . . . . . . . . . . . . . . .
54
2.2.3
Current Direct Detection Experiments
. . . . . . . . . . . . .
58
2.2.4
Annual Modulation Searches . . . . . . . . . . . . . . . . . . .
60
2.2.5
Summnary of Direct Detection Limits . . . . . . . . .
62
2.2.6
Daily \lodulation Searches (or Directional Detection) . . . . .
63
The DMTPC Dark Matter Search . . . . . . . . . . . . . . .
7
. .. .
71
3
4
73
Vacuum Chamber and Gas Systems ......
3.2
Field Cage and Drift Region . . . . . . . . . . . . . . . . . . . . . . .
75
3.3
Amplification Gap
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
3.4
CCD Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
3.5
Charge Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
3.5.1
Signal Generation . . . . . . . . . . . . . . . . . . . . . . . . .
81
3.5.2
Readout Channels
. . . . . . . . . . . . . . . . . . . . . . . .
83
3.6
PMT Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
3.7
Data Acquisition
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
Data Processing and Event Reconstruction
93
4.1
C C D D ata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
4.2
C harge Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
4.2.1
Anode and Veto Readout . . . . . . . . . . . . . . . . . . . . .
98
4.2.2
Mesh Readout . . . . . . . . . . . . . . . . . . . . . . . . . . .
101
PM T D ata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
104
107
Detector Calibration
5.1
5.2
. . . . . . . . . . . . . . . . . . . . . .
107
Fe Calibration . . . . . . . . . . . . . . . . . . . . . . . . . .
109
Charge Readout Energy Scale
5.1.1
55
5.1.2
Energy Scale Validation with
24
Am . . . . . . . . . . . . . . .
114
. . . . . . . . . . . . . . . . .
118
Optical
.Co Gain Map . . . . . . . . . . . . . . . . . . . . . . . . . .
119
Focusing, Length Scale, and Rotations
5.3
6
...................
3.1
4.3
5
73
The DMTPC 4-shooter Prototype
5.4
241
Am a Energy Calibration . . . . . . . . . . . . . . . . . . . . . . .
120
5.5
Directional Reconstruction . . . . . . . . . . . . . . . . . . . . . . . .
125
Characterization of Background Events
131
6.1
Electrons and MIPs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
132
6.2
Alpha Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . .
140
6.2.1
141
Alpha Data and Analysis . . . . . . . . . . . . . . . . . . . . .
8
6.3
7
6.2.2
Range. Energy, and Position Reconstruction
6.2.3
Decay Identification with Timing Information
. . . . . . . . . .
143
. . . . . . . . .
150
CCD Artifact Backgrounds . . . . . . . . . . . . . . . . . . . . . . . .
153
Searching for WIMPs with DMTPC 4-shooter Surface Data
159
7.1
Neutron and WIMP Data . . . . . . . . . . . . . . . . . . . . . . . .
160
7.2
Nuclear Recoil Selection
. . . . . . . . . . . . . . . . . . . . . . . . .
161
7.2.1
Charge Quality & Nuclear Recoil Selection Cuts . . . . . . . .
161
7.2.2
CCD Cuts and Charge/Light Matching . . . . . . . . . . . . .
164
7.2.3
Position Fiducialization
. . . . . . . . . . . . . . . . . . . . .
168
7.3
Expected Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . .
168
7.4
Results from AmBe and WIMP Data . . . . . . . . . . . . . . . . . .
171
7.5
Detection & Reconstruction Efficiency
. . . . . . . . . . . . . . . . .
178
7.6
WIMP Direct Detection Limits
. . . . . . . . . . . . . . . . . . . . .
181
8
Conclusions
185
9
Bibliography
191
9
10
List of Figures
1-1
A mosaic of a number of images from the Hubble Space Telescope
showing part of the Coma Cluster. From NASA [3].
1-2
. . . . . . . . .
31
A composite image of the Bullet Cluster (1E0657-56). The background
is from an optical telescope.
Red is from x-ray data indicating the
presence of x-ray emitting gas. The blue represents the distribution
of mass from gravitational lensing data and indicates that most of the
mass is separate from the gas, suggesting that the mass is largely due
to (lark matter. From NASA [10]
1-3
. . . . . . . . . . . . . . . . . . . .
33
Sky map of fluctuations in the CMB temperature, as measured by
P lanck [12].
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
1-4
The CMB pOWer spectrum, as measured by Planck [14]. . . . . . . . .
37
1-5
Example MSSM Neutralino-Quark Scattering Diagrams . . . . . . . .
43
2-1
Spin-independent form factors for fluorine. carbon, germanium, and
x en o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
2-2
Spin-dependent form factors for carbon, fluorine, germanium, and xenon. 54
2-3
C. F. Ge. and Xe recoil spectra for 10 GeV WIMPs. Form factors have
not been applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-4
C. F. Ge. and Xe recoil spectra for 50 GeV WIMPs. Form factors have
not, been applied.
2-5
56
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
C, F, Ge. and Xe recoil spectra for 100 GeV WIMIPs. Form factors
have not been applied.
. . . . . . . . . . . . . . . . . . . . . . . . . .
11
57
2-6
The annual modulation in the event rate for 100 GeV WIMPs on fluorine. The rate is normalized for a 1 kg mass, 0.3 GeV/cm 3 WIMP
density. and 1 pb cross section.
2-7
. . . . . . . . . . . . . . . . . . . . .
The annual modulation of the event rate in the 2-4 keV energy range
seen by DAMA/LIBRA. From [65].
2-8
61
. . . . . . . . . . . . . . . . . . .
62
Selection of current best spin-independent WIMP-nucleon cross section
measurements.
Dark green solid line: CDMS-II analysis [58].
Light
green solid line: CDMS-II low threshold analysis [68]. Solid red line:
XENON100 result [70].
region [63].
Light blue region:
CRESST-II 1
allowed
Blue dotted region: CRESST-II 3a allowed region[63].
Maroon region: DAMA/LIBRA 3a allowed region, no ion channeling
[71, 72]. Pink dotted region: DAMA/LIBRA 5a allowed region [71, 72].
Gray region: CoGeNT annual modulation region of interest [67]. Blue
(lashed line: LUX conservative sensitivity. Blue (lotted line: LZ projected sensitivity. Red dashed line: XENON1T projected sensitivity.
Made with DMTooIs dark matter limit plotter [73].
2-9
. . . . . . . . . .
63
Selection of current best spin-dependent WIMP-proton cross section
measurements. Green line: PICASSO limit [60].
limit [59].
Red line: SIMPLE
Blue line: COUPP limit, flat efficiency model [61]. Light
blue line: COUPP limit, exponential efficiency model [61]. Pink region:
DAMA/LIBRA 3u allowed region, no ion channeling [71, 72]. Made
with DMTools dark matter limit plotter [73]. . . . . . . . . . . . . . .
64
2-10 A Mollweide projection of the distribution of WIMP directions. The
spatial axes indicate the direction in a non-rotating frame, while the
color axis indicates relative flux. The latitude lines are placed every
30' while the longitude lines are every 60'. The center of the plot is
the position (lat.,long.) = (0', 00). In the coordinates chosen here. the
bright spot. indicating the average direction, points along (0",-900).
opposite Cygnus, which is at (00.900).
12
. . . . . . . . . . . . . . . . .
65
2-11 The distribution of nuclear recoil directions. As with the WIMP distribution, the average direction approximately points away from the
direction of the W IMP wind . . . . . . . . . . . . . . . . . . . . . . .
65
2-12 A histogram of the distribution of nuclear recoil energy versus recoil
direction with respect to the mean direction of the WIMP wind. The
recoil direction is defined here as trec * 9X where ^,.,
defining the recoil direction and
is the unit vector
, is the unit vector pointing toward
the mean WIMP wind direction.
. . . . . . . . . . . . . . . . . . . .
66
2-13 The mean direction of the WIMP wind over a 24-hour period, as seen
from Boston, MA. The horizontal axis represents azimuth and the.vertical axis represents altitude. On this plot, 0' latitude corresponds to
the horizon, while 90' latitude points vertically upward. . . . . . . . .
67
2-14 The mean direction of the WIMP wind over a 24-hour period, as seen
from the Waste Isolation Pilot Plant, near Carlsbad, NM. . . . . . . .
68
2-15 Basic sketch of a time projection chamber of the type used for directional dark matter detection. A WIMP scatters off a nucleus in a
volume of gas with a constant electric field. The resulting nuclear recoil
ionizes the gas as it loses energy, and charge carriers (electrons or ions)
are drifted toward a two-dimensional readout plane. The high field
near the readout plane causes avalanches whose induced signals on electrodes may be amplified and read out. Scintillation during avalanches
m ay also be measured.
3-1
. . . . . . . . . . . . . . . . . . . . . . . . . .
70
Left: The detector with the bell jar closed. The cameras (blue) can
be seen and are attached to the viewports via cylindrical mounts to
hold the lenses far enough back to focus properly. Right: The detector
opened. The copper field cage rings can be seen., with washers used to
separate them and resistors to attain a uniform field within the field
cage. Light reflecting off the cathode mesh can also be seen.
13
. . . . .
74
3-2
A schematic showing the various parts of the amplification region.
Electrons pass through the gaps in the grounded mesh into an amplification gap with a very large electric field. Avalanches proceed toward
the anode, which consists of a thin layer of copper on a GO plate.
Electrodes on the G10 plate are created by machining channels in the
copper coating. The mesh and anode are held apart by nonconducting
tubes with a radius of 435 pm. . . . . . . . . . . . . . . . . . . . . . .
3-3
78
Left: Detail of the top of the field cage. The top two rings (close together) hold the cathode mesh. Between each of the other rings is a
resistor to step down the voltage and several washers used as spacers.
Acetal washers prevent the copper washers from contacting the rings.
Right: High voltage contacts for the central anode electrodes. The outermost electrode (contact not visible) is connected to the amplification
mesh and held at ground. The inner electrodes consist of a veto ring
identifying events near the field cage and a central anode measuring
the energies of events in the central region of the detector.
3-4
. . . . . .
78
A CCD camera with lens attached. The lens is focused on the amplification gap to attain high resolution images of the ionization signals of
events in the detector. A metal plate is used to mount the camera to
the detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-5
80
Some example CCD tracks. Top left: An approximately 3.9 MeV a
track from an "'Am source. Top right: A 200 keVec nuclear recoil
from an AmBe neutron source. Bottom left: A 79 keVee recoil. Bottom
right: A 200 keV,, recoil. The color axis gives the amount of light, in
each pixel. proportional to the total ionization occurring in the region
imaged by the pixel. Nuclear recoils have an approximately elliptical
shape. with the direction of the major axis determining the axis of
motion. More ionization tends to occur at the beginning of the track
than at the end. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
82
3-6
Some example nuclear recoil mesh pulses. The recoils were created
with an AmBe neutron source.
structure of a low-Az pulse.
3-7
Note the characteristic two-peaked
. . . . . . . . . . . . . . . . . . . . . . .
Some example high Az mesh pulses.
84
These can be events such as
minimum ionizing particles, electrons, protons, and other high energy
particles with low stopping power. A wide variety of pulse shapes is
seen in the detector.
3-8
. . . . . . . . . . . . . . . . . . . . . . . . . . .
85
A diagram of the different electrodes on the anode plate. The central
anode and veto channels are held at the same voltage, while the outermost channel is electrically connected to the mesh and held at ground.
From [95]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-9
86
Some example charge-sensitive preamlplifier traces. The central anode
signal is given in blue, while the red signal is from the outer veto ring.
Left: An event in the central region of the detector. Right: An event
near the field cage rings. The small pulse in in the veto channel in the
plot on the left. shows that there is always a small crosstalk signal, even
when the event is far from the veto electrode.
. . . . . . . . . . . . .
87
3-10 Some example PMT traces from o particles. Left: A low Az o from
an
21 'Am
source. Right: A higher Az background c..
The stopping
power maximum correspondls to the position of the Bragg peak for an
a particle. That the peak occurs near the end of the pulse indicates
that the Bragg peak occurred farther from the anode than most of the
track. Hence. the event on the right is traveling away from the anode.
15
88
3-11 Schematic of the computing systems used to run the 4-shooter. The
DAQ computer is responsible solely for taking data files and transferring them to the temporary storage location on the slow control computer. For the 4-shooter, the DAQ process is started from a remote
login shell on the DAQ computer.
The slow control computer pro-
vides a web interface and controls detector systems other than readout
electronics. The files are transferred to the main MIT LNS computing cluster for processing and analysis. The files are also copied to an
offsite storage location to prevent data loss in the case of a disk failure.
4-1
91
The finite-impulse response coefficients used as a low-pass filter to reduce noise in anode and veto readout data. This is the response of the
filter to a unit im pulse. . . . . . . . . . . . . . . . . . . . . . . . . . .
4-2
99
The attenuation in magnitude (left) and phase shift (right) as a func-
tion of frequency of the noise reduction filter used in anode and veto
readout data .
4-3
. . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .
An example smoothed anode waveform.
The original waveform is
shown in blue, and the smoothed waveform is shown in red.
4-4
. . . . .
100
The finite-impulse response coefficients used as a low-pass filter to reduce noise in mesh readout data.
4-5
99
. . . . . . . . . . . . . . . . . . . .
102
The attenuation in magnitude (left) and phase shift (right) as a function of frequency of the noise reduction filter used in mesh readout
data.........
4-6
.....................................
103
An example smoothed mesh waveform. The original waveform is shown
in blue, and the smoothed waveform is shown in red. For the mesh
pulses, the smoothing slightly decreases the prominence of the fast.
peak, but also significantly decreases noise. The noise reduction becomes much more important at, lower energies. . . . . . . . . . . . . .
4-7
103
An annotated smoothed mesh pulse from a nuclear recoil created from
an AmBe neutron source.
. . . . . . . . . . . . . . . . . . . . . . . .
16
104
5-1
Charge readout setup used in x-ray calibration running. The Cr-112
charge sensitive preamplifier integrates the current signal, while an
Ortec 575A spectroscopy amplifier shapes the signals and is used for
triggering. The energy measurement comes from the Cr-112 output.
The veto channel is not read out in these runs. . . . . . . . . . . . . .
5-2
108
An example "Fe calibration event. The raw output is in gray with the
smoothed waveforms overlaid in red.
Top left: The charge-sensitive
preamp output used to obtain the calibration. Top right: The spectroscopy amp output used to trigger the digitizer. Bottom: The fast
amp output. At 5.9 keV, the pulse is too small to accurately reconstruct, but smoothing allows us to see it. . . . . . . . . . . . . . . . .
110
5-3
A typical fit of the "Fe peak to the Crystal Ball function.
111
5-4
Energy calibration vs anode voltage at three different pressures. The
. . . . . .
symbols are the data points and the lines are the best-fit curves for an
exponential function. The gas gain is calculated assuming W = 34 eV
and a preamplifier gain of G = 13 mV/pC. . . . . . . . . . . . . . . .
5-5
The
24
1
1i-Am
112
and x-ray spectrum. Left: Higher energies. The 59.5 keV
line appears as a. broad feature because electrons at that energy are
not typically fully contained in the active volune. The rate show an
additional increase near 25 keV. Right: Detail of lower energy region.
A number of clearly defined peaks are seen.
2 1
. . . . . . . . . . . . . .
116
. . . . . . . . . . . . . . . .
117
5-6
Detail of the low energy peaks of
5-7
Gain maps for cameras 110121 (top left), A80333 (top right), 100534
Am.
(bottom left). 100439 (bottom right). The maps provide a multiplicative scaling factor for each pixel where 1 is defined to be the average
of the active part of the image.
5-8
. . . . . . . . . . . . . . . . . . . . .
Anode energy distribution for each source.
Top left:
110121.
Top
right: A80333. Bottom left: 100534. Bottom right: 100439. . . . . . .
5-9
Range distribution for each source.
Top left:
110121.
122
Top right:
A80333. Bottom left: 100534, Bottom right: 100439 . . . . . . . . . .
17
121
122
5-10 Ratio of the gain-map-corrected CCD energy to anode peak voltage
for each source. This gives an approximate CCD energy scale, though
at a very different scale than for WIMP-induced nuclear recoils.
. .
123
5-11 PMT energy distribution for each source. Significant position dependence is seen here, allowing for the positions of some a particles to be
distinguished from others. PMT 1 has a significantly lower gain than
the other two but has a better energy resolution . . . . . . . . . . . .
124
5-12 Schematic of the experimental setup for directional studies with an a
source.
Only a small fraction of the a crosses the cathode into the
active region, leaving a, well-collimated distribution of low energy a
tracks. Not to scale.
. . . . . . . . . . . . . . . . . . . . . . . . . . .
126
5-13 The mean value of the reconstructed two-dimensional axis as a function
of energy for a source at different angles with respect to the camera
axes. The error bars here are the 1-o- error on the mean value.
. . . .
127
5-14 Example angular distributions of low energy a events in different energy ranges.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
128
5-15 The half-width of the band around the mean containing 68% of events.
This is roughly equivalent to the 1-o width of a Gaussian-distributed
variable.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
129
5-16 Fraction of events where the head-tail effect was used to correctly determine the sense of motion along the recoil axis as a function of energy.
The error bars here represent 95% confidence bands based on binomial
statistics.
6-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
130
The background energy spectra between 0 and 50 keVee at 45, 60, and
75 torr. The primary feature of each spectrum is a prominent peak
between 5 and 15 keV
6-2
. ...
. . . . . . . . . . .
. . . . . . . . . . . . .
134
A histogram of the anode pulse rise time versus energy deposited for
a 60 torr data set. The feature at high rise times (high Az) is what
leads to the peaks in the energy spectra.
18
. . . . . . . . . . . . . . . .
135
6-3
The peaks in data sets at 45. 60, and 75 torr after selecting events
where the 10% to 90% rise time of the anode pulse is greater than 1.8
6-4
s. 136
Schematic of the setup looking for ionization events in the detector
coincident with hits in two scintillator panels. Channels A and B are
the two readout channels of the digitizer used for triggering.
6-5
The energy spectrumn
75 torr CF
4
. . . . .
138
ineasured by the anode of ionization events in
triggered by simultaneous hits in the two scintillator l)an-
els. The peak in this spectrum matches the peak seen in the overall
background spectrum. Some events depositing much more energy than
minimnum ionizing particles are seen as well.
6-6
. . . . . . . . . . . . . .
139
The energy spectrum between 1 and 350 keVe(. for 45, 60, and 75 torr
CF 4 . The spectrum above the peak is a power law, with a prominent
knee between 60 and 100 keVe and a less-prominent ankle around 150
to 200 keV e..
6-7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Total rate of events between the energy threshold and 200 keVee at 45
torr (green), 60 torr (red), and 75 torr (blue).
6-8
140
. . . . . . . . . . . . .
141
Range versus energy for a events. The top plots include only events
originating near the field cage and ending in the central region of the
detector, while the bottom plot includes all events.
dimensional range as measured by the CCDs.
Top left: Two-
Top right:
Three-
dimensional range determined from the CCD range and the mean
width of the three PMT pulses.
Bottom:
Three-dimensional range
for all events. The red curves are the SRIM prediction for the mean
three-dimensional a range.
6-9
. . . . . . . . . . . . . . . . . . . . . . .
145
Diagram of the different parts associated with tihe support post. Left is
the outer edge of the rings while right is the active volume. Both leads
of the field cage resistor are wrapped around the post and connect to
the rings. Acetal washers are placed in between the rings to prevent
electrical contact from being made between the copper washers an(
th e rings.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
147
6-10 The position on the field cage of high-range events originating near the
field-shaping rings. In these coordinates, the field cage support posts
occur at ±45' and ±1350. The anode and veto connections are at -90'
and the grounded outer electrode connects at +90 . . . . . . . . . . .
147
6-11 Energy spectrum of a events with one end occurring near the field
cage rings. A single prominent peak is seen at 4.6 MeVee. Considering
that some energy is lost due to spacers and some is lost before the
a particles reach the volume measured by the central anode channel,
these are likely " 0Po decays. . . . . . . . . . . . . . . . . . . . . . . .
148
6-12 Energy spectrum of events with either both ends or neither end oc-
curring near the field cage rings. The peak at 4.9 MeVee is associated
with a decays in the central region of the detector. The ranges of these
events are consistent with 2"Po decays.
. . . . . . . . . . . . . . . .
149
6-13 Blue line: Energy spectrum of a events originating near the field cage
within 100 of the field cage support posts. Red clotted line: Energy
spectrum of a events originating near the field cage more than 100 from
. . . . . . . . . . . . . . . . . . . . . .
the field cage support posts.
6-14 A candidate
2 23
Ra
-+
21
Rn
-
2 15 Po -+
2
150
11
Ph event. The decays occur
with time separations At, = 1.47 s and At 2 = 3.20 ins, consistent with
what is expected from the decays
2 9
Rn
-
2 15
Po and
2
l5Po
-+
2 11
Pb.
The low diffusion of the tracks near the vertex suggests that this event
originates at the amplification region. The white clashed circle indicates
the outer edge of the central anode electrode.
The left-most track
appears to be fully contained and can be identified by its much longer
Az. It is the second a and has a measured energy of 6.2 MeVe, and a
range corresponding to nearly 7 MeV, consistent with a
20
21 9
Rn decay.
152
6-15 The distribution of the time separation between the a decays in events
with two a-like charge signals. Left: Distribution of all events (blue)
and events where the two a particles originate near a common vertex
(red). Right: The distribution of events near a common vertex (blue)
and the best fit to a histogram drawn from the function
f(t)
= A (})"
./1 5 4
6-16 Two n decays with a separation in time of At = 2.98 s. These are a
potential candidate
22
Ra -+
21 9
Rn
-+
21
Po
-
21
Pb event where one
of the three a Iparticles does not enter the active volume. This event.
and several others like it, appears to occur on one of the field cage rings.154
6-17 Two candidate
22 0
Rn
-
2
pio _,
2
12
Pb decay events. These decays
occur with a time separation of 142 is (left) and 164 ns (right). The
decays shown on the left occur in the active gas volume, while the ones
on the right occur near the field shaping rings. . . . . . . . . . . . . .
155
6-18 An example of a transient hot pixel event. Because this event includes
a number of pixels, it is likely that it is due to a charged particle causing
ionization within the CCD. . . . . . . . . . . . . . . . . . . . . . . . .
6-19 Left:
156
A spark produces a great deal of light that is imaged by the
CCD. Right: Following the spark, the CCD still measures an afterimage (residual bulk image) of the spark for some time. This effect
becomes more noticeable as the exposure length increases.
. . . . . .
157
7-1
Histograms of the anode, mesh, and veto channel baseline voltages.
7-2
Histograms of the anode, mesh, and veto channel voltage baseline RMS. 162
7-3
Three different
.
162
mesh pulse rise time variables versus energy using
AmBe neutron data. Left: 25% to 75%. Center: 10% to 90%. Right:
10% to 50%. The bands extending up to high energy (peak height)
are populated by nuclear recoils while the remaining events represent
backgrounds (muons, electrons, etc.). The center and right plots are
after several cuts have been applied so that the signal band is more
obvious.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
163
7-4
Left: Anode peak height versus fast peak height of mesh pulse. Right:
Anode peak versus veto peak. In both cases, the signal band is the
narrow band extending to high energies.
7-5
. . . . . . . . . . . . . . . .
164
Scatter plot: Anode peak voltage vs gain-map-corrected CCD energy
for each camera. Solid blue line: Parabolic fit. Dashed lines: Limits
of acceptance region. The cuts are chosen to be symmetric around the
blue line, with a generous width in three different energy bins. . . . .
7-6
167
The reconstructed track positions of passing events. Left: AmBe data.
Gray points are passing events not including the fiducial cuts. Red
points are events passing all cuts. Right: Source free data. . . . . . .
7-7
173
Histograms of the distance from the center of the anode of passing
events. Left: AmBe data. Fiducial cuts are not included in the AmBe
data used here.
The linear increase in event rate with radius indi-
cates that the events are approximately uniformly distributed in radius. Right: Source free data. A noticeable excess of events is seen at
high radii, near the field cage rings.
7-8
. . . . . . . . . . . . . . . . . .
174
Energy distributions for nuclear recoil candidates. Left: AmBe data.
The blue points with s/N error bars are the data. The red dashed line
is the expected spectrum from a Geant4 AmBe Monte Carlo program.
Right: Source free data. Again, the blue points with error bars are the
data. The red dashed line is the estimated spectrum of cosmic ray neu-
trons calculated using Geant4 and neglecting the effects of shielding.
In both cases the normalization of the model spectrum is arbitrary.
7-9
.
175
Left: Distribution of measured angles directions in laboratory coordinates from the source free run. Right: Distribution of measured angles
with respect to the direction of the WIMP wind. Both plots use the
two-dimensional projected angle.
22
. . . . . . . . . . . . . . . . . . . .
176
7-10 Reconstructed range vs. energy for AmBe (gray) and WIMP (red)
events.
The value shown is the standard reconstructed range with
twice the track width (2a,) subtracted to account for diffusion.
A
small number of events fall well above the expected range for fluorine
and carbon.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
177
7-11 CCD images of the WIMP run events with unusually large reconstructed ranges. These events are seen with very little diffusion, indicating that they occur very near the anode.
. . . . . . . . . . . . .
177
7-12 An example mesh trace of an event with a long mesh baseline to 50%
or veto rise time.
Two pulses are seen: a small electron-like pulse
immediately followed by a nuclear recoil signal.
. . . . . . . . . . . .
178
7-13 Plots of the three most powerful cut variables for nuclear recoil candidates. AmBe data is plotted in gray while source free (WIMP) data is
plotted in red. The cut limits are shown as blue lines. . . . . . . . . .
180
7-14 90% confidence level upper limits for WIMP masses between 30 GeV
and 10 TeV for the three background scenarios: zero background/signal
only (dotted blue), simple background estimate (dashed red), and background equal to measured value (solid green). The dashed and dotted
gray curve shows the equivalent limit for this exposure with no backgrounds and no measired events, as might be expected in an underground run.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
184
24
List of Tables
2.1
Spin-1/2 Bilinear Covariants in the Low Energy Limit . . . . . . . . .
50
2.2
Definitions of variables used in dark matter scattering calculations.
55
3.1
Electric field properties and various properties of CF 4 relevant to DMTPC
.
detectors. These values assume a pressure of 60 torr at 25'C. . . . . .
3.2
Summary of 4shooter readout channels under standard running conditio n s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
55
. . . . . . . . . . . . . .
Summary of estimates of systematic uncertainty in the "Fe
113
measure-
inen ts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3
104
Fe peak mean and width, as measured by the Cr- 112 preamplifier
over a single fill at three different pressures.
5.2
101
Pulse parameters reconstructed in the mesh reconstruction in addition
to the parameters also reconstructed for the anode and veto channels.
5.1
89
Pulse parameters reconstructed for anode and veto (charge-integrating)
ch an n els. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2
75
114
Recommended values for the avalanche gain and charge energy calibrations at 60 torr CF 4 with a 5 kV drift voltage and 670 V anode
voltage.
5.4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
115
Some x-ray andi-ray lines found in the decay of "4 Amn. Values taken
from [117].
Several additional -- ray lines are also present at much
lower frequency, and Np M-shell lines can be found at, lower energies.
25
115
5.5
Positions and widths of the five peaks in the
24 1Aim
spectrum between
1 and 23 keVec. The second and third columns show the values in the
low energy data set, and the fourth and fifth columns show the values
in the middle energy data set. The uncertainties are the statistical uncertainties reported by Minuit. The 6 keVc peak is near the threshold
in the middle energy data set and is likely underestimated due to the
small number of points included in the peak. . . . . . . . . . . . . . .
5.6
Summary of reconstructed
21
118
Am a properties for the source imaged
by each camera. o- here represents the 1-- width of the distribution. . 124
5.7
The average track angle for energies between 50 and 440 keVee for a
source at several different. angles with respect to the camera axes. The
change in measured track direction between each data set is consistent
with the known amount that the cameras were rotated with respect to
the source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1
Peak mean and height from a Gaussian fit to the region near the peak
in the three spectra from Figure 6-3.
6.2
127
. . . . . . . . . . . . . . . . . .
136
Energy thresholds in keVec required to achieve the given background
rates of events up to 200 keVec at 45, 60, and 75 torr CF 4 . These
results apply in a, surface lab with no shielding or vetoing to reduce
backgrounds such as cosmic ray events. . . . . . . . . . . . . . . . . .
6.3
140
Number of tracks in single-a events with start and end positions having
the given relationship with respect to the field cage rings. Positions
greater than 870 pixels (14 cm) from the center of the anode are defined
as being near the edge of the drift volume. . . . . . . . . . . . . . . .
7.1
7.2
144
List of basic charge quality cuts. Not included are cuts ensuring that
pulse rise and fall time information is properly reconstructed . . . . .
161
List of charge Az and fiducial cuts. . . . . . . . . . . . . . . . . . . .
165
26
7.3
The number of events (40 keV,., < E, < 200 keVce) passing each
successive cut in the AmBe neutron dataset and a WIMP (source free)
dataset. The change gives the fraction of of events passing the cut in
each previous row but failing the cut in that row. The first line shows
the events passing all basic quality cuts.
7.4
. . . . . . . . . . . . . . . .
171
The number of events (40 keV,, < E, < 200 keV,,) passing each
successive cut in the WIMP (source free) dataset. The change gives
the fraction of of events passing the cut in each previous row but failing
the cut in that row .
7.5
. . . . . . . . . . . . . . . . . . . . . . . . . . .
172
Number of passing events in each camera in the 80 to 200 keV,. range
in both AmBe and WIMP data. . . . . . . . . . . . . . . . . . . . . .
27
173
28
Chapter 1
Introduction
The problem of (lark matter is one of the oldest outstanding questions in modern
physics. Despite an abundance of indirect evidence from astrophysical observations
and many years of searching, physicists have yet to observe
convince other physicists that they have observed
or at least have yet to
(lark matter (DM). This thesis
describes work toward developing a new class of -direct detection" apparatus
a
directional Weakly interacting Massive Particle (WIMP) detector.
This first chapter presents the case for WIMP (lark matter, and Chapter 2 provides
an overview of WIMP dark matter searches.
Chapters 3, 4, and 5 describe the
design, event reconstruction, and calibration of a small prototype (lark matter detector
with directional sensitivity. Chapter 6 describes several studies taken to understand
the origins of several classes of background events.
The first dark matter results
with this detector. obtained from several weeks of running in a laboratory at the
surface in Cambridge, Massachusetts., are presented in Chapter 7. Finally, Chapter
8 discusses the implications of this work for underground (lark matter analyses with
similar detectors, as well as for planned much larger detectors.
1.1
Observational Evidence For Dark Matter
The earliest an(d. perhaps, most convincing pieces of evidence supporting the existence
of dark matter come from astrophysical observations.
Much of the observational
evidence can understood using just elementary mechanics.
In the 1930s, Fritz Zwicky. in Ref. [1], used the virial theorem to estimate the
29
gravitational mass of the Coma cluster of galaxies. The Coma cluster lies at a redshift
of 0.024 (approximately 100 Mpc from Earth) [2] and contains many galaxies. For
a collection of objects gravitationally bound through the standard 1/r potential, the
virial theorem gives the relationship between the mean kinetic energy (T) in the
center of mass frame and the mean potential energy (U),
(T)
1
(U) .(1.1)
2
=
If the objects are contained within a sphere of radius R and are not too concentrated
in the center, then the total potential energy of the system can be described by
GM 2
= -x R
R
Utotai
(1.2)
where M is the total mass of the system and x is a constant of order 1 depending on
the mass distribution. For example, x = 3/5 for a uniform distribution. The total
kinetic energy is TtotaI i(v
2
). However, on such scales only the radial velocity v,,
along the line of sight of the observer, is measurable. Due to the spherical symmetry of
the gravitational force, the mean velocity in each dimension should be approximately
the same value. The total kinetic energy, then, can be estimated by
3
Total =
2
v
2
(1.3)
Applying the virial theorem, the total gravitational mass of the system can be calculated from the mean radial velocity and the radius,
Al
-
x
r
G
(1.4)
Using a similar technique, Zwicky measured the mass of the Coma cluster to be
greater than 9 x 104 kg, or 4.5 x 1013A
roughly an order of magnitude lower
than more modern measurements (see Ref. [2]). The mass of stars and gas can be
also be estimated from the total luminosity. Comparing the Coma cluster to the
nearby Kapteyn star system within the Milky Way, Zwicky found that the mass
30
Figure 1-1: A mosaic of a number of images from the Hubble Space Telescope showing
part of the Coma Cluster. From NASA [3].
to luminosity ratio M/L of the Coma cluster was over one hundred times larger.
Although Zwicky proposes a number of effects that may contribute to this discrepancy,
one particularly elegant solution that still has not been ruled out is to hypothesize a
type of nonluminous (or dark) matter that dominates the mass content of the universe
on large scales.
Several decades later, in the 1970s, Rubin et al. used the Doppler shift of hydrogen
emission lines to measure the rotational velocities of objects around spiral galaxies,
discovering that far from the galactic center the orbital velocities were constant or
even increasing with radius [4]. In the classical theory of gravitation, an object in
a circular orbit at radius r in a spherically symmetric mass distribution p(r) has an
orbital velocity of
1/2
r
v(r)=
4G J2p(x)dx
.
(1.5)
0
Solving this to find the mass distribution in terms of the radius and an orbital velocity
rotation curve, we find that
p(r)
4P Gr2
(v2
31
+ 2r,dr
.v
(1.6)
Although the previous equations are not strictly true as spiral galaxies are not spherically symmetric and orbits are not perfectly circular, a constant rotation curve (i.e.
a constant v(r)) implies that, in general,
p(r) oc
1
-~
(1.7)
far from the center of the galaxy. Luminous matter tends to be heavily concentrated
near the center of a galaxy, with little mass beyond some characteristic radius R.
If such matter provided all the mass of a galaxy, the rotational velocity should be
proportional to r 1 for r > R. Rubin and Ford found that the velocity curves for
galaxies typically fail to exhibit this Keplerian decrease in orbital rotational velocity
at any of the measured radii. As with Zwicky's result, one interpretation of this is
that much of the mass of a galaxy is made of some form of nonluminous matter.
This evidence, however, does not conclusively establish the existence of an enormous amount of missing nonluninous matter. Seemingly invisible clumps of normal
matter called massive compact halo objects, or MACHOs, could make up dark matter,
but have been largely ruled out by lensing measurements [5]. The success of models
of Big Bang nucleosynthesis (BBN) at accurately predicting the abundances of light
isotopes further bolsters the case that the dark matter problem cannot be explained
by missing baryonic matter [6].
One can also postulate that perhaps we simply do
not understand the behavior of gravity at very large distances.
Fortunately, more
recent observations challenge such theories of modified gravity. The so-called "Bullet
Cluster" (1E0657-56), believed to be the result of a collision between two clusters, is
the most famous example of such an observation. In a collision, the plasma and gas
from the clusters readily interact and merge in the center, while the galaxies continue
to move in two distinct lobes. Looking at the Bullet Cluster, Clowe et al. [7] used
x-ray emission measurements to study the distribution of plasma and weak gravitational lensing measurements to study the distribution of total mass. They found
that even though the x-ray emitting plasma, which makes up the bulk of the baryonic
matter in the cluster. was concentrated in the center, the gravitational mass generally
tracked the distribution of galaxies. Such a result would be very difficult, to explain
32
with a modification of the gravitational potential. Evidently, most of the mass of
the cluster consists of some form of nonbaryonic, noninteracting (except for gravity)
matter. Measurements of these types of clusters can be used to place constraints on
the interaction strength of this new matter [8, 9].
Figure 1-2: A composite image of the Bullet Cluster (1E0657-56). The background
is from an optical telescope. Red is from x-ray data indicating the presence of x-ray
emitting gas. The blue represents the distribution of mass from gravitational lensing
data and indicates that most of the mass is separate from the gas, suggesting that
the mass is largely due to dark matter. From NASA [10]
1.2
The Density of Dark Matter
With the existence of dark matter established by observational evidence, it is important to determine the amount of dark matter, both in the entire universe and
in the Milky Way near Earth. The average dark matter density of the universe is
determined via cosmological measurements and requires a brief introduction to some
of the elements of the theory of general relativity.
The evolution of the spacetime metric, gP" is described by Einstein's field equa-
33
tions.
R 4vwhere 'T
1
gpR + ytu A = 87GTI>,
2
is the stress-energy tensor, R,,
(1.8)
is the Ricci curvature tensor, and R is
the Ricci scalar. A accounts for a possible constant energy density permeating the
universe, known as a cosmological constant.
While Einstein's field equations describe the local behavior of gravity and the
metric tensor, they can also be used to analyze the global geometry of the universe.
Given the assumptions of homogeneity and isotropy, a differential proper time element
in a universe of constant density takes the form
dr 2 = dt2 - a(t)2 {dr 2 + Sk(r) 2 (d0 2 + sin 2 6d( 2 )}
(1.9)
where the functional form of Sk(r) depends on whether space is flat (k = 0), has
positive curvature like the surface of a sphere (k > 0), or has negative curvature like
a saddle (k < 0). The scale parameter a(t) describes the expansion and contraction of
the spatial dimensions with respect to time. The scale parameter at the present time
is typically defined to be a(today) = 1. Changes in the scale parameter cause the
redshift of electromagnetic radiation traveling over cosmological scales. The redshift,
z, defined as the ratio of the wavelength today to the wavelength at the time of
emission, is related to the scale parameter by a(temitei) = (1 + z)- 1 .
Allowing for a non-zero curvature and assuming that the energy content of the
universe consists of nonrelativistic (cold) matter (m), relativistic (hot) matter and
radiation (r), and dark energy or a cosmological constant (A), Einstein's field equations can be used to derive the Friedmann equation describing the time evolution of
the scale parameter,
H2
p,
6,)2
H3
87riG
PIP
+
Pr
PA
+
k2
.a
(1.10)
pr, and PA are the energy densities of matter, radiation, and (lark energy at a = 1.
In the dark energy term, it is -1
for a true cosmological constant of the form seen
in the field equations. The curvature k is 0 for flat space, 1 for positive curvature
34
and -1 for negative curvature. H is known as the Hubble parameter. We (an define
the Hubble constant Ho to be the value of H at a = 1 and then define a critical
density Pc = 3H(/87rG. Letting Qj = p1/pc, we arrive at the more familiar form of
the Friedmann equation,
(t)2
H~t
H()
Q
a-"4
03U + a
QA
I1 Qm
+ +0
a3(uw+l)
Qr -QA~'
(12
(-1
(i)
HO is the current, value Hubble parameter and Qj describe the fraction of the current energy density of the universe due to nonrelativistic matter (Qm), radiation
and relativistic matter (Q,), a cosmological constant
(k
=
-
-
-
(QA)
and an overall curvature
QA).
The "Standard Model" of cosmology is the ACIDM model, a six parameter model
including (lark energy (A), baryonic matter, and (old dark matter (CDM). Today,
radiation is expected to have an essentially negligible effect on the overall energy
content of the universe because of its a 4
dependence on the scale factor. The most
precise measurements of cosmological parameters come from measurements of the
cosmic microwave background (CMB). The early universe is characterized by a fluid
of photons and baryons at thermal equilibrium with one another. As the universe
expands and cools enough for recombination
the formation of neutral atoms
occur, the photons and baryons leave equilibrium.
to
Photons scatter one last time
and then typically continue to travel indefinitely. Today. the photons have a thermal
(Planck) distribution that is scaled by the redshift of the era of recombination or last
scattering, when z e 1100. These photons make up the CMB and have a temperature
of T = 2.7255 ± 0.0006 K [11].
The CIB temperature, however, is not completely uniform. Fluctuations in the
temlperature are related to density fluctuations and are thought to have originated
as quantum fluctuations from the very early universe that were magnified during
inflation. The initial fluctuations lead to acoustic oscillations in the btaryon-photon
fluid. The fluctuations seen in the CB show the amplitudes of these modes at the
time of last scattering.
The CMB fluctuations are typically characterized by their power spectrum. Tele35
Figure 1-3: Sky map of fluctuations in the CMB temperature, as measured by Planck
[12].
scopes measure the fluctuations as projected onto the sky, so the distance scale of
an oscillatory mode corresponds to a particular angular scale. The fluctuations are
decomposed into spherical harmonic modes,
6T '0 =M,"Y,"(,
(1.12)
t=O m=-e
and the power spectrum is taken to be the average power of the modes at each
multipole moment t,
1
Typically, the power spectra are plotted using f(f + 1)Ct rather than Ct [13].
Oscillatory modes that are near maxima or minima at the time of last scattering
lead to larger temperature fluctuations at the multipole moment corresponding to
that mode. This results in a series of acoustic peaks in the power spectrum, with
the first near C= 200. The exact positions and heights of these peaks depend on the
properties of the baryon-photon fluid in the early universe [13].
Many cosmological parameters can be extracted from the shape of the power
spectrum. Recent measurements from the Planck satellite along with a best-fit curve
36
Multipole moment, t
2
10
50
1000
500
2000
1500
2500
6000
5000
4000
3000
a))
CL
1000
E
000
W,
M8
1
0.2Angular scale
OT1
0.07'
Figure 1-4: The CMB power spectrum, as measured by Planck [14].
for the ACDM model are shown in Fig.
1-4.
Earlier measurements of the CMB
power spectrum were also made by WMAP, and a number of different experiments
have studied the higher multipole moments as well as other properties of the CMB.
The Planck results [15] yield best fit values of QA = 0.6825 and QM = 0.3125 for
dark energy and matter, respectively. The Planck Collaboration also find that cold
(nonrelativistic) nonbaryonic dark matter comprises 84.5% of all matter and 26.4%
of the total energy content of the universe. Planck's measurements show a slightly
larger percentage of cold dark matter than previous measurements by WMAP [16].
CMB measurements give the average density of cold dark matter in the entire
universe.
The observational evidence for dark matter shows that dark matter is
not evenly distributed throughout the entire universe.
Galaxies and even galactic
clusters are associated with regions of high dark matter density (p.), so the dark
matter density near Earth is likely to be much higher than average. Experimentalists
often use the canonical local dark matter density of p. =0.3 GeV/cm 3 [17], although
there is quite a bit of variation in estimates of p,.
One of the more recent analyses
suggests that a value of p. = 0.39 ±0.03 GeV/cm 3 might be more accurate [18]. This
work will use the value of p. = 0.3 GeV/cm 3 for consistency with other results.
37
1.3
Particle Dark Matter
With astrophysical and cosmological evidence for (lark matter converging on the idea
of cold nonbaryonic dark matter making up most of the mass of the universe, we can
then propose that perhaps dark matter is composed of some novel elementary particle
not found in the Standard Model of particle physics (SM). We must then determine
how such particles may be produced in the early universe and what kinds of particles
can be dark matter candidates.
1.3.1
Thermal Relics of the Big Bang
If cold particle dark matter is the correct paradigm for (lark matter, CDM mst be
produced in the early universe and it must maintain a significant density throughout
the history of the universe. That is, the annihilation rate of dark matter must become
essentially negligible compared to the rate of change in the dark matter density due to
the expansion of the universe in order to maintain the necessary amount of dark matter to match its present day density. Just as the CMB is produced as a consequence
of the thermal history of the universe, particle dark matter can also be generated as
a thermal relic of the early universe. There are three factors that contribute to the
evolution of the (lark matter density: 1) the expansion of the universe, 2) (lark matter
pair annihilation, and 3) dark matter production. "Freeze-out" occurs when 2) and
3) become much less important than 1), so today only 1) is relevant in changing the
physical dark matter density. Here, I provide a basic sketch of how a simple estimate
can be made.
Absent annihilation or production, the number density n is just n(t) = no/a(t)3 .
The change in density dn due to the expansion of the universe over time dt can be
easily calculated to be (n(expansion) = -3Hndt. We can also see that the comoving
density n.(t)O(t) 3 is unaffected by the expansion of the universe.
The rate of change from annihilation is a bit more complicated.
Assuming for
simplicity that the dark matter is its own antiparticle, we let the dark matter have a
velocity distribution f(v) and an annihilation cross section o
38
=o
- O(vi
-
v 2 ). Now
consider a single particle with velocity v. Its probability of annihilating against a
second particle with velocity v' in time dt is f(v')n(t)Iv - v'lu(jv - v'I)dt. The total
probability of annihilating with another particle is the integral of this with respect
to v'. An integral over v. weighted by the velocity distribution gives the total rate
of change of the particle density. Counting statistics add an additional factor of 1/2
that, is balanced by the annihilation of two particles in each interaction. Letting
d Jdv'f (v)f (v') v
(1,a) =
-
v'I(v
-
(1.14)
v'),
the total amount, of dark matter which annihilates in time di is dn(annihilation)
n(t) 2 (va)di. We can parameterize the rate of production as dn(prod) = (
W)nitdi
where nuq is the density at which thermal equilibrium is reached between production
and annihilation.
Combining the results for annihilation and production with the
result for expansion yields the Boltzmann equation for the number density of dark
matter
+n3H(l)n(t)
dt+
(va) (n(t) 2 _
HInt=
q
.
(1.15)
Ve can very simplistically see that, when
H (t) >(an)
(1.16)
annihilation is no longer able to have any significant effect on the dark matter density
and the comoving density n(t)a(t)3 settles to a constant value. We also know that the
early universe is dominated by relativistic particles. Using statistical mechanics to
calculate the energy density and applying the Friedmann equation, freeze-out occurs
near the temperat nre where
H
45h
,/21(kB)27)
The number of relativistic bosonic (gB) and relativistic fermionic (gy,-)
degrees of
freedom at teniperature T give g*,
7
# = qB(T) + -yjF(T).
8
39
(1.18)
If the dark matter mass is comparable to the those of heaviest standard model par-
ticles, then g,
~ 100.
Eq. 1.17 can be used to estimate the temperature T" and
corresponding dark matter mass density p, at which freeze-out happens.
The literature includes many careful calculations of the relic abundance of dark
matter, such as [19, 20, 21, 22]. Basic derivations starting with the arguments just
described can be found in textbooks such as [23] and [13]. The result for a typical
calculation can be found in Ref. [17], where freeze-out occurs at T, ~ m /20 and the
relic density is found to be
Q X12
-87rGp
x
3[100 (km/s)/Mpc]
2
3 x 10 7 cm 3 S-1
(o-v)
(1.19)
The value of Q h2 is known to be approximately 0.12 [15]. In order for the prediction
to match the measured value, we must require that
(u-v) = 3 x 10-26 cn3 s-1.
(1.20)
Remarkably, if the dark matter mass is of order 10 GeV and its couplings to Standard
Model particles are similar to those typical of weak interactions, then dimensional
analysis suggests that
(a-v)
~ G 212
3
1.4 x 1025 cm 3 S-1.
(1.21)
The fact that these two rough estimates agree to within about an order of magnitude
leads to the fancifully named "WIMP miracle." Weakly-interacting massive particles
(WIMPs) are a viable solution to the problem of dark matter. The WIMP solution
for dark matter is well-motivated not only from the idea of dark matter as a thermal
relic of the early universe but also by the predictions of many theories of physics
beyond the Standard Model (BSM). In fact., many of the most popular BSM physics
scenarios can be formulated to include candidates for WIMP dark matter.
1.3.2
Supersymmetry
The theory of supersymnmetry (SUSY) has been proposed as a possible solution to
a number of questions in particle physics. Supersymnmetry posits the existence of a
40
new symmetry allowing for transformations between fermionic and bosonic degrees
of freedom.
In order to achieve this, each Standard Model particle must have an
equivalent "superpartner" with the same quantum numbers but whose spin differs
by 1/2.
The SM fermions are partnered with new spin-0 "sfermions," while the
gauge bosons are partnered with new spin-1 /2 "gauginos." The hypothetical graviton
would have a sulperpartner in the form of the spin-3/2 gravitino.
The addition of
a set of new particles with identical (or nearly identical) couplings as the Standard
Model particles can be used to solve issues such as the hierarchy problem, where
the divergent corrections to the Higgs mass from heavy quark loop corrections are
cancelled out by the equivalent corrections from heavy sqIuark loops.
Many supersymnnetric theories include the conservation of a new discrete symnetry called R-parity. Each particle is assigned the value
R
=
(-
1
)3(L+B)+2S
where L and B are the lepton and baryon number and S is the spin. This simply
means that SM particles are assigned a value of 1 while the SUSY partners are
assigned a value of -1.
In theories where R-parity is preserved in all interactions,
we see that Standard Model particles can decay into any number of other Standard
Model particles (without violating any other symmetries) while the decay products
must contain an even number of SUSY partners.
In contrast, the decay products
of one of the new SUSY particles must contain an odd number of SUSY particles
and any number of SM particles. The lightest supersymmetric particle (LSP) cannot
decay at all because there is no other SUSY particle that is energetically allowed to be
a decay product. The LSP in a SUSY theory with conservation of R-parity is stable.
Of particular interest to experimentalists is the Minimal Supersvmmetric Standard
Model (NISSM),
the SUSY model with the fewest additional particles.
Supersymmetry., however, cannot be an exact symmetry because that would lead
to large production cross sections for SUSY particles even at low energies.
These
particles have not been seen experimentally, so unbroken SUSY is not. a viable theory.
Rather. SUSY must be broken through some process so that the masses of SUSY
41
particles are sufficiently high and their couplings are sufficiently low that they would
not have already been discovered. A number of scenarios for SUSY breaking have
been proposed. In particular, the minimal supergravity (mSUGRA), or Constrained
MSSM (CMSSM), model breaks SUSY at or near the Planck scale and can lead to
TeV-scale masses for SUSY particles. Additionally, the low-energy phenomenology of
mSUGRA can be described using just five new parameters. In mSUGRA models, the
LSP is typically the lightest neutralino'. As a weakly-interacting massive particle, a
stable neutralino is an attractive candidate for particle dark matter.
The MSSM Lagrangian includes several interaction terms involving the neutralino
and the electroweak sector. Standard Model fermions and neutralinos interact with
the Higgs fields via Yukawa couplings such as (suppressing the various fermion and
neutralino mixing matrices)
LAss.A
D gH ff +
0xk (g' + g'f ) x
(1.23)
to generate scalar and pseudoscalar couplings and with the Z boson to generate vector
and axial vector couplings,
2
AISSAI D Z,Y'(gV+
1
5 )x
)f + 2 Z,7"(g>+g>
g
(1.24)
Additional terms such as
L£SSM D fI(A + gp' 5)xf + h.c.
(1.25)
also appear in the MSSM. Together, these terms generate tree level neutralinostandard model fermion diagrams with weak-scale cross sections, consistent, with the
desired values for WIMP dark matter. Several possible MSSM Feynman diagrams
are shown in Fig. 1-5. A fully generic model of spin-1/2 dark matter may include additional interactions. Reference [24] provides an exhaustive overview of dark matter
in the context of supersymmetry, including the topics briefly mentioned here.
'Neutralinos are the superpartners of the neutral electroweak gauge bosons.
42
5
X
x
V Al
q
gs
q
qq
q
(b) Vector Exchange
(a) Scalar Exchange
X
,
s
(x
qx 5
gs "gp~
-
q
q
(c) Squark Exchange
Figure 1-5: These are several tree-level diagrams for neutralino-quark elastic scattering in the MSSM. The exact values of the couplings depends on the model chosen.
Neutralino pair production and annihilation diagrams can be derived from these via
crossing symmetry.
43
1.3.3
Universal Extra Dimensions
Supersynnetry is not the only BSM theory to include a candidate for WIMP dark
matter. Such a particle can also arise in theories of Universal Extra Dimensions
(UED), where one or more additional spatial dimensions exist and are accessible to
all Standard Model fields. As an example, we can consider a theory with a single
compactified extra dimension of radius R. The energy of a particle in such a system
will be
E2
=p
2
+ k2 +
772
(1.26)
where k is the momentum along the compactified dimension. From quantum mechanics, we know that the component of the wavefunction along the new dimension
is proportional to exp (in),
where n E Z. Using this, the energy can instead be
written as
2
E )2 +
2
p
2
+ mn.
(1.27)
In the three large dimensions, the propagating particle has an apparent mass of
2
=
2
+
2
71
.
(1.28)
For each field propagating in the extra dimensions (all particles in the case of universal
extra dimensions), an infinite number of possible masses will be present. At tree level,
all particles will converge on the same masses for large values of [n]. While a more
complete theory of extra dimensions is much more complicated than this, we see that
if the size of the extra dimensions are of order TeV-- or smaller, then experiments
have as yet only probed the Inj= 0 particles, leaving the excited states undiscovered.
Similarly to R-parity in SUSY, many UED models require the existence of a
Kaluza-Klein parity, PKjK. If this new discrete symmetry is preserved then just, as the
LSP is stable, the lightest Kaluza-Klein particle (LKP) will be stable as well. While
there are several possible WIMP candidates in UED models, the most popular LKP
is the first excited state of the B hypercharge gauge field, B(') [25.
This field, too,
will have tree-level interactions with Standard Model fermions, so that the processes
of elastic scattering with quarks, pair production, and pair annihilation will occur
44
just as in SUSY [26]. This particular choice would be an example of vector WIMP
dark matter.
1.3.4
Non-WIMP Dark Matter
The example WIMP models I have described are "weakly interacting" in the technical
sense of interacting through a modified Standard Model electroweak sector. This does
not, have to be the case. The correct relic density is obtained even if (lark matter is
"weakly interacting" in the more colloquial sense of -not interacting very much." If we
choose an alternative method of creating particle dark matter in the early universe,
then dark matter does not necessarily need to be composed of WIMPs at all. Many
alternative candidates have been proposed, with names such as superWIMPs. axions.
sterile neutrinos, WIMPzillas, and Q-balls.
There are too many candidates for a
detailed explanation of each one. Instead, I will briefly describe two such candidates:
superWI1MPs, which are closely related to WIMP (lark matter; and axions, which are
the subject of a dedicated research program.
The WIMP solution to the problem of dark matter proposes that (lark matter
is made of stable, nonrelativistic. weakly-interacting massive particles produced as
thermal relics of the early universe. These simple assumptions lead to a relic density
consistent with cosmological measurements. If the WIMPs produced in the early universe instead decay to a particle with a similar mass. the relic density of the WIMP
decay products will be consistent with the known (lark matter relic density.
The
decay product does not need to participate in Standard Model interactions at all, so
this model of decaying WIMPs is a theory of superweakly interacting massive particles, or superWIMPs.
This type of (lark matter can also appear in many of the
most common BSM scenarios. In particular, SUSY models with a gravitino LSP and
a WI
P next-to-lightest supersymmetric particle (NLSP) call provide such super-
WIMPs. The NLSP is produced thermally in the early universe and subsequently
decays into non-interacting gravit inos.
The gravitinos. then, are the superVIMP
(lark matter candidate. In such models, the (lark matter candidate is undetectable
by indirect and direct searches; the interaction rate is much too small to ever hope
45
to discover in a detector. Instead, the existence of superWIMP dark matter would
need to be inferred from high-precision measurements in cosmology and astrophysics
[27, 28].
CP violation in quantum chronodynamics is expected to lead to a large neutron
electric dipole moment. Experimental limits require that the neutron electric dipole
moment be very small, leading to the so-called "strong CP problem." Peccei and
Quinn proposed adding a new U(1) symmetry to the theory of quantum chromodynamics to resolve the strong CP problem [29].
This new symmetry requires the
introduction of the axion, a new light scalar particle [30]. Axions can be generated
in the early universe as a Bose-Einstein condensate, providing a, cold dark matter
candidate [31]. Axions with masses in the peV to meV scale can produce the correct
relic density of dark matter. The ADMX experiment is searching for (lark matter
axions by looking for axion conversion into a photon in the presence of a large magnetic field. The ADMX collaboration has already excluded (lark matter axions with
masses between 1.9 and 3.53 peV and axion-photon couplings greater than approximately 10-" GeV-
and hopes to eventually exclude all possible axion dark matter
models [32].
46
Chapter 2
WIMP Dark Matter Searches
Recalling the tree-level diagrams in
51.3.2,
we can see that there are three basic types
of interactions between WIMPs and Standard Model particles:
1. WIMP annihilation to SM particles,
2. WVIMP production in SM particle collisions, and
3. scattering of WIMPs and SM particles.
These interactions lead to three different approaches for WIMP dark matter searches
using the methods of high energy physics. The global dark matter effort includes a,
number of experiments of each type.
WIMP annihilation allows for indirect (lark matter searches, which look for hints
of dark matter in cosmic rays. Experiments at colliders such as the Large Hadron
Collider (LHC) look for evidence of WIMP production in high energy collisions. Finally, direct detection experiments look for the signatures of WIMPs scattering off of
particles in their detectors.
2.1
Collider and Indirect Searches
WIMP annihilation to SM particles can lead to quite striking features in the cosmic
ray spectrum. Searches for evidence of WIMP annihilation in cosmic rays are typically
known as -indirect- searches for (lark matter.
The indirect search method looks for
'The astronomical and cosmological methods described in the previous chapter are also indirect
methods. but in the context of particle physics searches for dark matter. "indirect" detection will
refer to these cosmic ray experiments.
47
hints of WIMPs through their decay products. A number of space-based experiments
have searched for WIMP dark natter, and in recent years, a number have obtained
similar, but still unexplained results. In particular, the PAMELA [33], Fermi [34],
and AMS-02 [35] experiments have ineasured the ratio of electrons to positrons in
cosmic rays. Each detector measured an excess in the fraction of positrons at energies
greater than 10 GeV compared to models of the cosmic ray spectrum. This result is
similar to what may be expected of a high mass WIMP signal, although astrophysical
phenomena have been proposed as alternative explanations. Searches for dark matter
annihilation using photons [36, 37, 38], antiprotons [39] and neutrinos [40] have yielded
results consistent with cosmic ray models. Antideuterons may provide a much less
ambiguous signature of dark matter in indirect searches, and the GAPS experiment
is planned to search for such a signal [41].
WIMP dark matter can appear in collider experiments in a number of ways.
One especially notable signature is that of WIMP pair production with associated
initial or final state radiation (ISR or FSR). The ISR or FSR would lead to a single
high energy photon or jet. WIMPs will not typically interact inside the detector, so
such events will appear in the detector as a photon or monojet with a large amount
of missing transverse momentum.
Both the ATLAS and CMS collaborations have
performed searches for dark matter using the single photon [42, 43] and monojet
[44, 45] topologies in proton-proton collisions at a center of mass energy of 7 TeV. Each
collaboration found results consistent with the predictions of the Standard Model.
Interpreting such collider results requires a number of assumptions that may not be
the same as those in other searches. Typically the analyses assume that the interaction
is mediated through a new particle that is much heavier than any of the scattering
particles and even heavier than the center of mass energy of the collision. The energies
of the colliding particles are very different in LHC searches than in other searches,
which involve nonrelativistic WIMPs.
Additionally, even if a WIMP is discovered
at the LHC. it is not necessarily the same as WIMP dark matter. Colliders will be
unable to determine if such a WIMP is stable, as particles very quickly leave the
detectors.
48
2.2
Direct Detection
The scattering
or direct detection
searches are the only experiments to actually
look for features of a local WIMP halo at the position of Earth. This has the advantage
of being able to conclusively determine that a signal is actually from dark matter.
but requires accurate knowledge of the astrophysics of WIMP dark matter. There
are myriad papers and reviews covering both the physics of WIM P-nucleus scattering
and the halo models used in dark matter direct detection experiments (see [46, 47,
48, 49, 50, 24] for some examples). I include here a sumnary of the relevant results.
2.2.1
WIMP-Nucleus Scattering
Because (old particle (lark matter is expected to be highly nonrelativistic, calculations
of its scattering cross sections with normal matter can be simplified from the usual tree
level calculations. The momentum transfer should be small enough that only terms
terms of order 0 with respect to the (lark matter momentum need to be considered and
propagators can be reduced to just, a coupling constant with dimensions of [energy]
2
(similarly to how GF is derived from electroweak vertex factors and propagators).
The scattering matrix elements and cross sections depend only on the particle masses,
spins, and a coupling constant from an effective four-particle interaction.
For Majorana WIMPs (for Dirac WIMPs, remove the factors of one half 2 ), the
interaction terms with quarks can be generalized as the product of two bilinear covariants,
'er ->
The operator 0, is one of {1.
!)Ojg]Ojq.
,/
f,
o"' = i/2[).
(2.1)
f]},
known as the scalar.
pseudoscalar. vector. axial vector. and tensor operators. respectively. These exhaust
all possible interaction terms. In the low energy limit, the bilinear covariants take
simple forms, summarized in Table 2.1.
The tensor and vector operators are odd under charge conjugation anti are not
allowed in bilinear terms of Majorana fermions such as neutralinos. For Majorana
2
The factors of 1/2 are following the conventions of [51] for Dirac and Majorana ferinions.
49
JDirac Fermion
Bilinear
Name
2m6,5 3
21'us
Scalar
Pseudoscalar
2t(s')(p
i '(p')yu,(p)
Vector
,
Axial Vector
0 Vs
2m6s,8
p') S'(s) 2Vft(s')(p - p') - SO(s)
-
0
0
us ius
0
us
0
0
4mnt(s')S'/7(s)
4m/t (s')Si (s)
0
0
0
4mneijkljt (s') Sk< (s)
0
y0 5u
i
5Us
fS' CLuS
fl'a-0usa
Tensor
Majorana Fermion
u_'
_
_ _us
0
Table 2.1: List of bilinear covariants and their values in the low-energy limit. u5 and
d' are the four-component spinor and adjoint spinors for a fermion with spin s. V)(s)
is the two-component spin state corresponding to s.
fermions. the allowed terms are
4
jDG~
,
-
2
5
(2.2)
+ 2qq
while for Dirac fermions, they are
5
Leff : G~skxqq + GV kyx1q + G
x
5
q + GTr
P","qorvj.
(2.3)
The scalar and vector terms give rise to spin-independent (SI) interactions while the
axial vector and tensor terms give rise to spin-dependent (SD) interactions. Ignoring
any possible interference between the SI and SD terms, a generic cross section can be
written as
da (xN
dus, I
XN)
2 2 + dosD IFsD(Q2)
= rs Fs1 (Q )1
dE,
d E,,
1
2
(2.4)
us, and osD are the spin-independent and spin-dependent cross sections at 0 morentum transfer. Er is the kinetic energy of the recoiling nucleus, and FsI and FSD are
the form factors for SI and SD scattering. The momentum transfer is
Q2
_-
2mnE,
(2.5)
In the cases considered here, the differential cross sections are isotropic in the centerof-mass frame, so
dusI/SD
(SI/SD
dE,
En
50
(2.6)
where Emi., is the maximum kinematically allowed recoil energy given some WIMP
energy.
Spin-Independent Cross Section
In the Majorana WIIP case, the SI cross section comes from the scalar interaction.
Let IX(J), s) represent a particle of type X with momentum j. and in spin state
Sz = s. Also let it =m7m1/(m1
± mN) be the reduced mass of the WIMP and
nucleus. The matrix element from scalar interactions is
Z GeiqgN(0),
)
(2.7)
.
The nucleons are also Dirac fermions, so we can alternatively write this as
Msl
(x(k'), s'Ix x (k), s)
(N(p), m'I E
GfffIN(0),
1)
.
(2.8)
Since we are considering the zero- momentum case, the first term is just the value
given in Table 2.1. The second term involves several nuclear matrix elements and so
more care is required in doing the calculation. Including contributions from heavy
quarks and following the treatment of Ref. [171, the WIMP-nucleon effective scalar
coupling constants are
f
+
2
I(2.9)
-
f7s
q=27,d.s
q=u .d.s
.
) q=cbtm
We consider the unpolarized case. so the squared amplitude is averaged across all
initial angular momentum states and summed over all final states, as usual. With
this, the total SI cross section is
=sp.=
7r
ZG'4 + (A - Z)G"| 1.2
(2.10)
In many models. the proton and neutron couplings are nearly identical. so uS1 is
generally proportional to p 2 A 2 . greatly favoring heavy nuclei over lighter ones.
51
Caron
L.._
Xenon
0.4.
-
-
---
0-4
0.3
--
-
-
- -
-
-
0.2
-
0.1
50
Figure 2-1:
xenon.
--
-.-.100
150
200
250
300
350
400
Recoil Energy [keV]
Spin-independent form factors for fluorine, carbon, germanium, and
Ref. [50] suggests that the spin-independent form factor can be approximated by
Fs)(Q)= fs 1 (qr.) -
3j(qr.)e-(S)2/2
qr,1
(2.11)
where ji is a spherical Bessel function of the first kind and has the analytic form
ji (x) = (sin(x) - x cos(x))/x 2 , s (~
1 fm) represents the nuclear skin thickness, and
qr. = r, V 2 mNER is the dimensionless product of the momentum transfer and an
approximate nuclear radius. The nuclear radius is approximately
r = c22 +-7r2a2 - 5s2
3
where c
=
1.23A1/
3
- 0.6 fm and a
=
(2.12)
0.52 fin. Using these values suggested by [50],
the SI form factors for several nuclei are plotted in Fig. 2-1.
Spin-Dependent Cross Section
As in the case of spin-independent interactions, we can write the matrix element from
spin-dependent interactions due to axial vector couplings as
MSD
=
(Xk). s'INpy5y~y(k), s) (N(), m'I
: G'jy1L q N(0), m)
q
52
(2.13)
or, using effective WIMP-nucleon couplings,
M4SD
=
(,(k'). s'I j
), '|~
~x(k) ,s) (
GIf~h
5fIN(0),m)
(2.14)
.
f =])-?
The axial vector operator is proportional to spin. so we can see that the nuclear
matrix elements are in fact proportional to the total spin contribution of each quark
or nucleon to the total nuclear angular momentum. If we let A"" be the fraction of
the nucleon spin carried by light quark q, we can define the WIMP-nucleon couplings
to be
Gpi"=
GqAp".
(2.15)
q=u.d~s
If we then let (SP") be the mean contribution of each proton (or neutron) to the total
nuclear spin, the spin-averaged SD WIMP-nucleus scattering cross section is
p)
1 G'Z(Sp) + G"N (Stl)1 2
7r~
(ySD(x-N
J
(2.16)
.1
This cross section lacks the A 2 dependence of the SI cross section, and so heavy
nuclei are not strongly favored as targets. The proton and neutron spin factors must
be determined separately for each nucleus. Fluorine-19 is a particularly attractive
nucleus to use for SD WIMP-proton interactions, while certain isotopes of elements
such as xenon and germanium are useful for SD WIMP-neutron interactions.
Again following the advice of Ref. [50], the spin-dependent form factor can be
approximated by a thin-shell model with partially filled zeros,
IFS D(
2j(qrnj)
fDqr )
j2
qvra < 2.55, qrtj > 4.5
0.047
2.55 < qr,, < 4.5
-
(2.17)
Here. r, = A' /: fm. The SD form factor for several nuclei is shown in Fig. 2-2.
Other WIMP Models
The cross sections discussed here are for the specific model of a Majorana fermion
WIMP. such as a SUSY neutralino. Similar cross sections can be derived for other
types of WIMPs. In the case of a Dirac fermion, the axial and scalar couplings also
53
10.9-
0.80.7
-
0.6
0.5-.4Carbon
0-0.3
-Fluorine
- - - - Germanium
....Xenon
0.2
0.1
....
..........
....
. .
0
50
100
150
200
250
Recoil Energy [keV]
Figure 2-2: Spin-dependent form factors for carbon, fluorine, germanium, and xenon.
appear, but additional interactions such as vector couplings may be important as well.
Scalar dark matter will obviously have different interactions. In the case of vector
dark matter, found in some models of universal extra dimensions, Ref. [26] shows
that the couplings can also be separated into SI and SD couplings, with cross sections
that are very similar to those in the Majorana fermion model considered here.
2.2.2
Recoil Energy Spectrum
The energy spectrum of WIMP-induced nuclear recoils in direct detection experiments
is dependent on the WIMP mass and velocity distribution as well as the properties
of the target nucleus.
In the general case of an isotropic cross section, the rate of WIMP-nuclei interactions is
R
-
UopA
mX mN I
f (v)d3v.
(2.18)
The different variables used in scattering calculations are defined in Table 2.2. This
rate ignores the effects of form factors and detector efficiency but is useful in normalizing distributions in order to properly set limits on the WIMP cross section. More
54
Variable
(-o
14
mh\
mIN
p
R
E,
F(x)
v
f(v)
vo
VE
VeSC
Definition
Local Dark Matter Density
WIMP-nucleus scattering cross section at zero momenturn transfer
Total target mass
WIMP mass
Target nuclear mass
WIMP-nucleus reduced mass
Scattering rate
Kinetic energy of recoiling nucleus
Nuclear form factor
WIMP velocity in the lab frame
WIMP velocity distribution in the lab frame
Typical velocity spread of WIMPs in local DM halo
Velocity of Earth through the local DM halo
Escape velocity of DM from galaxy, at position of Earth
Table 2.2: Definitions of variables used in dark matter scattering calculations.
useful, however, is the differential rate with respect to energy. This is expressed as
dR
dE,
where Vmh= (1 +
recoil energy E.
-
UoPxAJT IF(2mINEr)12
2pn,
d3
f(V),
(2.19)
'
f
is the minimum WIMP velocity required to attain the
"I
This equation includes the form factor, and an energy-dependent
detector efficiency is easily incorporated as well.
The local WIMP velocity distribution is typically modeled as a Maxwell-Boltzmann
distribution with a maximum cutoff velocity to represent the escape velocity of
WIMPs from the galaxy. In the laboratory frame, we must consider both the motion
of the solar system through the local WIMP halo and the revolution of Earth around
the sun. At any given time, if the velocity of the Earth through the (lark matter halo
is
VE.
the WIMP velocity distribution is, in this model,
k
f(V) =
2)3/2
0--
IV +
VEI <
C(es0
(2.20)
(-,v(
0
where A is a normalization constant.
IV+ VE I
Iesc
In the limit where the escape velocity I,,c is
infinite, the differential event rate with respect to recoil energy is just the difference
55
E
,Carbon
-
Fluorine
---
,.
~Germaniumn
W
Xenon
4---
-
-
q
-
-
14.
-
-
-
-
-
10
0
5
10
doR
15
20
-i
+
25
30
E
35
40
45
5
E [keV]
v
.in4.
Figure 2-3: C, F, Ge, and Xe recoil spectra for 10 GeV WIMPs. Form factors have
not been applied.
between two error functions 3
c erf
dEr
-+ erf
VO
.
VO
(2.21)
Figs. 2-3, 2-4, and 2-5 show differential event rates (not including form factors) for
m7n
10, 50, and 100 GeV mass WIMPs scattering with carbon, fluorine, germanium,
and xenon using 0 = 230 km/s, v,,,, = 650 km/s, and VE = 258 km/s. The velocity of
Earth used here is the maximum relative velocity between Earth and a non-rotating
dark matter halo.
Nuclear recoils from WIMPs in the dark matter halo have typical energies of tens
to several hundred keV. Because the differential event rate decreases exponentially
with recoil energy, the exact event rate expected in a direct search is highly dependent
on the energy thr e shold of the detector.
quite small ((1)
In any case, the expected event rate is
event per kilogram per day at a cross section of
pb).
n The most
traditional method for a dark matter search is to search for WIMP-induced nuclear
recoils following the expected energy spectrum and then use the candidate events to
set an upper on the scattering cross section as a function of WIMP mass. Because
3Note that
the equation given in Ref. [50] for the differential event rate including an escape
velocity is not correct due to improper construction of integral limits. The correct distribution can
be easily calculated through Monte Carlo methods.
56
-.
W 10.
+-
........
Carbob
Fluoriije
Germanium
SXenon
*:40
50
0
ISO
100
200
250
E [keV]
Figure 2-4: C, F, Ge, and Xe recoi spectra for 50 GeV WIMPs. Form factors have
not been applied.
.
+.
.
.......
.....
.....
...
..........I...
.
.....
......... -
F4--
e
:--Carbon:
- Fluorin4
:Germa
Ium
4.----Xenon
10-2 .
1
.......
.........
0-4...... ......... .
4
.
.
4P
0
50
100
150
200
250
300
350
400
500
450
E [keV]
Figure 2-5: C, F, Ge, and Xe recoil spectra for 100 GeV WIMPs. Form factors have
not been applied.
57
the expected event rate is very small, it is necessary for direct detection experiments
to minimize any backgrounds 4 in order to hope to discover a lark matter signal.
2.2.3
Current Direct Detection Experiments
Many of the most sensitive searches for spin-independent interactions use liquid noble
gases as target materials. The XENON100 and LUX collaborations use dual-phase
liquid xenon time projection chambers (TPCs). Readout of the primary scintillation
as well as the ionization signal using electroluminescence in a high electric field gaseous
region allows for the reconstruction of the position and energy deposition from a
recoiling nucleus, as well as differentiation of nuclear recoils from other particles
using the ratio of the scintillation to ionization. XENON100 has been operating for
several years at the LNGS site and at present has set the most stringent limits on the
SI WIMP-nucleon interaction cross section, reaching a minimum of than 2-"
cm
2
at,
a 55 GeV WIMP mass [52]. The LUX experiment [53] began taking physics data in
2013 and will improve upon the XENON100 results. Much larger ton- to multitonscale dual-phase xenon experiments such as XENONITon and LZ are planned over
the coming years.
Xenon is not, the only noble gas of interest to direct detection groups. Dual phase
argon TPC groups include DarkSide [54] and ArDM [55]. Single phase detectors such
as MiniCLEAN [56] and DEAP-3600 [57] will look at the scintillation signal from
argon. Argon is particularly useful because the time structure of scintillation signals
can be used to distinguish nuclear recoils from other events.
Cryogenic germanium detectors are the other leading technology for SI interaction searches.
The CDMS collaboration is the leading such group, measuring the
ionization and phonon signals in germanium detectors. Such detectors have excellent
energy resolution. a low energy threshold, and can reject backgrounds with position
reconstruction and particle identification using the ratio of ionization to phonon excitation. CDMS-II germanium and silicon detectors have been operated in the Soudan
mine in Minnesota.
The germanium detectors have set some of the best limits on
'Backgrounds here are any signals that are not WIMP-induced nuclear recoils.
58
spin-independent interactions,. reaching less than 1043 Cm2 near 60 GeV [58]. The
SuperCDMS experiment, planned to be installed at SNOLAB. will be a much larger
iteration of CDMS using more advanced germanium detectors.
Current dedicated SD WIMP-proton searches are much smaller in fiducial mass
than the most sensitive SI experiments, having masses of only a few kilograms. The
difference in mass and the different dependences of the SI and SD cross sections
on target atomic mass mean that the SD searches have much less sensitivity to the
WIM P-nucleon cross section. The most sensitive experiients for SD WIMP-proton
interactions use bubble chambers or superheated droplet detectors with fluorine-rich
target materials. Such detectors can be designed to be insensitive to common backgrounds such as electrons and minimum ionizing particles (MIPs) by adjusting the
temperature and pressure of the target until bubble formation requires the high ionization stopping power of nuclear recoils. Acoustic readout using piezoelectric devices
allows for particle identification. Among the leading SD WIMP-proton searches are
the PICASSO, a C 4 F1 0 superheated droplet detector with acoustic readout; COUPP,
a CF 3 1 bubble chamber with optical and acoustic readout; and SIMPLE, a C 2 CIF 5 a
superheated droplet detector with acoustic readout. The SIMPLE experiment has set
the best limit on SD WIMP-proton interactions over a wide range of WIMP masses,
reaching a minimum of less than 10-1 cm 2 at a WIMP mass of approximately 30 GeV
[59]. The PICASSO experiment is the most sensitive at very low WIMP masses [60].
As with the SI experiments, many of the current suite of SD experiments are planning
to scale their detectors to much larger sizes. The COUPP experiment has already
increased in mass from 4 kg [61] to 60 kg and has plans to increase by another order
of magnitude to 500 kg, allowing them to set much more stringent limits than ever
before in a SD search.
The leading limit-setting analyses. however, do not provide a complete picture
of dark matter direct detection. In recent years, several experiments have reported
intriguing results that may
ultimately point. to a nascent experimental signature of
WIMP dark matter. Recent results from both XENON100 and CDMS-II [62. 58]
found slightlv more events than were expected from their estimated backgrounds.
59
though still within reasonable statistical bounds. XENON100 found 3 events with
an expected background of 1.8±0.6, while CDMS-II found two events with an expected background of 0.9±0.2. The CRESST-II experiment, using cryogenic calcium
tungstate crystal detectors with scintillation and phonon readout, found a small excess
of events that was difficult to explain with expected backgrounds [63]. If interpreted
as a WIMP signal, this excess is consistent with a 25 GeV WIMP with a scattering
cross section of 10-42 cm 2 . Similarly, the recent CDMS-II silicon result found three
events in the signal region out of an expected background of less than one event [64].
A likelihood analysis rejects known backgrounds as the source of this excess at better
than 99% confidence.
If this excess is interpreted as a WIMP signal, it favors an
8.6 GeV WIMP with a cross section of 1.9 x 1(
41
cm 2 . Although these results po-
tentially offer tantalizing hints of a dark matter signal, none of them is strong enough
to claim a discovery of dark matter, particularly given the sensitivity of many of the
searches setting upper limits on the interaction cross section.
2.2.4
Annual Modulation Searches
Now that many experiments are measuring possible signal events, it is necessary to
develop methods to determine whether or not a proposed signal is actually from dark
matter. The proposed annual modulation of the (lark matter signal is a simple and
relatively model-independent signature that can be used to help distinguish a true
dark matter signal from backgrounds.
Earth's velocity around the Sun has a component that is parallel to the solar
system's motion around the center of the galaxy.
The magnitude of this parallel
component changes as Earth revolves around the Sun, creating a small annual modulation in the magnitude and direction of the velocity of the WIMP wind. This in
turn leads to a small modulation in the total WIMP recoil rate in a detector and a
small modulation in the nuclear recoil energy spectrum. For a 100 GeV WIMP on a
fluorine target and using the standard halo parameters (plotted in Figure 2-6), the
modulation in total event rate has a peak-to-peak amplitude of approximately 5%.
with a maximum near the
2
,,d
of June each year. This modulation may be increased
60
by looking at only a certain energy range, although that will also limit the event rate.
0.3
0.25
'E
0.05
_0
200
400
600
800
100
Time [day)
Figure 2-6: The annual modulation in the event rate for 100 GeV WIMPs on fluorine.
The rate is normalized for a I kg mass, 0.3 GeV/cm 3 WIMP density, and 1 pb cross
section.
With sufficient statistics, an experiment counting the dark matter induced recoil event rate can search for such an annual modulation in different energy bins.
The most famous of the annual modulation searches are those of DAMA/NaI and
DAMA/LIBRA collaborations, who have measured an annually modulating signal
for more than a decade using radiopure NaI(TI) scintillation detectors. The DAMA
modulation signal (see Fig. 2-7 for some of the results) has a period and phase consistent with those expected in WIMP dark matter models [65]. If interpreted as a
dark matter signal, the DAMA result is consistent with an approximately 10 GeV
WIMP with a WIMP-nucleon SI cross section of 10-41 to 10~40 CM2 [66].
The CoGeNT experiment has also performed a search for an annual modulation
using germanium detectors, finding a possible annual modulation at 2.8a- significance
[67]. The CoGeNT results are also consistent with low mass WIMP dark matter.
However, these possible annual modulation signals have been the source of considerable controversy amongst, the dark matter community. The CDMS collaboration has
performed a. dedicated analysis of low energy events [68], and a similar search for an
61
2-4 keV
O.
DAMAILIBRA
0.08
250 k
(0.87
wonxyr)
0.06
0.04
0.02
0
--0.02
-~
-0.04
-0.06
'
0.08
-0.1
3250
3500
3750
4000
4250
4500
4750
5000
5250
Time (day)
Figure 2-7: The annual modulation of the event rate in the 2-4 keV energy range seen
by DAMA/LIBRA. From [65].
annual modulation in low energy events found no evidence for such a signal. CDMS
has placed strong constraints on modulations of both nuclear and electronic recoils
[69].
2.2.5
Summary of Direct Detection Limits
Constraints on WIMP-nucleus cross sections are normalized to an equivalent WIMPnucleon cross section (an A = 1 and S =
nucleus), usually assuming for simplicity
that the proton and neutron couplings are nearly identical. Combining the various
results, we find that there is clearly disagreement between the best dark matter exclusion limits and the putative dark matter signals of DAMA, CoGeNT, and CRESST
in both the spin-independent (Figure 2-8) and spin-dependent WIMP-proton (Figure
2-9) cases. Nearly all the favored regions of the claimed signals are already seemingly
excluded by other experiments. Unfortunately, the most favored WIMP masses occur
near the rising edge of the limit curves, where halo parameters, quenching 5, and the
energy threshold will have a significant effect, on whether or not that region is truly
excluded. While various models that have been proposed in recent years to resolve
this tension, the greater dark matter community remains unconvinced that a true
signal has been found.
5
The difference between the measured energy deposition and the true deposition
62
C)
10'-
E
-
10
S10-5
10
10
WIMP Mass [GeV/c 2
Figure 2-8: Selection of current best spin-independent WIMP-nucleon cross section
measurements. Dark green solid line: CDMS-II analysis [58]. Light green solid line:
CDMS-II low threshold analysis [68]. Solid red line: XENON100 result [70]. Light
blue region: CRESST-II la allowed region [63]. Blue dotted region: CRESST-II
3a allowed region[63].
Maroon region:
DAMA/LIBRA 3u allowed region, no ion
channeling [71, 72]. Pink dotted region: DAMA/LIBRA 5or allowed region [71, 72].
Gray region: CoGeNT annual modulation region of interest [67]. Blue dashed line:
LUX conservative sensitivity. Blue dotted line: LZ projected sensitivity. Red dashed
line: XENON1T projected sensitivity. Made with DMTools dark matter limit plotter
[73].
2.2.6
Daily Modulation Searches (or Directional Detection)
The confusing and possibly contradictory results from current direct detection experiments show that the more traditional event counting strategies and even annual
modulation analyses may not be sufficient to make a definitive discovery of dark matter. Fortunately, there is an additional signal proposed by Spergel in [74] that can be
used in direct detection experiments.
Recall that in the usual picture of direct detection, the solar system is revolving
around the center of the galaxy through a non-rotating halo of dark matter.
The
relative motion of a detector on Earth with respect to the WIMP halo creates an
apparent "WIMP wind" coming from opposite the direction of motion around the
63
0
G.)
-34
Q
8 10
0
36
0
04
101
102
103
WIMP Mass [GeV/c 2
Figure 2-9: Selection of current best spin-dependent WIMP-proton cross section measurements. Green line: PICASSO limit [60]. Red line: SIMPLE limit [59]. Blue line:
COUPP limit, flat efficiency model [61]. Light blue line: COUPP limit, exponential efficiency model [61]. Pink region: DAMA/LIBRA 3- allowed region, no ion
channeling [71, 72]. Made with DMTools dark matter limit plotter [73].
galaxy. Taking into account the expected velocity distribution of WIMPs, the WIMP
wind has a broad distribution of directions with a mean direction pointing away from
the approximate direction of the constellation Cygnus (Figure 2-10).
The highly anisotropic distribution of WIMP directions causes a large anisotropy
in the directions of nuclear recoils caused by the WIMPs (Figure 2-11). The distribution also displays a strong energy dependence, with the anisotropy getting more
prominent at higher energies (Figure 2-12). A detector that can measure the directions of nuclear recoils, then, could search for an anisotropy that points away from
Cygnus in order to distinguish a true WIMP signal from backgrounds.
The distributions shown in Figures 2-10 to 2-12 are what is expected in coordinate
systems where positions on the sky are fixed, such as galactic coordinates. A detector
in a laboratory on Earth does not naturally exist in such a coordinate system; Earth
is rotating around its axis so objects with a fixed position in the sky, such as stars,
appear to move. The direction of the WIMP wind is approximately 45' away from
64
1.0
0.5
0.0
Figure 2-10: A Mollweide projection of the (listribution of WIMP directions. The
spatial axes indicate the direction in a non-rotating frame, while the color axis indicates relative flux. The latitude lines are placed every 30' while the longitude lines
are every 60'. The center of the plot is the position (lat..long.) = (00, 00). In the coordinates ciosen here. tIhe bright spot, indicating t he average direction, points along
(o. ,-90'). opposite Cygnus, which is at (0,900).
1.0
0.5
0.0
Figure 2-11: The distribution of nuclear recoil directions. As with the WIMP distribution, the average direction approximately points away from the direction of the
VIMP wilid.
65
0.8
0.9
0.6
0.8
0.4
0.7
0.2
0.6
0
0.5
-0.2
0.4
-0.4
0.3
-0.6
0.2
-0.8
0.1
20
40
60
80
100
120
140
180
200
160
Recoil Energy [keV]
E
0
Figure 2-12: A histogram of the distribution of nuclear recoil energy versus recoil
direction with respect to the mean direction of the WIMP wind. The recoil direction
is defined here as ^rec - ^x where _r, is the unit vector defining the recoil direction
and (r is the unit vector pointing toward the mean WIMP wind direction.
the direction of Earth's rotational axis, so the position of the WIMP wind in the
laboratory frame undergoes a very large daily modulation due to Earth's rotation.
In Boston (Figure 2-13) and at WIPP (Figure 2-14), the daily modulation causes the
direction of the WIMP wind to move from being aligned nearly along the horizon to
being nearly vertical. The period of the daily modulation is also not the standard
24 hour solar day, but is rather the 23 hour 56 minute sidereal day, which is the
true rotational period of Earth's rotation. Because of this small difference, the daily
modulation goes in and out of phase with the regular solar day cycle throughout each
year, allowing for discrimination between the daily dark matter modulation and any
daily modulations in backgrounds due to environmental effects.
There are a number of proposed strategies for analyzing directional dark matter
data sets (including Refs. [75, 76, 77, 78, 79, 80, 81, 82]). As dark matter has not yet
been found, many of these methods focus on using directional information to search
for an anisotropy in the directional distribution, intending to either reject a simplified isotropic background model or to set stronger limits on the WIMP-nucleon cross
66
WIMP Wind Direction Modulation, Boston
60
-3 0
-
-
-6 0
0
........
...
- - .. ....
.......... : ......
-...
...
.....- . .....
6
12
18
24
Time [hours)
Figure 2-13: The mean direction of the WIMP vind over a 24-hour period, as seen
from Boston, MA. The horizontal axis represents azinuth and the vertical axis represents altitude. On this plot, 0 latitude corresponds to the horizon. while 900 latitude
points vertically upward.
67
WIMP Wind Direction Modulation, WIPP
60-
00East
Nbrt
West
-.
-30
....-
0
*
6
12
18
24
Time [hours]
Figure 2-14: The mean direction of the WIMP wind over a 24-hour period, as seen
from the Waste Isolation Pilot Plant, near Carlsbad, NM.
68
section if background events are found. More complicated methods such as likelihood
fitting may be capable of extracting much more information from directional data
[80]. Several general themes emerge from these proposals. Few events may be needed
to confirm the existence of a directional signal, and directional detectors will be able
to study (lark matter even in the presence of significant background contamination.
Finally, if dark matter is discovered, directional detectors will be better able to constrain (lark matter halo parameters such as the WIMP mass and the shape of the
velocity distribution than other methods of direct detection.
Although no collaboration has yet deployed a directional detector with comparable
sensitivity to the leading dark matter experiments, there are a number of different
collaborations attempting to develop such detectors.
Reference [83] provides a de-
tailed overview of directional detection and most of the experimental groups. Most
directional dark matter searches have focused on the concept of a low-pressure gas
TPC with various readout schemes in order to create an image of the ionization trail
left by a nuclear recoil in the detector.
detector.
Figure 2-15 shows a basic sketch of such a,
The low pressure extends the typical recoil track to 0(1 mm) in length.
With fine segmentation of the readout plane and good timing resolution to measure
pulse shapes, the shape of the trail of ionization left by the recoiling nucleus may
be determined and used to reconstruct the direction.
While the reconstruction of
the track axis in some cases is fairly straightforward, the sense of motion along the
axis of motion is typically determined via the "head-tail" effect. The head-tail effect
refers to the variation in the stopping power of the recoiling nucleus as it loses energy.
At energies relevant for dark matter detection, the stopping power is highest, at the
beginning of the track, leading to an asymmetry that can be used to reconstruct the
sense of motion.
One of the earliest directional detection efforts was that of Buckland et al. [84].
using optical charge-coupled device (CCD) readout of a TPC coupled to a parallelplate avalanche chamber. The DRIFT-lId detector [85] uses a negative-ion TPC filled
with a mixture of CS 2 and CF 4 . Rather than measuring the direction of each recoil,
DRIFT-I1d utilizes a standard multiwire proportional chamber (M\WPC)
69
readout
Optical Readout
Vacuum
Chamber
Cathode
C=
C=
Ln
C Ionization
C
C=
IDrift
C=2
Charge
Readout
-=
cintillation
Amplificatiorc
g=syStage
t
Anodevalanclhe
Figure 2-15: Basic sketch of a time projection chamber of the type used for directional
dark matter detection. A WIMP scatters off a nucleus in a volume of gas with a
constant electric field. The resulting nuclear recoil ionizes the gas as it loses energy,
and charge carriers (electrons or ions) are drifted toward a two-dimensional readout
plane. The high field near the readout plane causes avalanches whose induced signals
on electrodes may be amplified and read out. Scintillation during avalanches may
also be measured.
scheme to attain sensitivity to a forward-backward asymmetry of events along its drift
axis. The MIMAC [86], D3 [871, and NEWAGE [88] collaborations use microchannel
readout with gas electron multiplier (GEM) or micromesh amplification stages to
attain very fine segmentation of the readout plane and allow for three-dimensional
event reconstruction. MIMAC and D' in particular are sensitive to very low energy
recoils. The DMTPC collaboration [89] uses CCD readout of photons generated in
electron avalanches in order to attain similar segmentation.
Of these directional searches, DRIFT is currently the most sensitive, operating a
cubic meter scale detector filled with 10 torr CF 4 and 30 torr CS 2 underground at the
Boulby Mine in northeast, England. The DRIFT-Ild analysis [85] is presently limited
by backgrounds from the decay of radon and its daughter nuclei. The DRIFT collaboration is able to generally identify these events through rudimentary fiducialization
using pulse shapes. Unfortunately, removing these radon progeny backgrounds would
also remove most. WIMP-induced nuclear recoils in the detector, greatly reducing the
70
sensitivity to WVIMP dark matter. The most recent limit set by the DRIFT collaboration reaches a SD WIMP-proton cross section of approximately 2x1i0-6 Cm
2
at
a WIMP mass of 100 GeV. This result is several orders of magnitude behind the
strongest direct detection SD limits, which is not surprising due to the small fiducial
mass of the detector. Because current directional technologies rely on low pressure
gases, a very large volume detector will be necessary in order to set competitive limits on dark matter interactions in the coming years. The need for a large fiducial
mass presents perhaps the most challenging problem for the continued viability of
directional detection as a technique for dark matter searches.
Several alternative technologies for directional detection are being investigated as
well. It has been shown that directional information from low energy nuclear recoils
can be extracted from automated readout of nuclear emulsions [90, 91]. Furthermore,
it has recently been proposed that some directional information may be obtained from
more traditional gaseous xenon TPCs [92]. More exotic detector concepts have been
imagined as well, such as using DNA strands as a detector medium and measuring
the positions of strands broken by recoils [93].
2.3
The DMTPC Dark Matter Search
The DMTPC, or Dark Matter Time Projection Chamber, collaboration is one of
the groups developing detectors to search for the aforementioned daily directional
modulation from WIMP dark matter. The DMTPC collaboration has constructed
and operated numerous prototype detectors. On such detector, the "OL"'
prototype
was used to set the first limit on WIMP-nucleon SD interactions from a DMTPC
detector using data taken at the surface in 2008 [89]. Because a true low-background
search is not feasible at the surface due to cosmogenic backgrounds. the DMTPC
collaboration constructed an underground laboratory at the Waste Isolation Pilot
Plant (WIPP) in southeastern New Mexico. The DMTPC 10L detector was installed
underground in Fall 2010 and has been running for nich of the time since then.
In the initial underground running of the 10L detector at XIPP. described in the
PhD thesis of Asher Kaboth [94]. it was found that the rate of nuclear recoil candi71
date events did not significantly decrease compared to the surface run, as would be
expected when cosmic-ray-induced neutron events are eliminated by moving underground. However, significant changes were made to the detector between the surface
runs and the underground runs, so the two runs are not easily comparable. Several
charge readout channels measuring the induced signals on electrodes at the readout
plane were added for underground running, and different cameras were used. The
detector operating conditions were changed as well. The gas pressure was reduced
from 75 to 60 torr to improve the direction reconstruction. Finally, the environmental
conditions of the laboratories are very different as well. As a result, the collaboration
does not yet know why the event rate did not decrease as expected or what the events
measured underground are.
To answer the various questions raised by the operation of earlier detectors and to
test new technologies to be used in future larger detectors, the DMTPC collaboration
has constructed a more advanced prototype detector, called the "4-shooter." The
operation of this detector is focused on two principal goals:
1. how well we can reconstruct the directions of low energy nuclear recoils, and
2. what backgrounds are likely to be encountered in a much larger scale detector.
The recent PhD thesis by Shawn Henderson [95] addresses the first point, and in the
remainder of this work, I hope to address the second.
72
Chapter 3
The DMTPC 4-shooter Prototype
The DMTPC 4-shooter prototype is the newest detector constructed by the DMTPC
collaboration. It has a simple target drift volume design with a mesh-based amplification region. The detector measures the ionization occurring inside an active volume
filled with low pressure gas. The drift, volume has a constant electric field that drifts
electrons left from ionization events toward an amplification gap. The electrons enter
the amplification region, which has a very high electric field, and undergo proportional amplification. Induced currents on the electrodes in the amplification region
caused by the moving charge carriers in the avalanches are read out by preamplifiers.
Scintillation light accompanying the avalanches is also read out by CCD cameras and
photonuiltiplier tubes (PMTs). The information from the different channels is used
to reconstruct the energy, position, and direction of low energy nuclear recoils. The
detector, both opened to atmosphere and closed, is shown in Figure 3-1. This type of
design is similar in many respects to the earlier CCD-based detectors used by Buckland et al. [84] and Charpak et al. [96]. The specifics of the detector design are given
in [95], so I will include only some of the details that are most relevant, for this work.
3.1
Vacuum Chamber and Gas Systems
The TPC is held within a vacuum vessel composed of two main parts: an upper
bell jar and a base. Under normal operations. the two are sealed together with an
elastonier o-ring. The chamber has four viewports used for CCD cameras and an
additional viewport for PI\'Ts. There are also a number of flanges and feedthroughs
73
Figure 3-1: Left: The detector with the bell jar closed. The cameras (blue) can
be seen and are attached to the viewports via cylindrical mounts to hold the lenses
far enough back to focus properly. Right: The detector opened. The copper field
cage rings can be seen, with washers used to separate them and resistors to attain a
uniform field within the field cage. Light reflecting off the cathode mesh can also be
seen.
used for the gas and high voltage systems.
The vacuum vessel is filled with 45 to 100 torr CF 4 gas. The target gas is refilled
daily to avoid degradation of detector performance over time. When refilling, a mass
flow controller limits the flow of CF 4 gas into the chamber. Two pumps are used
to remove either old target gas or air when the chamber is opened. A scroll pump
is used to reach pressures as low as 1 torr, while a turbomolecular pump is used to
reach lower pressures. The gas volume is typically pumped to a pressure of less than
10-5 torr at room temperature (luring a normal refill cycle.
CF 4 , also known as tetrafluoromethane, has been used and studied quite extensively in particle detectors. As its mass is mostly 19 F, it is a useful material for
searching for spin-dependent WIMP-proton interactions. Table 3.1 summarizes some
of the properties of CF 4 relevant to DMTPC detectors.
74
Property I Description
u
Number density
Mass density
p
Eat /n
Reduced drift field
Egap/n
Reduced amplification field
W1
Work function
I
Ionization energy
1
drift
Electron drift velocity
Dj/p
Transverse diffusion to mobility ratio
DL /p
Longitudinal diffusion to mobility ratio
pion
Ion mobility in amlplification gap
Value
0.00323 mol/liter
0.284 g/liter
9.5 Td
790 Td
34 eV
16.2 eV
11.9 cm/ps
0.0505 V
0.0275 V
~1.0 cm 2 / V s
Reference
[97]
[98]
[99]
[99]
[100]
[101]
Table 3. 1: Electric field properties and various properties of CF 4 relevant to DMTPC
detectors. These values assume a pressure of 60 torr at 25'C.
3.2
Field Cage and Drift Region
The 4-shooter prototype has a simple TPC design.
A cylindrical drift volume is
created using a series of high purity 3 mm thick copper rings with an inner diameter
of 12.1" (30.734 cm) and an outer diameter of 13.3" (33.782 cm). Threaded acetal
rods support the field cage via four evenly-spaced holes drilled into each ring. Placed
onto the acetal rods between each pair of field cage rings are three copper washers as
well as two acetal washers to prevent the copper washers from contacting the rings.
A single 1 MQ resistor is the only electrical contact between adjacent field cage rings.
The field cage consists of twenty eight rings (including two rings connected to the
cathode), resulting in a total drift length of 26.7±0.1 cm and a total active volume
of approximately 20 liters.
At the top of the field cage is the cathode, held at negative high voltage and
constructed from a woven stainless steel mesh. The cathode is powered by a Bertan
380N 10 kV negative high voltage power supply. At the bottom of the field cage is
the amplification mesh. held at ground. The amplification mesh is constructed from
a 100 line per inch woven stainless steel mesh with a wire diamneter of 30 pm and
held approximately at ground through a preamplifier (described later).
This field
cage design provides a nearly-uniform electric field, with deviations occurring in the
region very close to the field cage rings. The detector measures energy depositions
75
inside this volume. Textbooks such as [102] provide overviews of detector technologies
such as TPCs. For completeness, I describe how the detector operates here.
When a charged particle with energy E enters the detector, it will deposit an
amount of energy AE at some position (x, y, z), where z = 0 represents the readout
plane. DMTPC detectors measure only energy loss contributing to ionization, so the
measured energy must be corrected to obtain the total energy loss. The mean number
of electrons created in this energy deposition is Ae = q(E. AE)AE/W.
W is the work
function while q(E, AE) is the fraction of energy loss contributing to ionization for
the given particle at an energy E. If the particle loses all of its energy, AE = E,
then q(E, E) = NW/E is the nuclear quenching factor Q(E). In recent years, there
have been several attempts to calculate [103] and measure [104] the quenching factor
of ions in CF 4 gas.
Once ionization occurs, leaving electron-ion pairs at a position (x, y, z), the electrons drift toward the amplification gap at an approximately constant drift velocity
Vdrift
.
In reality, the drifting electrons interact with other electrons in the gas, moving
in a random walk as they are pulled toward the readout, plane by the electric field.
Electron attachment in the drift, volume is negligible.
After drifting a time t, this random walk process causes diffusion that, results in
a spatial distribution of
f(AX,Ay,AzIt)
(
I1
j
1/2
t3)+exp
134T,3DTDL3
y2_(z+
2+
-4Th(Z
4D74
aie)
4drt2
4DLt
(3.1)
Dy, represents diffusion in each transverse dimension (perpendicular to the electric
field), while DL represents longitudinal diffusion (parallel to the field). The electrons
are measured at a well-defined plane, so the time t is (ignoring longitudinal diffusion)
Z/Vdrift. The transverse diffusion for a particle drifting from position z is
f 7 (Ax, Ayz)
1
47rDT
exp
Ax
2
+ Ay 2
-_._(3.2)
4D 7 'Z/Vcrift
(3.2)
Longitudinal diffusion is not measured directly, but rather affects the times at which
'Positive ions drift toward the cathode at a much slower velocity and are not measured.
76
Spacer
Mesh (Ground)
110
Anode (+HV)
Figure 3-2: A schematic showing the various parts of the amplification region. Elec-
trons pass through the gaps in the grounded mesh into an amplification gap with
a very large electric field. Avalanches proceed toward the anode, which consists of
a thin layer of copper on a GI plate. Electrodes on the G10 plate are created by
machining channels in the copper coating. The mesh and anode are held apart by
nonconducting tubes with a radius of 435 pm.
Figure 3-3: Left: Detail of the top of the field cage. The top two rings (close together)
hold the cathode mesh. Between each of the other rings is a resistor to step down
the voltage and several washers used as spacers. Acetal washers prevent the copper
washers from contacting the rings. Right: High voltage contacts for the central
anode electrodes. The outermost electrode (contact not visible) is connected to the
amplification mesh and held at ground. The inner electrodes consist of a veto ring
identifying events near the field cage and a central anode measuring the energies of
events in the central region of the detector.
78
electrons enter the amplification gap. In the limit that Z >> DL/vdriftthe drift time
distribution of electrons reaching the readout plane after drifting a distance z is
approximately
fL(tIZ)
dtrift
(
t 'drift
:rDz
47r DL zD
4
-x
- Z/drift) 2
( 4DLZ
)(3-3)
.
At the standard running conditions, electrons generated near the cathode will traverse
the full drift length, reaching the readout plane just 2.3 its after the energy deposition.
These electrons will also undergo the maximal amount of diffusion, leading to a spatial
width of oylnax =
UL,max
1.2 mm in each transverse dimension and a temporal width of
= 7.5 ns. As a 50 keV fluorine recoil has a range of only ~1 mm, we see
that diffusion is one of the principal factors limiting the length of the drift volume if
directional information is to be extracted from the data.
3.3
Amplification Gap
The amplification mesh marks the boundary between the drift volume and the amplification gap. The anode is constructed from a plate of copper-clad G10, with the
copper coating divided into three unconnected electrodes. The electrodes form approximately three concentric rings, with only a small portion of each machined to
the edge of the plate to allow for electrical connections to be made. The amplification mesh is glued with epoxy to the outermost (ground) electrode. The remaining
electrodes are held at positive high voltage using a single channel of a Bertan 375P
5kV positive high voltage power supply. This provides the large potential needed
to attain proportional amplification of electrons. Silica rods with an outer diameter
of 0.435 mm are placed between the mesh and the inner electrodes to maintain a,
uniform gap size. Figure 3-2 contains a diagram of the amplification region.
Electrons from the drift, volume pass through the holes in the mesh and enter the
amplification gap. There, they form avalanches with gains of order 104 to 105. Because
the mesh pitch is over 50% of the size of the gap, the field in the amplification gap
is not particularly well modeled as a parallel plate geometry. Most of the ionization
77
caused by the avalanche occurs in the region closest to the anode. While the electrons
in the avalanche reach the anode in 0(1 ns), the ions drift much more slowly. The ion
drift time between the anode and the mesh is expected to be 2-3 ps. At the same time,
approximately 0.3 photons per electron-ion pair are also emitted [105, 106. Much of
this light is at visible wavelengths, where it can easily be read out by photodetectors
such as CCDs and PMTs.
3.4
CCD Readout
The 4-shooter measures light from avalanches using four Apogee Alta U6 CCD cameras. Each camera images the interior of the chamber through a dedicated viewport.
The cameras are attached to the vacuum chamber using cylindrical mounts, and
Canon DF 85 mn
f/1.2 lenses focus light from the readout plane onto each CCD.
While some scintillation occurs with the initial energy deposition, this light is primar-
ily at ultraviolet frequencies [107, 108] and is not efficiently collected by the CCDs.
Additionally, the solid angle coverage of the light sensors is too small to hope to
measure the primary scintillation even if the efficiency could be increased. A CCD
with lens attached is shown in Figure 3-4.
The Apogee Alta U6 camera uses a 1024 by 1024 pixel Kodak KAF-1001 CCD
chip.
Each pixel is a 24 pim by 24 pm square, so the CCD chip has a total area
of 6.04 cm 2 . Each pixel images an approximately 161 p/m by 161 pm region of the
readout plane. In most runs, the pixels are grouped together in four pixel by four pixel
bins, resulting in 256 by 256 bin images with each bin covering a 644 pm by 644 pm
region of the anode. The binning is done on-chip and enhances the signal-to-noise
significantly compared to performing the identical binning during image processing.
The bin size projected onto the readout plane results in a per-pixel spatial resolution
of o-pix = 640/v/12 pm = 185 pin.
The quantum efficiency of the KAF-1001 CCD reaches a maximum of approximately 72% at 560 nmn and is greater than 40% between .450 im and 860 nm. Thus.
it is most sensitive to visible wavelengths and is well matched for the scintillation
spectrum of electron avalanches in CF 4 . The Alta U6 cameras have a typical noise of
79
Figure 3-4: A CCD camera with lens attached. The lens is focused on the amplification gap to attain high resolution images of the ionization signals of events in the
detector. A metal plate is used to mount the camera to the detector.
80
8 e- per pixel. To reduce dark noise to less than 1 e- per pixel per second, the CCD
chip is cooled to -20'C. In most data taking, this is much less than the readout noise
and can be ignored. The CCD data uses 16 bit digitization. with approximately 1.3
electrons (photon interactions) per analog-to-digital unit (ADU).
The four CCDs provide a two-dimensional projection of the ionization left in the
active volume of the detector. Unlike previous DMTPC prototypes, which used a
single CCD to image only part of each drift volume, the 4shooter uses four CCDs to
image the entirety of a single drift volume. This has the advantage of more efficiently
utilizing the active volume and allowing for better characterization of any backgrounds
coming from the edges of the field cage. Figure 3-5 shows some example ionization
events seen in the CCD.
3.5
Charge Readout
The earliest DMTPC prototypes included only CCD readout. This allows for reconstruction of a two-dimensional projection of the ionization profile of a recoil, but has
a number of limitations. In addition to several classes of CCD specific backgrounds
that must, be identified, CCDs also operate by integrating light over a period of time
orders of magnitude longer than that associated with an ionization track. Lacking
any timing information, CCDs have little to no sensitivity to the ionization profile as
projected onto the drift axis. The inclusion of charge and PMT readout allows the
4-shooter prototype to use timing information to reconstruct information about the
ionization profile along the drift axis.
3.5.1
Signal Generation
The charge readout systems of the 4-shooter measure induced currents on electrodes
cauised by moving electrons and ions inside the amplification gap.
The electrons
reach the anode within 0(1 ns) of the primary electron reaching the amplification
gap. resulting in a sharp current spike with a very short length. In contrast to the
sharp current peak from the electrons, the slowly drifting ions induce a small current
lasting several microseconds.
81
Figure 3-5: Some example CCD tracks. Top left: An approximately 3.9 MeV a track
from an "'Am source. Top right: A 200 keVe, nuclear recoil from an AmBe neutron
source. Bottom left: A 79 keVee recoil. Bottom right: A 200 keVee recoil. The
color axis gives the amount of light in each pixel, proportional to the total ionization
occurring in the region imaged by the pixel. Nuclear recoils have an approximately
elliptical shape, with the direction of the major axis determining the axis of motion.
More ionization tends to occur at the beginning of the track than at the end.
82
Because about 30 primary electrons are generated per keV of energy lost, the
current signal from an actual event will be the superposition of the signals from the
individual primary electrons. For a point-like source of electrons in the drift region,.
the signal is broadened in time by diffusion. Additionally the ionization profile along
the drift axis must be considered as well. The idealized current signal of an event, is
the convolution of this profile (adding in diffusion) with the single-electron response.
Due to the electron drift velocity, a track with Az
=1 mm will be broadened by
approximately 9 ns. This broadening will be most, apparent in the shape and height
of the rising edge of the current pulse, which is dominated by the fast signal of the
avalanche electrons.
A real detector, however, would not measure this idealized signal.
Drift field
nonuniformities will affect the signal, as they can lead to position-dependent changes
in the drift time. The capacitances of the various electrodes can lead to crosstalk
between readout channels. Finally, the detector and readout electronics will simply
be unable to perfectly transmit, an arbitrary current signal. The readout electronics
(including the detector itself) have a finite bandwidth, so signals including frequencies
outside the passband of the electronics can have significant distortion.
3.5.2
Readout Channels
While pure CFI has many attractive properties for use as a target material in a
gaseous (lark matter detector, it has several drawbacks.
In particular, discharge in
the form of a spark at the readout plane occurs intermittently. These sparks can
be induced by events with very high ionization density, such as (t particles traveling
along the drift direction near the anode. While there has been no evidence of sparks
damaging the detector, it was discovered that many amplifiers can be damaged when
this occurs. Thus. many amplifiers are unsuitable for use with the amplification stage
design of the -4-shooter. The current signal on the amplification mesh is read out by
a Route2Electronics HS-A\MP-CF fast preamplifier, which includes input protection
to prevent such damage. The preamplifier is connected to the bottom of the chamber
base through a BNC feedthrough. The input signal from the detector passes through
83
400
E
5
E
29300
200
1001
-
100--
0
-1
01
2
T
3e[
ime fps]
-1
0
1
2
T
p 3e
lime
[ps]
Figure 3-6: Some example nuclear recoil mesh pulses. The recoils were created with
an AmBe neutron source. Note the characteristic two-peaked structure of a low-Az
pulse.
a. 20 Q resistor held to ground in parallel with a voltage amplifier with a gain of
approximately 80. The resistor provides a voltage at the preamplifier input that
is proportional to the current, and the output of the preamplifier is digitized for
later analysis. While the ideal signal will be a large current spike from the electrons
followed by a longer ion signal with a small current, the resulting pulses from a pointlike source of ionization display a characteristic two-peaked structure. An initial fast
peak with a short (0(10 ns)) rise time is seen, as expected from the electrons, while
a second broader peak with a similar height as the fast peak occurs a short time
later. Low Az events, such as nuclear recoils display this structure, as can be seen in
Figure 3-6. A variety of pulse shapes is seen in higher Az events. A fast peak is not
identifiable, but one or more broader peaks are typically seen. Several such long Az
events are shown in Figure 3-7.
The anode is separated into two concentric electrodes, an inner central anode
channel (henceforth just called the "anode" channel) and an outer electrode (the
"veto" channel). This design is shown in Figure 3-8 Signals on the (central) anode
channel are shaped by a Cremat Cr-113 charge-sensitive preamplifier (CSP), also
known as a charge-integrating preamplifier. The Cr- 113 preamplifier integrates the
total charge induced in a pulse and the shaped pulse decays with an exponential
decay constant of 50 its, much longer than the time scale of the current pulses. With
this decay time, event rates up to 1 kHz or so can be sustained without suffering
84
571 UU
E
Z
60--
:R50
-1
0
-50'01
Time [IsT
1 M)
I
I
I
I
I
I
I
I
I
I
.
-2L
Time
[ps?
.
E
10
21o
50
0
-1
0
1
2
ime [pisi3
Figure 3-7: Some example high Az mesh pulses. These can be events such as minimum ionizing particles, electrons, protons, and other high energy particles with low
stopping power. A wide variety of pulse shapes is seen in the detector.
85
0.070THRU #0
0.281 THRU
LEARANCE LOOSE
ANODE CENTRAL
ELECTRODE
ANODE VETO
RING ELECTRODE
MESH ELECTRODE
0.039THRU
013.700_0.064 THRU #0
Figure 3-8: A diagram of the different electrodes on the anode plate. The central
anode and veto channels are held at the same voltage, while the outermost channel
is electrically connected to the mesh and held at ground. From [95].
significant dead time due to pileup of pulses. The Cr-113 has a nominal gain of
1.3 mV/pC and an output impedance of 50 Q. The veto channel is read out using a
Cremat Cr-112 CSP. This preamplifier is similar to the Cr-113 in most respects but
has a nominal gain of 13 mV/pC. The anode channel measures the total integrated
charge in avalanches in the central region of the detector, which is proportional to
the energy lost due to ionization processes. The veto channel, in contrast, is used to
determine if an ionization event happened at or very near the field cage rings. The
anode and veto signals for an event in the central region and an event near the edge
of the drift volume are shown in Figure 3-9.
The anode and veto preamplifiers are connected to their respective electrodes using
Cremat CR-150 evaluation boards. The anode bias voltage is applied to the channel
through the board, which includes circuits to These evaluation board allows for a
bias voltage to be applied to the electrode. The board and preamplifier are placed
inside an aluminum box and are connected to an SHV coaxial feedthrough on the
bottom of the chamber. The evaluation board also contains a test input consisting of
a 1 pF capacitor connected to the preamplifier input in parallel with a 47 Q resistor
86
E
E
60
50-
-
40
20
0
02
I
'
-10
0
-20
' ' ' ' ' '
10
20
30
Time L[is]
-10
0
10
20
30
lime fjis]
Figure 3-9: Some example charge-sensitive preamplifier traces. The central anode
signal is given in blue, while the red signal is from the outer veto ring. Left: An event
in the central region of the detector. Right: An event near the field cage rings. The
small pulse in in the veto channel in the plot on the left shows that there is always a
small crosstalk signal, even when the event is far from the veto electrode.
connected to ground.
All three preamplifiers are powered through the ±12 V supplies provided by the
NIM bin used to power the high voltage power supplies. The maximum output voltage
of each preamplifier is approximately 3 V. In the initial operation of the detector, a
great deal of noise was encountered in the charge channels. The mesh readout was
particularly affected. The power spectrum of the noise showed a number of prominent
peaks near 100 MHz, suggesting that the problem was related to one of the channels
picking up signals from the FM radio band. This noise was largely eliminated by
using a simple LC filter (described in [95]) at the power input of the fast preamplifier
on the mesh channel.
3.6
PMT Readout
The light signal is also measured by three Hamamatsu R.7400U-20 PMTs using a
single 2.75" CF viewport located at the center of the top of the bell jar, between
the four CCD viewports. The PMTs are powered with Hamamatsu E5780 assemblies
and run at a bias voltage of -925 V. One PMT is powered by the same Bertan 380N
power supply used to power the cathode, while the others are powered by a Bertan
375N 5 kV negative high voltage power supply. Due to space constraints, each PMTs
87
E
CD
E
0
a4
- s jruI'r-Trwh-
M
rn
0
-
m
-100
-500
-200-
-1000-
-300-
-1
-1
-0.5
0
05
Time [Ws]
-1
-0.5
0
T
[
5
lMme (LisJ
Figure 3-10: Some example PMT traces from a particles. Left: A low Az a from
an 241Am source. Right: A higher Az background a. The stopping power maximum
corresponds to the position of the Bragg peak for an a particle. That the peak occurs
near the end of the pulse indicates that the Bragg peak occurred farther from the
anode than most of the track. Hence, the event on the right is traveling away from
the anode.
has a diameter of only 8 mm, which limits the amount of light that can be collected.
Unlike the CCDs, the PMTs measure the time profile of the light emitted during
avalanches. Thus, the PMT signals contain similar information as the mesh readout
signals. The pulse widths and shapes yield information about the track geometry
when projected along the drift axis. While the energy resolution of the PMT signals
is not as good as that of the charge channels, the PMTs have the advantage of being
inherently decoupled from the high voltage electronics of the TPC. The ideal PMT
signal will be expected to more accurately reflect the time profile of electrons reaching
the amplification gap than the mesh signal.
3.7
Data Acquisition
Data is taken using a dedicated data acquisition (DAQ) computer. The CCD cameras
are connected to the DAQ machine with USB connectors while the remaining channels
are digitized using AlazarTech ATS860 PCI digitizers. Each digitizer includes two
input channels, labeled A and B. One digitizer is designated as the master board
and controls triggering. When the mast board triggers, a signal is sent to the other
boards to concurrently save data. The 4-shooter prototype uses three boards. A
88
Channel I Readout Type
CCD 0
Light
CCD 1
Light
CCD 2
Light
CCD 3
Light
Mesh
Charge
Anode
Charge
Veto
Charge
PMT 0
Light
PMT 1
Light
PMT 2
Light
Model
Alta U6
Alta U6
Alta U6
Alta U6
HS-AMP-CF
Cr-113
Cr-112
R7400U-20
R7400U-20
R7400U-20
Readout
USB
USB
USB
USB
Board 0,
Board 0,
Board 1,
Board 1,
Board 2,
Board 2,
Method
Channel
Channel
Channel
Channel
Channel
Channel
A
B
A
B
A
B
Table 3.2: Summary of 4shooter readout channels under standard running conditions.
simple threshold trigger on the anode channel, which has the best signal-to-noise is
typically used to trigger readout of the charge and PMT channels. Upon triggering,
data from each channel is stored into the digitizer's flash memory. 4096 samples
prior to the trigger and 8192 post-trigger samples are saved with each waveform. The
boards are run with a sample rate of 250 MS/s. The boards use 8-bit digitization,
limiting the dynamic range. but also allow for different voltage ranges.
Different
voltage settings can be used to study different energy ranges.
The charge readout channels are AC-coupled with 1 M
termination.
Despite
using AC coupling, a noticeable DC offset was seen in the mesh channel. This was
corrected by placing a 50 Q terminator at the preamplifier output in parallel with
the digitizer input, effectively terminating the channel at 50 Q. Under these settings,
the board has a -3 dB bandwidth of 10 Hz to 65 MHz. The PMTs are DC-coupled
with 50 Q termination. For the PMTs, the board has a -3 dB bandwidth of DC to
100 MHz.
The DAQ process and supporting code are written in C++ using CERN's ROOT
analysis toolkit and the C/C++ APIs of the readout hardware. Data acquisition is
performed in "'witness" mode. where the CCDs are continually being read out and
saved to disk at a fixed interval. Digitizer traces. trigoered from the central anode
channel. are taken concurrently with each CCD exposure. The DAQ process saves all
images and all digitizer traces. an(l event selection is left, to the reconstruction and
89
analysis processes. Updates to the DMTPC software package are planned to allow
for software triggers during the DAQ process to reduce data storage requirements.
An "event" consists of an image from each CCD for a given time interval, the
digitizer traces for each charge and PMT channel for triggers during that time interval, a time stamp for the event and for each digitizer trigger, and various other
relevant data such as detector and environmental conditions. In an event, the DAQ
process exposes the CCDs for the same amount, of time that the digitizer collects
data. However, the Alta U6 camera digitizes the data by shifting the charge between
pixels to a single analog-to-digital converter (ADC). At a clock speed of 1 MHz, this
process takes a sizable fraction of a second to complete. The camera shutters are not
used during event readout, leading to a significant amount of "parasitic" exposure
during which the CCDs are exposed to light from the detector while the charge and
PIT channels are not, active.
Data taking is separated into short data "runs," consisting of 1000 events each in
standard running conditions. Each run also includes one hundred dark frames (full
length exposures with the shutter left closed) for each camera in order to properly
account for the background bias level of the CCDs. Some additional data beyond the
event data is required for each run. Upon completion, each run is saved to a, ROOT
data file. The file is then copied to a DMTPC data server for processing and analysis.
Basic information outlining each completed run is saved into a MySQL database.
A second dedicated computer is responsible for monitoring and slow control of
the 4-shooter. Detector and environmental parameters such as the temperature, gas
pressure, the measured output voltage and current from power supplies are constantly
monitored and saved to a MySQL database. The slow control computer uses various scripts primarily to control the power supplies and the gas systems. Most basic
detector operations can be performed through the slow control computer. The turbomolecular pump is not operated remotely, so gas refilling is currently performed in
person. The slow control computer also hosts an Apache2 web server to aid in detector monitoring and operations. The computing systems are summarized in Figure
3-11.
90
Detector------*
.
Monitoring,
Gas, HV
Systems
-
Readout
Electronics
rS' toCntr fomputer
MySQL
Database
S
M
Web Server
.
AQO~ffsit~e
DAQ
Temporary
trage
Backiu
P
Data
File
Data Storage Disks
User
L-JL2L
MIT LNS Computing Cluster.
Figure 3-11: Schematic of the computing systems used to run the 4-shooter.
The
DAQ computer is responsible solely for taking data files and transferring them to
the temporary storage location on the slow control computer. For the 4-shooter, the
DAQ process is started from a remote login shell on the DAQ computer. The slow
control computer provides a web interface and controls detector systems other than
readout electronics. The files are transferred to the main MIT LNS computing cluster
for processing and analysis. The files are also copied to an offsite storage location to
prevent data loss in the case of a disk failure.
91
92
Chapter 4
Data Processing and Event
Reconstruction
The DMTPC event reconstruction framework seeks to reduce the raw data output in a
run file to a much smaller set of variables describing all the ionization tracks occurring
within the run. The CCD., charge, and PMT reconstructions proceed independently
from one another, with the data from the different channels being combined later
in the post-reconstruction analysis process. In the CCD, clusters of adjacent pixels
thought to correspond to recoils in the active gas volume are identified and characterized. In the charge and PMT data, pulses corresponding to recoils and other ionization
events are identified and parameters related to their shapes are reconstructed.
4.1
CCD Data
The CCD readout reconstruction consists primarily of two steps
image cleaning and
track recognition. The methods used to analyze CCD data are described in detail in
several earlier works (see, for example, Refs. [89. 94, 95] and need not be described
in too much detail here. Image cleaning must be performed because the raw images
output by the cameras often contain various artifacts that must be removed before
searching for events in the detector. Isolated pixels ,vith values far above or below the
Typical noise are identified and removed from each image. An averaged (lark frame.
created from a series of exposures with the shutter closed taken at the beginning of
each run. is subtracted from each image to remove pixel-to-pixel variations in the
93
baseline ADU value. The mean ADU values of the image and the averaged dark
frame are used to correct for any image pedestal drift between exposures.
The track recognition routine identifies sets of adjacent image bins1 that are believed to correspond to an ionization event in the detector. Such a set is known as
a cluster. The cluster finding algorithm has been described in a number of different
notes and papers. The details are not particularly relevant for this work, so I will not
describe it here. For each image, a list of clusters is obtained, and operations on the
pixels pertaining to the cluster characterize the properties of the ionization event.
In more mathematical language, a digital image I is just a list of Npixis pixels pi,
I
={pi
E N, 0 < i < Nixels}
.
(4.1)
Each pixel is a tuple pi E R3 containing a two-dimensional position and a weight,
A = Xi,
X yi, Wi}.
(4.2)
In practice, the positions (xi, yi) are distributed in a regular square grid and the digitization reduces the wj to integral values (prior to image cleaning). Calibrations are
necessary to convert the pixels given in camera units (bin number and light in ADU)
to physical units (length and ionization yield). The track finding algorithm reduces
images to small subsets C C I containing only pixels associated with potentially interesting physics events. These subsets are then characterized by a set of functions
f : 'P(R)
--
R transforming any cluster C into a small list. of numbers describing
the physical attributes of the ionization event. Among the most important attributes
calculated are
Energy The energy loss due to ionization, or ionization yield, of a recoil is proportional to the amount of light seen by the camera. For a given cluster C, the
energy is
E =
wi.
(4.3)
PjEC
Basic variables related to the energy such as the total number of pixels in the
1Remember that an image bin or pixel (an represent a block of CCD pixels.
94
cluster, the amount of light in the highest-weighted bin, andl the variance of the
weights in the cluster are recorded as well.
Position The mean position of the recoil is just the weighted average of the pixels
in the cluster,
(4.4)
-) ((", y)) C
( 0
where a weighted average is defined as
Z wif(xi , y, wi)
(X, Y,
(4.5)
.
,))c = Pi
Pi eC
Projected Range The projected two-diniensional range is estimated from the maximum distance between pixels in a subset of the cluster passing a threshold
chosen using simulated data to obtain a value close to the true range.
Two-Dimensional Direction The direction of the recoil in the two-dimensional
E [0, 27r) that is calculated
plane read out by the CCDs is a single angle
in two steps. The axial angle, defined as cIxi
= 4 mod 7 estimates the axis
along which the recoil occurred. The default algorithm uses principal component
analysis to find the major and minor axes of the recoil. which is approximately
elliptical in shape. Letting
f=
((f(x. y, w)
-
(f(x, y, '))c)
y,')
(g(
-
(g(x Y, ))c))c
(4.6)
the covariance matrix of the cluster is
(T2
o2
"
O"
E =
2
2)
Iry
iY
.
(4.7)
/
The covariance matrix has eigenvalues
+= a
±i
95
(
-
2
2
_ 4(a)2
2
(4.8)
with corresponding unnormalized eigenvectors
22
U
2
o±
-
i±2
(.22
2
L(2
_
-
4(oy)2(4.9
The eigenvectors give two perpendicular angles, 0±, defining the axis of motion
and the transverse axis of the recoil. The eigenvector with the largest projected
spatial variance with respect to the cluster mean,
o2(#)
([(x
2
-
]2
z)cos
C)Osin+ (y -
0 1
2
., + ( Y
+
2
XCOS b-1-
Silsin
22
S l l ] 2)(
+ 2o-
s
cos (
in
4 .1 0 )
6.
is identified as the axis of motion of the track.
Once the axis is calculated, the sense of motion along the axis (or head-tail
effect) is determined by estimating the sign of the track skewness. The light in
the track is projected onto the axis, and the start of the track is taken to be on
the half of the projection that contains the most light.
Moments The projected spatial variance given above can be generalized to a projected nth moment,
M(I
)
-
([(x - x) cos 6.+ (y - 9) sin 5]")
.
(4.11)
The second, third, and fourth moments along the axis of motion and transverse
axis are recorded. The transverse second nioment paraimeterizes the effect of
diffusion on the track, providing a weak estimate of the position of the track
along the drift axis. The third and fourth moments parameterize how asymmetric the projection is and how the tails of the diffusion conipare to a. normal
distribution.
The longitudinal nmoients provide alternative estimates of the
range and skewness.
96
4.2
Charge Data
The charge and PMT data is saved as a series of voltages at evenly-spaced time
samples. By reading the entire amplification plane., these channels can achieve much
greater sensitivity to low-energy recoils than the CCDs. The charge and PMT recon-
struction processes are characterized by pulse identification and pulse shape analysis.
These processes are roughly described in Refs. [109] and
[I 10]. Here I include a more
detailed discussion of the waveform reconstruction.
In the charge data reconstruction, some basic data is recorded for all waveforms.
The baseline is estimated from the mean of the first five hundred samples, while the
root-mean-square of those samples is used to estimate the noise level of the waveform.
The mininmum and maximum voltages of the waveforms are also recorded, as are the
times at which these values occur.
Once the waveform is characterized, pulse reconstruction is performed. Because
the data, is only digitized at 8 bits, the dynamic range is limited and, at lower energies,
noise can be particularly problematic in accurately reconstructing pulse parameters.
To reduce noise, a digital low-pass filter is first applied to each waveform after calculating the basic global waveform parameters but prior to pulse reconstruction.
Implementations of a number filters are included in the DMTPC signal processing
toolkit.
The default analysis for 4-shooter data uses finite-impulse response (FIR)
filters., which are the digital analog to the convolution for continuous data. A lowpass FIR filter smooths the data by defining the output as a weighted average of the
data points near a given sample. An FIR filter is defined by a set of coefficients {bn}.
If the data points are represented by {x,}, where n is the index of the time samples
and there are N such coefficients, the filtered output points {y ,}
y1 =
are defined by
(4.12)
bxnk..
k=O
Since there are only a finite number N, of samples, there are only
-
N,
' + 1 well-
defined data points in the output of the filter. The frequency response of an FIR
filter is defined by its output for an input of the form xk(V) = exp (2irkv). where
97
v-' is the oscillation period in number of time samples. The transfer function (or
z-transform) for such a signal is
N,-1
2
bke 2 inkv.
T(e i?") = E
(4.13)
k=O
The amplitude response to a signal with frequency iv' is just IT(e2 ix ), while the phase
response is arg (T(e2iT")). This numbers characterize how much an oscillating signal
at this frequency is attenuated in amplitude and how much the phase shifts after
applying the filter. The default analysis uses a Gaussian convolution as the basis for
setting the coefficients. The coefficients for a filter of length 2N+ 1 and characteristic
width a are defined by
b0 ;k = erf
k-
N+1
-
-
erf
k-
N (4.14)
The continuous analog of this filter, defined by a Gaussian with standard deviation a,
is a low-pass filter with a Gaussian response in the frequency domain with a standard
2N
deviation of a, = (27a)-1. The coefficients are then normalized so that E b;k = 1
k=O
which enforces the condition that, pulse integrals are preserved by the filter. The
DMTPC signal processing toolkit implements a number of alternative FIR filters as
well for both smoothing and derivative estimation.
FIR filters are attractive because they are simple to design and implement, have
stable output, and a well-defined linear frequency response. However, they are not
necessarily ideal. In particular, FIR filters are unable to implement features such as a
steel) frequency roll-off or a narrow stopband, which is useful is there is a particularly
problematic frequency present in the noise. Implementations of more advanced filters
that can reduce these problems are included in the signal processing toolkit but are
not currently in use.
4.2.1
Anode and Veto Readout
The anode and veto channel signals use charge-integrating preamplifiers, and the resulting pulses have very similar shapes. Most of the integrated charge signal comes
98
from the ions drifting across the amplification gap. This process takes several microseconds, determining the time scale of the rising edge of the anode and veto pulses.
The amplifiers have a characteristic exponential time decay constant of 50 ps. Because the pulses found in the anode and veto channels have broad, long time-scale
features, a filter of the type described in the previous section with a = 20 bins, or
80 ps is used to reduce the noise without degrading the features of the signal. The
coefficients of this filter are found in Figure 4-1, while the frequency response is deFigure 4-3 shows the result of smoothing a charge-integrating
tailed in Figure 4-2.
II
.80.0 8
80.
-0.0 7 -0.0 60.0 5
0.0 4
0.0 3
-
-
0.0 2 1
0.0
ii
.
-,
h
10
20
40
30
50
60
Bin
Figure 4-1: The finite-impulse response coefficients used as a low-pass filter to reduce
noise in anode and veto readout data. This is the response of the filter to a unit
impulse.
:
I
-
WIN
100-
~YT
_X
IM
1...
-24
-M
.1
-1
~0
20
40
80
IOU18
120
FreqWi-e Rk"*
0
2D
40
60
s0
100
120
Frequ&enCy IMAzI
Figure 4-2: The attenuation in magnitude (left) and phase shift (right) as a function
of frequency of the noise reduction filter used in anode and veto readout data.
preamplifier signal.
99
57100
8,80
60
40200-15
-10
-5
0
5
10
15
20
25
30
Time [ps]
Figure 4-3: An example smoothed anode waveform. The original waveform is shown
in blue, and the smoothed waveform is shown in red.
Because of the decay constant, the anode and veto channels are susceptible to
pileup for very large event rates (kHz or higher). This is a much higher rate than
seen in source-free runs such as WIMP searches. Care must be taken when using
calibration sources, which can lead to such high event rates. Pileup can be reduced
by using the charge-sensitive preamplifier output as the input to a shaping amplifier
rather than directly measuring the preamplifier output.
The charge data contains 32.8 ys following the trigger and 16.4 As prior to the
trigger, so a typical waveform contains the rising part of the waveform but only part
of the falling edge, which is characterized by the decay constant. Even pileup traces,
with two or more ionization events in a single waveform, appear as a single pulse with
multiple peaks. Because these events are quite rare in normal running, the default 4shooter anode and veto reconstruction identifies only a single pulse in each waveform
and characterizes its shape. The pulse peak time is identified as the time in the
smoothed waveform at which the highest voltage is reached. The peak voltage is the
difference between the highest voltage and the baseline of the trace. The pulse start
is defined as the nearest time prior to the peak position at, which the voltage equals
the baseline value. Similarly, the pulse end is defined as the nearest time after the
peak time at which the voltage equals the baseline. If such a value does not occur,
the pulse start (or end) is defined to be the first (or last) sample in the smoothed
100
Parameter
Description
Vk
Peak pulse voltage above baseline
Time at which the peak voltage is found
Time between the peak and the beginning of the pulse
Time between the peak and the end of the pulse
The 10% peak to 100% peak rise time
Rise times (see above)
The 100% peak to 10% peak fall time
Fall times (see above)
Tpk
Ti
Tf
Rio
R 25 , R 50 . R 75 , Ro
Flo
F2 5 , F5 0 - F75 - F90
Table 4.1: Pulse parameters reconstructed for anode and veto (charge-integrating)
channels.
waveform.
Once the peak and the pulse start and end times are determined, several shape
parameters are determined. The 10% rise time, defined as the time between the peak
time and when the pulse first reaches 10% of its peak, is calculated. Similarly, the
25%, 50%, 75%, and 90% rise times are calculated. Fall times are defined as the time
between the peak and when the pulse last reaches a given value, are also calculated.
The same percentages are calculated for fall times as for rise times. A typical pulse
falls to only approximately 55% of its peak height at the end of the saved waveform,
so only some of the fall times can be accurately reconstructed.
4.2.2
Mesh Readout
The mesh readout uses a fast amplifier to study the current signal with a much higher
bandwidth than in the anode and veto channels, so much more structure is seen in
the resulting pulses. As briefly described previously, the avalanche of a single electron
left in the drift region contains two contributions
electrons and ions. The electron
part of the signal evolves rapidly. with electrons crossing the gap with a time of
0(1) ns. The avalanche develops in an approximately exponential fashion. with most
electron-ion pairs being produced near the anode. The electron signal of the singleelectron pulse. then is a large current lasting over a very short period of time. The
ions drift from the anode toward the amplification mesh at a much slower velocity,
so the ion signal for a single-electron pulse is a small current lasting over 0(1) ps. A
101
realistic detector, with a detector capacitance, preamplifier bandwidth, and digitizer
bandwidth, will not
Because the mesh pulses contain much sharper features, the a = 80 ns filter
used on the anode and veto channels is not appropriate. Instead, a much higher
bandwidth a = 1.5 bin or 6 ns filter is used to reduce noise. While this filter does
significantly reduce noise, which is particularly important for lower energy events
where the noise peak-to-peak is a significant fraction of the total peak height, there
is some distortion seen in the pulse shapes in the mesh pulses. The fast electron peak
is slightly broadened and lowered after filtering. The width of the filter is similar
in magnitude to the effects of diffusion, so this broadening, while noticeable, will
not affect the reconstruction much. As for the anode and veto signals, the filter
coefficients are shown in Figure 4-4 while the frequency response is shown in Figure
4-5. An example smoothed mesh pulse is shown in Figure 4-6.
30.25
0.2-
015 -
0.05
0
1
2
3
4
5
6
7
8
9
Time Sample
Figure 4-4: The finite-impulse response coefficients used as a low-pass filter to reduce
noise in mesh readout data.
The pulse reconstruction begins with the same reconstruction as for the anode
and veto channels. A single pulse is identified with the peak voltage in the smoothed
waveform. The pulse start and end times and global pulse rise and fall times are reconstructed in the same manner as for the other channels. Once those basic parameters
are calculated, the mesh pulse reconstruction calculates a number of additional pulse
shape parameters in order to identify pulses with the characteristic double-peaked
102
-2C
0
-4C
N-
f
.5C
-00
i
-5C
2
-
-
AM0
-70
-I M
00
40
60
so
100
LZ
120
Frequency jHxj
Frequency (MMz]
Figure 4-5: The attenuation in magnitude (left) and phase shift (right) as a function
of frequency of the noise reduction filter used in mesh readout data.
300
E
w250
200
150
10050
0
-5r
-1
-0.5
0
0.5
1
1.5
2
2.5
3
lime Vs]
Figure 4-6: An example smoothed mesh waveform. The original waveform is shown
in blue, and the smoothed waveform is shown in red. For the mesh pulses, the
smoothing slightly decreases the prominence of the fast peak, but also significantly
decreases noise. The noise reduction becomes much more important at lower energies.
structure associated with low Az events.
A local peak is defined as a data point with a voltage equal to or higher than all
points within a window with a half-width of five time samples. The reconstructed fast
peak is defined to be the first local peak within the pulse with a peak voltage greater
than 65% of the total peak voltage. The reconstructed slow peak is defined to be the
highest local peak in the pulse occurring at least 40 ns after the reconstructed fast
peak. The times and voltages of these two peaks are recorded, as are the voltage and
time of the minimum voltage in the trough between the peaks. Rise times between
the pulse start and the fast peak and fall times between the slow peak and the pulse
103
Parameter
Parameter
VF
Vs
VT
TF
Ts
TT
Description
Description
Fast peak voltage
Slow peak voltage
Trough voltage
Fast peak time
Slow peak time
Trough time
The 10% fast peak to 100% fast peak rise time
Pulse start to fast peak rise times (see above)
The 100% slow peak to 10% slow peak fall time
Slow peak to pulse end fall times (see above)
RF
io
FS, F50, FA, PFqO
Table 4.2: Pulse parameters reconstructed in the mesh reconstruction in addition to
the parameters also reconstructed for the anode and veto channels.
;jUU
Slow Peak
E
Fast Pea
e250
200
150
100
Trough
50% Fall Time
50% Rise Time
50
0
:.1
Pulse Start Time
-0.5
0
0.5
1
Time [Iis]
Figure 4-7: An annotated smoothed mesh pulse from a nuclear recoil created from
an AmBe neutron source.
end are reconstructed in the same manner as the global pulse rise and start times.
Table 4.2 summarizes the various parameters reconstructed for mesh waveforms in
addition to parameters reconstructed for the anode waveforms as well, and Figure 4-7
shows some of the reconstructed pulse parameters for a smoothed mesh pulse.
4.3
PMT Data
The PMT analysis is the least developed of the channels. With the current, readout,
electronics, the bandwidth of the digitizer is not well-suited to digitize the fast light
signals output by the PMTs. Additionally, some large noise spikes are often seen to
104
accompany PMT pulses while the PMTs only collect a very small fraction of the light,
making it difficult to use the PMTs for analysis of nuclear recoil signals. However.
some useful information is seen in a pulses.
At present. the default PMIT reconstruction used for nuclear recoil analyses is
nearly identical to the anode channel reconstruction.
however, pulse smoothing is not performed.
In the PMT reconstruction,
In future detectors, the PMT pulse
integrals will provide additional estimates of the event energy deposition and the
pulse shapes should yield more accurate Az information than can be obtained with
the charge readout, channels.
105
106
Chapter 5
Detector Calibration
In order to measure low-energy nuclear recoils and search for evidence of WIMP
(lark matter, the energies of ionization events occurring in the detector must be wellunderstood. Furthermore, directional detection requires a careful understanding of
the detector's response to a directional source of nuclear recoils. Because of the vary-
ing capabilities of the different readout channels, the DMTPC collaboration utilizes
a series of calibration methods to study the detector performance. These methods
include measuring
1. the charge energy scale with x-ray sources,
2. the CCD length scale with an LED.,
3. point-to-point gain and light, throughput variations with
sources,
4. the CCD energy scale with o sources, and
5. the CCD directional reconstruction with low-energy (t particles.
Further studies are performed with fast neutron sources.
As neutron studies are
closely tied to background nuclear recoil and (lark matter searches, a discussion of
them is left until Chapter 7.
5.1
Charge Readout Energy Scale
The charge readout channels are generally expected to have a better energy resolution
than the optical sensors. The signals on the electrodes measure all the charge in the
107
Charge Sensitive
Preamplifier
Shaping
Amplifier
Anode
Ch. A: Used to trigger
Mesh
Ch. B
Fast
Amplifier
Board 0
Ch. A: Measures energy
Board 1
Figure 5-1: Charge readout setup used in x-ray calibration running.
The Cr-112
charge sensitive preamplifier integrates the current signal, while an Ortec 575A spectroscopy amplifier shapes the signals and is used for triggering. The energy measurement comes from the Cr-1 12 output. The veto channel is not read out in these
runs.
amplification gap, while only a tiny fraction of the total light produced is collected by
the CCDs or PMTs. Unlike the CCDs, where the light is separated into many pixels,
the charge channels also measure signals from the entire anode at once, improving the
signal to noise ratio of the energy measurement. The charge readout energy scale is
calibrated using x-ray sources of known energies. The gain of the Cr- 113 preamplifier
used in normal running is not sufficient to measure most x-ray signals, so a modified
amplifier setup, sketched in Figure 5-1 is used instead. The Cr-113 preamplifier is
generally sensitive to ionization signals between 20 keV and 6 MeV. Pulses at lower
energies can be measured but, have substantial amounts of noise that will degrade the
signal.
A Cr-112 CSP is used to amplify the signals from the central anode instead,
increasing the signal size by a factor of 10 compared to the Cr-113. The output is
split into two lines.
One is fed directly into one of the digitizer inputs while the
other provides the input signal for an Ortec 575A spectroscopy amplifier (spec amp)
with the variable gain set to 50.
Because of the impedances of the digitizer and
the spec amp. splitting the signal does not measurably affect the signal strength.
The spectroscopy amplifier shapes the pulses into an approximately Gaussian shape.
108
imlproves the signal-to-noise ratio, and provides a much more stable baseline. The
spec anip output is used to trigger the digitizers, while the charge-sensitive preamp
output is used to make the energy calibration.
5.1.1
"Fe Calibration
The 4-shooter charge readout is typically calibrated using an approximately 33 pCil
55Fe x-ray source.
The source emits x-ray lines at 5.888, 5.899. and 6.49 keV at
relative intensities of 0.506, 1.0, and 0.176, respectively [111]. At these energies, xrays interact with CF 4 gas primarily through photoelectric absorption [112].
The
x-rays can also cause the emission of a K, x-ray from a fluorine or carbon nucleus,
leading to an escape peak, where the energy of the secondary x-ray is not measured.
The K,, lines of carbon and fluorine, however, are only 277 eV and 676.8 eV [113].
respectively, so the escape peaks differ from the photoelectric absorption peaks only
by approximately 10%. The resulting true electron recoil spectrum consists of several
monoenergetic peaks. The spectrum measured by the detector is affected by the
detector resolution and geometric effects. Recoils left near the edges of the field cage
or near one of the spacers used to separate the amplification mesh from the anode
electrodes will often only deposit part of their energy in the active volume of the
detector. causing the distribution to have a tail of lower energy events where some of
the ionization was not measured by the detector.
The anode output is smoothed with a a = 10 bin (40 ns) filter of the type described
in the previous chapter. and the standard charge-integrating preamplifier reconstruction is applied. An example "Fe event is shown in Figure 5-2. Electrons emitted
with ~ 6 keV of energy only have a range of approximately 0.5 cm [114], so the rise
time of the anode signal is used to remove background events such as MIPs.
The event rate during "Fe running is much higher than in source free running.
The rate from the unshielded source has been measured to significantly reduce the
detector gain. A number of layers of aluminum foil are used to attenuate the x-rays.
reducing the event rate (both "Fe and background) above I keV to approximately
'Activity as of runs taken during June 2013
109
JEE
1200
25-
91000
15
800-
10
60000
-
200
01
-5
52
0
10
15
2
0
50
5
10
15
*20
25
30
-005
00
20
15
-4
-2
2
4
Time (jpsj]
Figure 5-2: An example 5 5Fe calibration event. The raw output is in gray with the
smoothed waveforms overlaid in red. Top left: The charge-sensitive preamnp output
used to obtain the calibration. Top right: The spectroscopy amp output used to
trigger the digitizer. Bottom: The fast amp output. At 5.9 keV, the pulse is too
small to accurately reconstruct, but smoothing allows us to see it.
170 Hz. At this rate, the reduction in signal strength compared to source free running
is less than 0.5%.
The shielding also alters the x-ray spectrum, causing the relative intensity of the
6.49 keV x-rays to increase. The detector is unable to resolve the individual peaks, but
instead sees a Gaussian-like peak with an extended low-energy tail at approximately
6 keV. The spectrum is well modeled by a Crystal Ball distribution-
a Gaussian
with an extended polynomial tail to one side. The mean and standard deviation of
the Gaussian part of the best-fit functions provide estimates of the energy scale and
resolution of the detector. This is used to set the electron-equivalent energy scale,
written with the subscript ee. The Gaussian mean is defined to be equal to 6 keVee.
An example fit is shown in Figure 5-3.
The most extensive energy calibration measurements were taken at the "standard"
running conditions of 60 torr CF 4 with a 5 kV drift voltage and a 670 V anode
110
5001
E 450
400
350
300
250
200
150
100
50r
5
10
15
20
40
35
30
25
Anode Peak Voltage [mV]
Figure 5-3: A typical fit of the "Fe peak to the Crystal Ball function.
voltage. Estimates of the various systematic uncertainties in energy calibration and
gain measurements are summarized in Table 5.2.
The avalanche gain varies with each gas fill, falling by 1-2% over the first few hours
after refilling the gas, and by somewhat less than 3% total over a typical 24 hour
period. Because this is such a small effect, it is treated as a systematic uncertainty
although in the future it may be modeled to improve energy measurements.
The source generates electron recoils throughout a sizable fraction of the detector,
but does not uniformly sample the anode. Large scale gain variations across the anode
are measured by performing the calibration with the source at different positions
above the cathode, showing that such spatial variations are significantly smaller than
other sources of uncertainty.
The fit function used, a Crystal Ball function, can also induce a small systematic
uncertainty if the peak position is not at the expected energy. Measurements of
different x-ray lines from other sources (see §5.1.2) show that this effect, as well as
any nonlinearities in the detector response are limited to no more than about 1.5%.
Finally, the geometry of electron recoils caused
55Fe
x-rays is different from the
geometry of nuclear recoils. Nuclear recoils have much smaller ranges than the 6 keV
electrons from the "Fe source. The
55 Fe
pulses will have longer rise times than those of
nuclear recoils due to the longer typical Az. Due to the finite electron drift velocity,
the difference in pulse rise time could conceivably be as much as 50 ns. Because
111
/
75 torr
45
E
0
-60
120
torr
45 torr
100-
/
3080
LL25-/
20
60
15
A
40
10A
Ar
560
-
580 600
20
620
640 660 680
0
700
720
740
Anode Voltage [V1
Figure 5-4: Energy calibration vs anode voltage at three different pressures. The
symbols are the data points and the lines are the best-fit curves for an exponential
function. The gas gain is calculated assuming W = 34 eV and a preamplifier gain of
G = 13 mV/pC.
this is much faster than the RC decay constant of the charge-sensitive preamplifiers,
the 5 5Fe calibration may slightly underestimate the correct calibration from nuclear
recoils, but this effect will be much less than 1%.
The energy scale was also measured at various anode bias voltages for a single fill
each of 45, 60, and 75 torr CF 4 . Table 5.1 shows the mean and standard deviation of
the
55
Fe distribution using a Crystal Ball fit for these detector settings. Figure 5-4
plots the same and shows the best fit to an exponential function. For this data, the
best fit curves for the three different pressures are
V 45
(7.60
-mV]
0.09) x 10-5 exp
Vanodc[V]
51.26 ± 0.05,)
p
V"[mV] =
(3.06± 0.02) x 10-5 exp
peak
7ea[mV] = (8.91 ± 0.07) x 10~ exp
Vanode
49.28 t 0.03)
(
(5.1)
VanodeV]
47.08 ± 0.02/
The relative gain ratio between the Cr-113 preamplifier and Cr-112 amplifier is
found by matching identical spectra taken with both amplifiers at the same running
conditions. At an anode voltage of 670 V in 60 torr CF 4 , the effective gain ratio of the
112
p [torr]
45
45
45
45
45
45
60
60
60
60
60
60
60
60
75
75
75
75
"15
75
75
75
75
V'drift
[kV]
4
4
[V]
Yinod
4
580
590
600
610
620
630
4
4
4
5
600
610
620
630
640
650
660
670
640
650
660
670
680
690
700
710
720
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
Fit Mean [mV
Fit (- [mV]
6.277
7.551
9.140
11.246
13.559
16.475
5.962
7.217
8.887
10.916
13.43
16.286
20.062
24.557
7.196
8.740
10.903
13.472
16.636
20.601
25.531
31.47
39.15
0.501
0.591
0.747
0.926
1.063
1.306
0.487
0.578
0.728
0.919
1.073
1.310
1.654
1.987
0.602
0.737
0.914
1.112
1.402
1.756
2.221
2.72
3.45
Table 5.1: '5 Fe peak mean and width, as me asured by the Cr-112 preamplifier over a
single fill at three diiTerent. pressures.
two amplifiers was found to be G 113 /G
12
0.112.2 Significant differences between
the spectra are seen when varying the gain even by 5%. Furthermore, the total rate
in the 40 to 200 keVe,, energy range suggests that the calibrations match to within
1%. To be conservative, an uncertainty of 2% will be assigned to this value.
The avalanche gain. defined as the number of electron-ion pairs generated in the
amplification gap per electron left in the drift volume, is estimated from the energy
calibration as well. Typically, if there are N electron-ion lairs in the amplification
gap. the drifting charge carriers will induce an integrated charge of Ne on the anode.
If AE is the energy deposited contributing to ionization aid I"
is the work function
2This is in fact different from the measured gain ratio by using a pulser on the test input of one
of the Cr-150 boards.
113
Measurement
Source
Uncertainty
Cr-112
Cr-112
Cr-112
Cr-112
Fill Variation
Daily Variation
Fit Function & Linearity
Spatial Variation
2%
1.5%
1.5%
0(1%)
Cr-112
Cr-112
Az Dependence
Event Rate Dependence
< 1%
<0.5%
Cr-113
Aval. Gain
Gain Ratio
Cr-112 Gain
2%
5%
Table 5.2: Summary of estimates of systematic uncertainty in the
55
Fe measurements.
of the gas, then N = AE/W. Letting G be the gain of the amplifier and V be the
output voltage of the amplifier, the avalanche gain is
Gava =
AEGe
.
(5.2)
Using W = 34 eV, and G = 13 mV/pC, the gain as a function of peak voltage from
the Cr-112 preamplifier is
Gavai = (2720 mV 1 )V
(5.3)
This equation is useful in obtaining a rough estimate of the gain rather than a precise
value. The preamplifier gain has a typical variation of 5%, while the integrated charge
induced on the central anode will not precisely be the total amount of charge in the
amplification gap. Additionally, the pulses do not have an instantaneous rising edge.
Rather, the pulse rising edge lasts for 2 to 3 ps. The 50 Its RC decay time of the
preamplifier circuit, means that the pulse height is underestimated by as much as 5%.
The reconstruction does not correct for this effect because it will have no bearing on
the energy calibration for nuclear recoils.
Table 5.3 summarizes the recommended energy calibrations used here at the standard run conditions of 60 torr CF 4 with
5.1.2
rift
5 kV and
Energy Scale Validation with
'4 moce=
670 V.
2 4 1Am
Additional energy calibration points are useful in validating the
55
Fe calibration and
testing the linearity of the detector and electronics response. Americium-241. a com114
Calibration
Cr- 112
Cr-113
Gain
Rec. Value
4.03 mV/keV,
0.45 mV/keV,
66000
Table 5.3: Recommended values for the avalanche gain and charge energy calibrations
at 60 torr CF 4 with a 5 kV drift voltage and 670 V anode voltage.
mon radioisotope that decays primarily by emitting 5.5 MeV o particles [115], is an
attractive isotope for calibrating the detectors using a number of different x-ray and
'f-ray lines [116, 117].
The most prominent lines expected to be seen in DMTPC
detectors are summarized in Table 5.4. Several prominent -- ray lines are found from
the decay of 2"Am, while the Np L-shell lines are also quite prominent.
Line
Energy
Neptunium La, 13.9 keV
Neptunium L 3 17.5 keV
Neptunium L, 21.1 keV
26.3 keV
Y26
59.5 keV
159
Table 5.4: Some x-ray and '-ray lines found in the decay of 24 Am. Values taken
from [117]. Several additional 7-ray lines are also present at much lower frequency,
and Np M-shell lines can be found at lower energies.
To measure tlese lines in the
2 1Am
spectrum, a 1 ptCi
24
Am a calibration source
was placed inside the detector. The americium in the source is housed in a metal
casing with a thin gold foil on one side to allow a particles out. Measurements with
an Ortec ULTRA ion-implanted silicon detector show that the 5.5 MeV a particles
lose nearly I MeV on energy prior to being emitted through the foil. The source is
fixed in an acrylic collimator and placed several inches above the cathode mesh to
prevent the n particles from
4' Am
decay from reaching the active volume. Using
the same detector and amplifier setup as for the "Fe calibration, the spectrum was
measured across a wide range of energies. To determine the contribution of the source
to the spectrum. a measured background spectrum (described in the next chapter)
was subtracted. leaving just the source spectrum.
Three data sets with different
energy ranges were taken: 10 to 100 keV (high energy). 5 to 45 keV (middle energy).
115
and 2 to 23 keV (low energy). Figure 5-5 shows the high energy and middle energy
spectra, while Figure 5-6 shows the low energy spectrum.
In the high energy set, a distinct 59.5 keV photoelectric absorption peak is not
seen. Rather, the event rate increases well above the background level near 60 keV,
and a broad continuum of events is seen in the region between 25 and 60 keV. The
range of a 60 keV electron in 60 torr CF 4 is approximately 25 cm [114]. This is the
approximate size of the detector, so such electrons are typically not fully contained
within the active volume. A very small peak near 26.3 keV and not far above the
bin-to-bin noise is evident in the middle energy set, while at lower energies a series
of peaks is clearly seen above background.
~2.5
14
-
10E5
-
-
10
15
4
)
Energy IkeVI
20
25
30
35
4
45
Energy [keVJ
Figure 5-5: The 2 4 'Am -y and x-ray spectrum. Left: Higher energies. The 59.5 keV
line appears as a broad feature because electrons at that energy are not typically fully
contained in the active volume. The rate show an additional increase near 25 keV.
Right: Detail of lower energy region. A number of clearly defined peaks are seen.
To study the peaks in the low energy data set in detail, the energy of the peak
near 14 keVec was fixed using a separate run with both
24 1Am
and
5 5Fe.
This reduces
systematic uncertainties from the daily gain variation and fill-to-fill gain variation. To
study the peaks in detail, low energy datasets were taken with just the
and with both the
24
iAm source and an "Fe source.
24
'Am source
In both the low and middle
energy data sets, five clear peaks are seen between 1 and 23 keV. Numbering these in
order of increasing energy, peaks 1 and 2 are fitted to two Gaussians and a constant,
while peaks 3-5 are fitted separately with three Gaussians and a constant. The peaks
as measured in the two data sets are described in Table 5.5. The Compton edge of
116
the 59.5 keV -y-rays, at 11.2 keV, is not clearly distinguishable in the spectrum.
3.5 -...
.
. . .. . .I
-0
2
4
6
8
10
12
I
I
14
16
I. . I .
22
18
20
Energy [keVA+
Figure 5-6: Detail of the low energy peaks of
24
Am.
In the low and middle energy data sets, peaks three through five agree quite well
with the expected energies of the neptunium L0 , Lfl and L, lines. That the measured
values agree so well with the expected values of the peaks shows that systematic
uncertainties from the iron-55 peak fitting and the linearity of the detector response
are limited to about 1.5%.
The two lower energy peaks, near 6 and 8 keV, are not found in typical Am241 spectra. However, their energies are consistent with the peaks expected from K0
emission from copper and from the various elements contained in stainless steel. These
are the two most common materials containing heavier elements used in detector
construction, so interactions between the metal in the detector and the
24 'Am
-y rays
may be causing such emission. The various peaks have widths of approximately 6%,
less than the typical width of the
55 Fe
peak. Because the
5 5Fe
peak is due to several
x-ray lines about 10% apart, this width of 6% is a more accurate measurement of the
energy resolution of the detector at these energies.
117
Peak
1
2
3
4
5
Energy [keV)
6.16±0.05
8.14±0.02
13.87±0.02
17.32±0.03
21.15±0.08
o [keV]
0.92±0.07
0.45±0.02
0.76±0.03
1.02±0.05
0.85±0.15
Energy [keV]
6.31±0.02
8.04±0.01
13.96±0.02
17.40±0.02
21.38±0.05
a [keVi
0.38 ± 0.02
0.50 ± 0.01
0.74 ± 0.02
1.03 ± 0.02
1.00 ± 0.06
Table 5.5: Positions and widths of the five peaks in the 2 41 Am spectrum between 1
and 23 keVec. The second and third colunms show the values in the low energy data,
set, and the fourth and fifth columns show the values in the middle energy data set.
The uncertainties are the statistical uncertainties reported by Minuit. The 6 keVec
peak is near the threshold in the middle energy data set and is likely underestimated
due to the small number of points included in the peak.
5.2
Focusing, Length Scale, and Rotations
In order to accurately measure the position of ionization left in the detector, the
lens mounted to each camera must be focused on the readout plane. A light-emitting
diode placed inside the mount for camera port D (holding camera A80333) illuminates
the chamber with a, small enough amount of light to be measured by the cameras.
The channels between the electrodes on the anode and the spacers separating the
amplification mesh from the anode are the most prominent features imaged by the
cameras. To focus the lenses, a potential of 2.5 V is placed across the LED and light,
is prevented from entering the chamber. The cameras are then read out with full 1024
by 1024 pixel binning. The focal lengths of the lenses are then successively changed
in order to minimize the widths of the aforementioned features. Once the lenses are
satisfactorily focused, the cameras are bolted to the mounts to fix them in place.
After focusing, a series of images, also at full resolution, are taken with the LED
on. The features in the images are then analyzed to obtain the length scale of the
images. In particular, the channel between the central anode and veto electrodes has
a diameter of 11.5 inches. Less light reflects off the bare GlO in the channel than off
the copper coating of the electrodes, so this shows up as a (lark arc in each image.
A circular Hough transform [118] is used to obtain the position of the anode center
and the radius of the channel in camera pixels. The radius is found to be 909 pixels,
yielding a length calibration of 161 pm/pixel.
118
The spacers between the mesh and anode appear approximately as lines. In particular, they cross between the areas imaged by each camera. By matching the spacer
positions and directions, the relative rotations of the cameras can be determined.
With the rotations, length scale, and position of the center of the anode measure for
each camera, positions in camera coordinates can be mapped onto the readout, plane.
5.3
"Co Optical Gain Map
Although large scale gain variations across the anode are measured to be quite small
using the
55
Fe source, the same is not trie for the amount of light measured by the
cameras. The amount of light passing through the meshes is dependent on the angle
at which the light is emitted, reducing the light seen at, larger angles from the lens.
This causes a reduction in light yield away from the center of the image. The light
yield is further reduced by various vignetting effects. The camera mounts attached to
the viewports block light, at larger angles while the lens introduces additional angledependent effects. These effects result in a significant loss of light at the edges of the
images compared to the centers.
To account for spatial variations in the relative light yield due to the CCD optics,
an approximately 1 mCi cobalt-57 -- ray source, with two main 'y-ray lines at 122 and
136 keV. is used to uniformly illuminate the readout, plane with electron recoils. The
source is placed on top of the bell jar of the vacuum chamber, near the PMT viewport
between camera ports A and B. The mean free path of -rays at these energies is only
approximately 5 mm [112], so most of the '-rays either scatter or are absorbed in the
stainless steel of the chamber wall. The remainder, however, are free to scatter off
the gas. creating electron recoils uniformly through the active volume of the detector.
This in turn leads to an approximately uniform amount of light generated at the
anode.
Point-to-point maps of the amount of light measured by the cameras are generated
from a series of runs with 10 second exposures of the CCDs (Figure 5-7). For each
run, events containing sparks are removed. For the remaining events, the average of
the difference between the exposure and the bias frame is calculated for each pixel.
119
Outliers from any nuclear recoils, alpha particles, or CCD artifacts such as persistently
hot pixels are removed by requiring that the difference between a pixel's value in an
exposure and the bias frame be less than 40 ADU.
5.4
14'Am a Energy Calibration
Previous results from the DMTPC collaboration [95, 94, 89, 109] have depended on
24'Am
a sources for energy calibration. A complete analysis of' a calibration data
compares the average energy loss at each position along the tracks to the equivalent
value reconstructed from SRIM-based Mionte Carlo data. It was shown in
[95]
that
this complete a calibration and the x-ray calibration result in very similar energy
calibrations. The uncertainties involved in the x-ray calibration are better understood
than those in the a calibration, and the charge readout also has a better resolution and
much lower energy threshold than CCD readout. As a result, energy measurements
in this work will depend on the charge signals. The energy measured by the CCDs is
useful in matching CCD tracks to charge signals.
To perform an a calibration, four collimated "'Am a sources are placed between
two field cage rings using a source holder designed to point the collimators parallel
to the spacers separating the mesh and anode. This ensures that the a tracks do not
pass through any low gain regions created by the spacers. One source is placed in the
region measured by each CCD. In these runs, the sources were placed approximately
10 cm above the anode, and data was taken with all channels with the digitizer settings
set to measure the charge and PMT signals from the a sources. Although the signals
are too large to be measured accurately by the fast, amplifier, the charge-sensitive
amplifiers are able to measure the full pulse height. The pulse height distributions,
converted to keV,-. are shown in Figure 5-8. The two-dimensional range distributions
are shown in Figure 5-9. Because the a tracks are also parallel to the readout plane,
the two-dimensional range will differ very little from the full three-dimensional range.
Finally, the ratio of light, as measured by gain-map-corrected CCD images. to charge,
as measured by the central anode channel is shown in 5-10. This gives the approximate
energy scale.
120
1.4
0.2
200
400
600
800
1000
200
-0.4
400
600
400
600
x [pixel]
60s
B00
1000
x [pixel]
-O
60
1.2-0.2
204
400
600
eoo
1
-4A
400
200
-
x[pixel]
x [pixell
Figure 5-7: Gain maps for cameras 110121 (top left), A80333 (top right), 100534
(bottom left), 100439 (bottom right). The maps provide a multiplicative scaling
factor for each pixel where 1 is defined to be the average of the active part of the
image.
121
12W0j
400200
00
3020-
0
000 00 06
2W
0-
080{
2
0
0 4080
50
Aj80d Emigy ]eVJ
$
0
Anode Enengy
(keVl
jamo
3W00
480D
100-
200
-D 180W
200
W8 40M
808
am802M08a0
Anod Elmoy (eVj
Figure 5-8: Anode energy distribution for each source. Top left: 110121. Top right:
A80333, Bottom left: 100534, Bottom right: 100439.
I
24-
0-
0
2D Range
I
32
1-m
o0
100
12
0
1k
20
10
Range
M
MM
28
4W
12
20
100--
0
{
0
60
100
120
140
180
180
20 Rang
8
.1
200
m
0 10
WD 10 100
100W
20 Rge
1ljb2D
Imm)
Figure 5-9: Range distribution for each source. Top left: 110121. Top right: A80333,
Bottom left: 100534, Bottom right: 100439.
122
30-
500-1
21
10
n
X
1191 to Ct-wget
Rtio [A
100
j183
10D0
400-
"D
10
20
30
40
s0o0 70
80
11914 to ChSWg R85io £AD4V)
11
10
20
30
40
0
60
UL" W Clwgo RAWi
70
W0
IADUOMV)
Figure 5-10: Ratio of the gain-map-corrected CCD energy to anode peak voltage for
each source. This gives an approximate CCD energy scale, though at a very different
scale than for WIMP-induced nuclear recoils.
The mean and width of these distributions for each camera are given in Table 5.6.
The approximate energy calibrations for the cameras are slightly lower than the values
measured with a more complete analysis in [95].' The numbers are not expected to
be exactly equal, as this measurement uses a different gain map and does not attempt
to perform the full calibration procedure. The energies of such long tracks may also
be estimated from the reconstructed track range. Tabulated data from SRIM [119]
predicts that a particles with the measured ranges have energies of approximately
3.7 MeV, slightly lower than the energy from the anode measurement. Because the
range calculation was tuned for low energy nuclear recoils, it is likely that it is slightly
underestimating the ranges by missing pixels in the low stopping power regions at
the ends of tracks. Even so, the charge calibration obtains ~ 5% agreement with the
energies extrapolated from the range despite the two order of magnitude difference
in energy between the calibration and the a particles.
A mature PMT analysis is not yet implemented for nuclear recoil runs, but the
large signals of a particles are useful for beginning to analyze signals from the PMT
3
Note that camera A80334 in [95] has been replaced here by 100439. A80334 was found to have
a nonlinear light to ADU conversion.
123
Camera
110121
A80333
100534
100439
Range (±a)
11.75 ± 0.62 cm
11.55 ± 0.60 cm
11.44 ± 0.79 cm
10.89 ± 0.73 cm
EA..de(+U)
3.74 ± 0.22
3.81 ± 0.20
3.94 ± 0.18
3.88 ± 0.18
MeV
MeV
MeV
MeV
Approx. Calib. (±a)
17.94 ± 0.76 ADU/keVee
16.40 ± 0.79 ADU/keVee
17.89 ± 0.80 ADU/keV.e
15.74 ± 0.62 ADU/keVee
Table 5.6: Summary of reconstructed 241 Am a properties for the source imaged by
each camera. a here represents the 1-a width of the distribution.
- 1rtr400
MTery
-MT P0T0a
sur
Pd
s
a700
-n
PThh
t
300400
2007
300
100
200
-W0-18.-18-14 -12-10 -8
1400
-s
e
r
d
----
-6
-4
-2
Pulse
0
018
614
itagrs
21
8
-4
Pute 84t8
ta
0
ight
yedf
m
b0pe
PMT1
2PMT2
i00
11000-
PMT
100
407
400energy10
200
reouin
-_1 -165
-14
-12
-10.8-a
-4
-2
0
Pu.. kft1. ob,
1 .V1s1
-18
-16 -14-.12-.10.8
-a
-4.
Ps
61Ib
slou
]
Figure 5-11: PMT energy distribution for each source. Significant position dependence is seen here, allowing for the positions of some a particles to be distinguished
fromdistributi
others. PMT
1 has
i
00
the other two but has a better
T a significantly
h
oremaue
PMT lower gain
----than
Ioyechcmr.Srrsnlee
energy resolution.
channels. The integral of a PMT pulse is proportional to the total light yield from
the event, so the integrals give an additional energy measurement. As with CCDs,
the measured light, yield can be position dependent. Figure 5-11 shows the energy
distributions in each PMT for the source measured by each camera.. Surprisingly, even
with three PMTs placed very close together at the center of the anode, significant,
spatial dependence is seein. The sources in cameras A80333 and 100534 can be clearly
distinguished fromn the other sources using the relative sizes of the three PMT signals.
It is also clear that, while PMTs 0 and 2 have a, similar gain, the gain of PMT 1 is
much
lower. PMT 1 however, has the best resolution.
124
5.5
Directional Reconstruction
The principal motivation for using low pressure gas detectors for dark matter searches
is to utilize the ability to reconstruct the directions of nuclear recoils. Ideally, a calibration of the directional reconstruction would yield the direction resolution as a
function of energy and recoil direction. Much of the recent thesis by Shawn Henderson [95] focuses on the extraction of directional information from fast neutron data.
While fast neutrons are the most effective way of generating nuclear recoils inside the
detector, interpreting such data can be quite challenging. Shielding and even detector
materials are not transparent to fast neutrons, and can significantly alter the energy
and direction (listribution nuclear recoils. A 100 keV fluorine recoil generated from a
4 MeV neutron
typical of many fast neutron sources such as AmBe
is scattered at
a nearly 700 angle with respect to the neutron's direction. Even a monoenergetic Linidirectional source of neutrons is incapable of generating nuclear recoils with a narrow
distribution of angles.
Alpha-emitting sources provide an alternative path to evaluating detector performance while avoiding
or at least minimizing
many of the challenges of neutron
data. A collimated a source is easily constructed and provides a much more strongly
directional signal than is possible with a neutron source. Alpha tracks have longer
ranges and somewhat less straggling than nuclear recoils of the same energy and also
lose most of their energy due to electronic processes. As a result,
data will generally
yield better results than could be expected for nuclear recoils. However, by reducing
many of the effects that degrade the directional signal in neutron data, a data allows
for a much more straightforward evaluation of reconstruction algorithms.
To study the directional reconstruction capabilities of the 4-shooter prototype. a
collimated I pCi
2"Am
source is used to create a tracks in the detector. The
21Am
is held within a metal casing with a thin gold foil allowing o particles out of the souce
without losing too much energy. The source is placed within an acrylic collimator,
resulting in a nearly unidirectional source of a particles with ~ 4 MeV of energy. The
collimated source is affixed to an acetal threaded rod and placed above the cathode
125
241AM &
Collimator
Support
Post
Cathode
n
Alpha Path .....-
Field Shaping Ring
Figure 5-12: Schematic of the experimental setup for directional studies with an a
source. Only a small fraction of the a crosses the cathode into the active region,
leaving a well-collimated distribution of low energy a tracks. Not to scale.
mesh. The source assembly is held in place by the field cage support posts.
The source was then positioned so that a particles leaving the collimator would
enter the active volume through the cathode at an approximately 100 angle between
the readout plane and the drift direction. The height above the cathode was chosen
so that the a particles would appear in the central region of one of the cameras
(A80333) and so that only a small fraction of the track would be measured by the
detector. The digitizers were set to measure tracks with energies between 50 and
440 keVee. A diagram of the source placement in the detector is provided in Figure
5-12. The electrons from ionization drift across the full drift length of the field cage,
so the tracks display the maximum amount of diffusion seen in the 4-shooter. As a
result, these tracks are much lower quality than average, and represent a worst-case
scenario for low-energy a reconstruction. The two-dimensional direction of the tracks
as viewed by the cameras can be changed in increments of 10' by rotating the top
section of the vacuum vessel (which holds the cameras). Data sets were taken at four
such rotations: (1) the usual rotation, (2) -10' from usual. (3)
(4) +20' from usual.
126
+10
from usual, and
50 -- ----
-
-
-
-
a Agle: 25 deg
--.
A.ge:4.-deg-
-
--
30
-
a Agge: 5 deg
--
+ -
- - + ---
-
-
CN
20
10
-
-
-
-
-
.-
- -
0
0
50
100
-
150
250
200
300
350
400
EAnode [keV
]
Figure 5-13: The mean value of the reconstructed two-dimensional axis as a function
of energy for a source at different angles with respect to the camera axes. The error
bars here are the 1-u- error on the mean value.
Mean Track Axis
Measured Rotation
± 0.130
± 0.160
-10.140 ± 0.210
100
15.340 i 0.140
20~
25.17~ ± 0.150
± 0.210
19.800 ± 0.220
Rotation Angle
-
4.770
0
5.370
N/A
9.970
Table 5.7: The average track angle for energies between 50 and 440 keVee for a source
at several different angles with respect to the camera axes. The change in measured
track direction between each data set is consistent with the known amount that the
cameras were rotated with respect to the source.
The accuracy of the reconstruction algorithm is evaluated by comparing the measured rotation angles to the known angles. The axial directions of the tracks are
histogrammed into 20 keVee bins up to 440 keV. Figure 5-13 shows the mean direction in each energy bin for all four data sets. Above 60 keVee, the mean angle in each
bin varies by no more than a few degrees from the mean. Table 5.7 shows the overall
mean angle between 50 and 440 keVee for the four data sets. The measured rotation
angles from the standard rotation for the three rotated data sets are all consistent
with the known values t~o within lc. Any overall bias in the reconstruction algorithm
is less than 10.
Because the track axis and the sense of motion along the axis are calculated
127
9;0
9_0
5
135
ISO
13
'0
226
45
i
11I5
0
22i
A5
135
i 1
1SO
115
22
0ZI
315
270
270
270
(a) 50 to 70 keVee.
(b) 100 to 120 keVee.
(c) 200 to 250 keVee.
Figure 5-14: Example angular distributions of low energy a events in different energy
ranges.
separately, the axial and sense reconstructions are considered separately.
Several
example angular distributions are shown in Figure 5-14.
The axial resolution is estimated from the angular spread of track angles in each
energy bin (Fig. 5-15). If f(01Emin, Emax) is the angular distribution of events with
energies in the range [Emili, Emax), the axial distribution is
f(|Emin, Ema) = f (OIEmin, Emax) + f (0 + nrjE 1 in, Emax).
(5.4)
Given the axial distribution and a mean axial direction Oa, the spread s is the angled
defined by
0.683
=
Jf(Enjin,
Ena)d.
(5.5)
Due to the periodicity of angles, Gaussian statistics are often not appropriate for
angular data, so this provides an alternative way to describe the width of the distri-
bution than the usual standard deviation. With this definition of spread, a uniform
distribution (no axial information) will have a spread of 61.50.
At 50 keVee, the 68% spread is 35%, showing that even at the lowest energies studied here, the axial reconstruction provides useful information. The spread quickly falls
to approximately 14' at 100 keVee and 90 at 200 keVee, Even at 400 keVe,
where
the axial reconstruction should be very precise, the angular spread is approximately
128
0
b
,D 40
Q.
---
-
-
S30-
- aAngle: 5 deg
ccAn91e 25 dea
--
-
25
20
C15
O ~~
1
-
-
--
-
--
-
--
-
.. . ....
..
.......... ..
............
..-..
.
-
-
- -
105-
0
50
100
150
200
250
300
350
400
EAnode [keV ee]
Figure 5-15: The half-width of the band around the mean containing 68% of events.
This is roughly equivalent to the 1-- width of a Gaussian-distributed variable.
60. However, simulations of a particles in CF 4 gas with TRIM show that the measured distribution widths are generally comparable to the expected broadening from
straggling at energies greater than 100 keVee. Even 50 keV, the expected width from
straggling is 220, so a substantial fraction of the width at all energies is due just to
straggling. The widths of the distributions provide a very conservative estimate of the
detector angular resolution for low-energy a particles. There is also little difference
between the different data sets4 , showing that the angle of the track with respect to
the camera axes does have much of an effect on the axial reconstruction.
Finally, the head-tail discrimination is estimated by determining the fraction of
events with an angle ( such that
-
01 < 90 . 0 describes the mean axis with
the known sense of motion added to obtain a vector angle. As a function of energy
(Figure 5-16), little head-tail discrimination is seen below 60 keVee. By 100 keVee,
the head-tail effect is accurately reconstructed for approximately 70% of events. This
increases to 85% at 150 keVee and over 90% at 200 keVee.
4
The 250 data set seems to show a slightly better resolution at low energy, but the difference is
only a few degrees.
129
F-
- -.- .6 0.9 - .......
-....
-..........
.......
<08
0 0.6
- -....
...-...
............. - -------
30.4-2
-+
-............ .. ...... . . ..
0
50
100
150
-.... - -..- --..............
OAngle: 5 de
Angd: 25 deg
..
.,...,
..
,. .. 1 .
200
250
300
. 1 .
.
350
400
EAnode [keV ee
Figure 5-16: Fraction of events where the head-tail effect was used to correctly determine the sense of motion along the recoil axis as a function of energy. The error
bars here represent 95% confidence bands based on binomial statistics.
130
Chapter 6
Characterization of Background
Events
Understanding and removing background events is of utmost importance to lowbackground experiments such as dark matter searches. In the context of the DMTPC
4-shooter detector. there are physics backgrounds, from ionization left in the chainber, and detector readout backgrounds, mostly from various features seen in CCD
images not related to ionization in the gas. Section 6.3 describes the detector readout
backgrounds.
I will divide physics backgrounds into three basic types.
1. Many types of events, such as electrons and minimum-ionizing particles leave
low-density ionization trails due to their low stopping power.
These are de-
scribed in @6.1.
2. Alpha particles have high stopping power, similar to nuclear recoils, but typically have higher energies than recoils from WIMP dark matter.
These are
described in §6.2.
3. Nuclear recoils and nuclear recoil-like events are the most problematic type
of background, as these are also the standard signal of VIMP dark matter.
The selection of nuclear recoil and nuclear-recoil-like events requires a much
more substantive discussion than the others and is the subject of the following
chapter.
131
6.1
Electrons and MIPs
In DMTPC detectors, electrons are characterized by their low stopping powers, leading to tracks with high ranges but little total energy loss. They can be directly created
in the detector by 13 decay, which leads to a broad spectrum of electron energies up to
some endpoint energy. Electron recoils are also common and are often created from
interactions of photons with the target gas. At photon energies below approximately
33 keV, photoelectric absorption, where the photon transfers all its energy to an electron, is the most probable recoil process. Above this energy, Compton scattering is
the most important process, creating recoils with energies up to the Compton edge
of E,
- 2E /(me + 2EI)[112].
1
Similarly to electrons, high energy charged particles also leave tracks with a low
ionization density. These are most commonly found as remnants of air showers from
cosmic rays interacting high in the atmosphere.
By far the most common type of
these Particles will be muons, which are created in large numbers from the decays of
charged pions and other unstable hadrons in cosmic ray air showers. Because of their
relatively small mass (106 MeV) and long lifetime (2.2 jys), a large fraction of muons
created in the atmosphere have enough energy to reach the surface before decaying.
Reference [120] provides a good introduction to the properties of cosmic rays relevant
to a DMTPC run at the surface. Above 1 GeV, the energy spectrum is steeply falling,
resulting in an average muon energy of around 4 GeV. The 4-shooter laboratory at
MIT is located on the ground floor of a one-floor section of a building, and the
detector has no shielding other than the wall of the vacmin chamber.
This is not
enough material to stop the vast majority of cosmic ray mons, so the rate measured
by the 4-shooter will be similar to the rate measured by a completely unshielded
detector. Using the connon rule-of-thumb muon flux of 1 per square centimeter per
minute with a cos2
angular distribution, as suggested by [120], we would generally
expect the 4-shooter to measure a muon rate of approximately 25 Hz. Muons with
Above approximately I MeV. c,+cpair production is also possible, and this becomes the dominant energy loss mechanism for MeV and higher scale energies. These types of events, leading to
electromagnetic showers, should be quite rare in a dark matter search.
132
energies of 300 MeV and greater are minimum ionizing particles (MIPs), losing only
a tiny fraction of their energy in the gas of the detector and ionizing the gas with a
constant stopping power of approximately 2 MeV/(g/cm 2). Muons are not the only
particles from cosmic rays that reach the surface. The proton flux is ~1(% of the
muon flux while smaller but still measurable numbers of electrons and positrons are
expected as well [120].
Because electrons and high energy charged particles have such low stopping powers, they are very rarely seen in CCD readout. Too few photons interact in any individual pixel to see such signals above the background noise of the usual CCDs used
by the DMTPC collaboration. As a result, background electrons, MIPs., and other
low stopping power particles have not been studied in detail with earlier DMTPC
detectors. With the ability to reliably trigger on ionization events with as little as
1 keVec, of deposited energy, the 4-shooter provides an excellent opportunity to begin
to study and understand these classes of events in DMTPC detectors.
To better understand what types of backgrounds are seen, it is useful to see how
the rate and energy loss spectrum vary with target density. Different backgrounds
will change in different ways. For example, the rate of MIPs will remain constant as
it depends on the detector geometry, but the energy depositions are proportional to
the density. Similarly. 3 decays occurring in solid materials in the detector will occur
with the same rate, although the spectrum may change due to partially-contained
events. The rates of recoils due to neutral particles such as -- rays and neutrons are
proportional to the target density, as is the rate of 3 decays from impurities in the gas.
To measure the energy spectrum of electrons and MIPs, charge-readout-only data was
taken with 45, 60, and 75 torr CF4 using the same amplifier and trigger setup as for
the "Fe energy measurement. Because the digitizers only use an 8-bit encoding, data
sets at different digitizer voltage settings were combined to obtain a single spectrum
covering energies from approximately I keV,. to several hundred keV((.
To trigger
at different energies. the gain of the Ortec 575A spectroscopy amplifier was changed.
with runs at gains of 50. 25, 10. and 5. The 45 and 60 torr data used only the Cr-
112 preamplifier. while the highest-energy data set at 75 torr required the use of the
133
---- 45 Torr
2
60 Torr
~
24
0
75 Thrr
4-
5
10
15
20
25
30
35
40
45
50
Energy (keV.]
Figure 6-1: The background energy spectra between 0 and 50 keVee at 45, 60, and
75 torr. The primary feature of each spectrum is a prominent peak between 5 and
15 keVee.
Cr-113 preamplifier. The data in each set is normalized by the total live time after
removing events near sparks. After normalization, all the data at each pressure is
placed into a histogram, with the bins normalized by the total live time of the data
sets measuring that energy and by the bin width, which is variable to accommodate
the ADC binning of the digitizer. The spectrum is then reported as a rate in events
per unit time per unit energy.
At energies below 50 keVe,
the resulting spectra (Figure 6-1) look quite simi-
lar. The most striking feature in each spectrum is a prominent peak between 5 and
15 keVee. As the pressure increases, its energy increases. The peak width increases
with pressure as well, but the peak's maximum rate decreases at the same time. At
lower energies than the peak, the rate remains relatively constant. At very low en-
ergies, the rate increases somewhat at 60 torr, but a dramatic increase is seen at 75
torr. This occurs at approximately 1 keVee, near the low energy threshold of the
data sets. At energies greater than the peak energy, the rate quickly decreases as the
energy increases. Unfortunately, the peak energy is too low for the mesh pulses to be
faithfully reconstructed with the standard algorithms, so the mesh data is of limited
use in characterizing the pulses. While the anode pulse shape contains much more
134
3r
~2.2
25.
0200
2.8
0150
1.6
1.000r
-
1.2
2
84
1
12
14
1
1
50
Energy [eV,]
Figure 6-2: A histogram of the anode pulse rise time versus energy deposited for a
60 torr data set. The feature at high rise times (high Az) is what leads to the peaks
in the energy spectra.
limited information than is held in the mesh pulse, the rising edge of the pulse is still
useful at characterizing the event geometry. A two-dimensional histogram of pulse
energies and rise times at 60 torr (Figure 6-2) shows that the peak is associated with
high rise time
-~and
thus high Az -events.
By selecting events with a rise time greater than 1.8 pis, the peak at each pressure
can be separated from the other events (Figure 6-3). These events will largely consist
of charged particles traversing most of the drift volume. Fitting a Gaussian to the
region near the peak to determine the approximate peak energy and height results
in the values in Table 6.1. Notably, the energies scale approximately linearly with
pressure while the peak heights (reported in events per unit time per unit energy)
scale approximately with inverse pressure. This is the expected signature of particles
with constant (dE/d(px)), where p is the target density. Minimum-ionizing particles
are one example of such particles. A fast simulation using Geant4 shows that the
energy is consistent with what is expected of MIPs traveling nearly vertically through
the field cage. Furthermore, the leveling off of the spectrum of all events below the
peak energy can be understood as a geometric effect of MIPs passing through only a
fraction of the field cage.
135
45 Torr
60 Torr
2
*
75:Torr
4
1.5
0 %i
I
*
1
0.5
-A
%
4
5
A
10
15
20
25
30
Energy [keV.]
Figure 6-3: The peaks in data sets at 45, 60, and 75 torr after selecting events where
the 10% to 90% rise time of the anode pulse is greater than 1.8 ys.
Pressure [torr]
45
60
75
Peak Energy [keVee]
6.85 ± 0.02
9.39 ± 0.04
12.13 ± 0.05
Peak Height [keV;- s-1]
2.13 ± 0.01
1.54 ± 0.01
1.275 ± 0.009
Table 6.1: Peak mean and height from a Gaussian fit to the region near the peak in
the three spectra from Figure 6-3.
136
Low-energy and high-rise-time spectra consistent with a constant flux of nearvertical MIPs of order 25 Hz are highly suggestive of the expected signal from cosmic
ray muons. However, the presence of MIPs in the detector does not prove that these
are cosmic rays. Because of the small size of the detector, electrons with several MeV
of energy will also effectively be MIPs. so internal backgrounds such as J3 decays with
high endpoint energies could potentially lead to such a signal.
To determine if the detector is in fact measuring cosmic ray events a dedicated
muon run was taken using the setup diagrammed in Figure 6-4. One small scintillator
paddle read out by a PMT was held above the detector, while an identical scintillator
paddle was placed on the laboratory floor directly below the detector. The output of
each PMT was fed into a discriminator and the logic pulses from the discriminator
were then fed into a multichannel coincidence module acting as an AND gate. The
coincidence output was used to trigger the digitizers via the external trigger input of
the master digitizer. Other than the external trigger operation, the data, acquisition
process was identical to standard runs using CCD and charge information.
This
trigger setup is designed to save data, only when near-vertical muons or other highenergy charged particles pass through both paddles. The coincidence setup eliminates
backgrounds from effects such as internal radiation in the paddles, light leaks, or dark
noise in the PMTs. A charged particle depositing energy in both paddles will typically
also deposit energy in the TPC. The corresponding charge signal will appear no more
than 3 ps after the trigger.
Due to time constraints using some of the equipment required for the coincidence
trigger, only a short run at 75 torr using the Cr-113 preamplifier could be taken.
Although the trigger setup was found to be somewhat unreliable, the data recorded
was sufficient to obtain a preliminary energy spectrum (Figure 6-5).
Most of the
resulting events were contained in a peak between 10 and 15 keV,, confirming our
suspicion that at least some of the events in the peaks found in 6-3 are due to cosmic
ray imions.
There is also a population of events with much higher energies than
are expected from MIPs. with some energy depositions reaching well over 100 keV,,.
This high energy loss population is a signature of non-MIP events, such as muons with
137
Scint. Paddle
PMT
Discriminator
Digitizer
Vi
D cVbias
Detector
-
-----
-
F
Vthreshold
Coincidence
Ext.
Trig.
--------------------------------- Ch.A
Readout Channels
--------------------------------- Ch. B
-
Scint. Paddle
PMT
Discriminator
Vbias
Vthreshold
Figure 6-4: Schematic of the setup looking for ionization events in the detector coincident with hits in two scintillator panels. Channels A and B are the two readout
channels of the digitizer used for triggering.
energies of order 100 MeV or less. These are cosmic ray events that have been mostly
stopped prior to reaching the detector. While none of these has a corresponding track
seen in CCD data, such high energy charge triggers appear within the energy range
of interest for nuclear recoils and are potentially a source of backgrounds in a WIMP
search at the surface.
In addition to the MIP peak near 10 keVee, the background energy spectra display
several more prominent features. At higher energies than the peak, the spectrum is
a.
power law with ;
oc E-".
A prominent knee appears in each spectrum at,
approximately 60 to 100 keVee, with a steeper power law spectrum (A
oc E-)
extending up to 150 keVee or so. At this point, an ankle appears in the spectra,
which continue to decrease at a slower rate at higher energies.
Once again, this
spectral shape can be qualitatively understood using the Geant4 simulation package.
Electrons with energies higher than approximately 60 keVe, are typically not fully
contained within the active volume.2
2
Few electrons will deposit more energy than
The exact value will depend on the pressure and the positions at which electrons enter the drift
138
E
Z
20-
15
10-
5-
06
20
40
60
80
100
120
Energy Deposited [keV.n
Figure 6-5: The energy spectrum measured by the anode of ionization events in 75
torr CF 4 triggered by simultaneous hits in the two scintillator panels. The peak in this
spectrum matches the peak seen in the overall background spectrum. Some events
depositing much more energy than minimum ionizing particles are seen as well.
this, regardless of their initial energy. This effect creates a knee in the spectrum.
The typical energy deposition from electrons will decrease as the energy increases
from the knee. In fact, a broad spectrum of electron energies such as from /-decays
or Compton scattering can lead to a power-law-like spectrum with a knee where
electrons range out in the detector. The ankle likely occurs where other types of
events, such as a decays, nuclear recoils, and high energy cosmic ray events are the
dominant contributors to the spectrum.
The total rate of events with energies up to 200 keVe as a function of energy
threshold is shown in Figure 6-7. The total event rate between 2 and 200 keVe is
51.4 Hz at 45 torr, 53.0 Hz at 60 torr, and 55.2 Hz at 75 torr. Because the rate
increases by only 7% with an increase in target mass of 67%, we can determine
that the most common background events are from charged particles such as muons
or electrons from
/
decays entering the active volume. The rates of these classes of
events will stay approximately constant as the target mass increases. Neutral particles
such as photons and neutrons with mean free paths much larger than the size of the
volume.
139
-2
10-
-.-.
10-
45 Tdrr
60 Tdrr::
75 Torr
10
JLL
1
I
J
L
10
L..L..
102 Energy [keV.J
Figure 6-6: The energy spectrum between 1 and 350 keVee for 45, 60, and 75 torr
CF 4 . The spectrum above the peak is a power law, with a prominent knee between
60 and 100 keVe and a less-prominent ankle around 150 to 200 keVee.
Pressure
45 torr
60 torr
75 torr
50 Hz
2.36
3.06
4.13
10 Hz
16.3
21.5
26.8
1 Hz
52.9
64.7
76.5
100 mHz
84.9
104
120
10 mHz
134
158
172
Table 6.2: Energy thresholds in keVee required to achieve the given background rates
of events up to 200 keVee at 45, 60, and 75 torr CF 4 . These results apply in a surface
lab with no shielding or vetoing to reduce backgrounds such as cosmic ray events.
detector will lead to recoil event rates proportional to the target mass, and are likely
associated with the slight increase in event rate with pressure. The trigger threshold
required to achieve a given rate of background events is shown in Table 6.2.
6.2
Alpha Backgrounds
At higher energies, the principal type of background events expected to be measured
are a decays. Because a particles cannot penetrate through walls of the vacuum
chamber, their presence in the detector is indicative of contamination in detector
materials. The decay chains of the naturally-occurring isotopes
23 8 U, 2 35 U,
and
23 2Th
include many a-emitting radioisotopes. Contamination at the surfaces of materials
in contact with the target gas can cause a particles to appear in the active volume.
140
E
-
10
10
102
20
40
60
80
100
120 140 160 180 200
Energy Threshold [keVJ
Figure 6-7: Total rate of events between the energy threshold and 200 keVee at 45
torr (green), 60 torr (red), and 75 torr (blue).
Furthermore,
22 2 Rn
is a gas with a half-life of 3.8 days [121], allowing it to persist
inside the detector for some time even if no additional radon is added. While
contamination is a source of
22 2
23 8U
Rn, it can also be introduced into the detector from
22 2
the environment or from contamination in the gas system. Most a-emitting
Rn
daughter nuclei quickly decay within minutes of the initial radon decay. Polonium210, however, has a half-life of 138 days
[122],
so even past radon exposure can lead
to long-lasting a backgrounds from polonium, which will appear at the surfaces of
solid detector materials.
Section 6.2.1 gives an overview of the a data and the overall a event rate. Section
6.2.2 discusses the energy, range, and position distributions of the measured a particles, while Section 6.2.3 discusses measurements of several decays in the
2 32
23 5
U and
Th decay chains that~ can be identified through their distinctive timing signatures.
6.2.1
Alpha Data and Analysis
A series of (dedicated a runs were taken with 60 torr CF 4 to study these background
events. Charge, CCD, and PMT data was taken with an exposure time of 8 seconds
to improve the duty cycle compared to most runs. The anode voltage was lowered to
650 V to reduce the spark rate and to prevent sparks from occurring in regions with
141
a very high ionization density. After removing events near sparks, 28 740 exposures
- or 2.66 live days split over three gas fills - were used in the analysis.
Because most runs using 60 torr CF 4 are operated with an anode voltage of 670
V, the energy scale at 650 V has not been as extensively studied. An anode energy
calibration of 0.298 mV/keVec may be extrapolated from the values in Table 5.1,
and matching the spectrum to the background spectrum in 60 torr described in §6.1
shows that this calibration should be accurate to within a few percent. The energies
of a decays are not as well determined by the charge measurements as for the x-ray
calibration sources, nuclear recoils, or event a calibration sources. Alpha particles
from a decays typically cross over a large fraction of the readout plane3 , passing over
features such as the spacers used to separate the mesh from the anode. The spacers
create "dead" regions with no gain, so some small fraction of the signal is lost. In
general, we might expect typical a particles to leave signals 5-10% smaller than the
value expected from the calibration.
Additionally, a particles with large Az may
also leave signals a few percent smaller than expected due to the decay time of the
integrating preamplifiers.
Because many a particles cross between the different cameras. image stitching
routines are used to generate a single seamless image from the four CCDs. Cluster
finding on these stitched images allows for the position, angle, and projected twodimensional range to be determined. PMT data is useful in determining the projected
vertical range of the tracks. After smoothing the tracks with a a = 5 bin (20 ns) filter,
the mean 10% rise time to 10% fall time width of the three pulses is used to estimate
Az. The smoothing reduces large fluctuations often found in the PMT signals so
that the reconstructed pulse parameters more accurately reflect the true pulse width.
Friom the estimated electron drift, properties, the projected vertical range of the tracks
are given by Az ~ (11.2 cm/ps)AT, where AT is the pulse width. The energy may
also be extrapolated from the three-dimensional range. While the range is not as
precisely determined as the measured energy, the range does not suffer from loss of
signal due to the a passing over regions with low or no gain.
35 MeV
a particles will have typical ranges of 14. 17.5. and 23.3 cm in 45, 60, and 75 torr CF 4 .
142
At an energy threshold of 250 mV (840 keVee), a total of 2278 charge triggers
are seen.
There are 1 993 events with a single charge trigger, 135 events with two
triggers, and 5 events with three triggers.
Not all of these triggers appear to be
from o particles, and in some cases only very faint CCD tracks or even no tracks at
all are seen. There are 1824 events having single charge trigger and a single a-like
CCD track. 4 Based on Poisson statistics. the rate of a decays leaving greater than
840 keV,, in the detector is 8.8±0.2 mHz.
Only 67 events with two a decays are
expected, so 68±8 of the double-o events are likely to be from processes other than
random uncorrelated a decays. The a rate remained constant throughout the data
taking period.
6.2.2
Range, Energy, and Position Reconstruction
Because the CCD analysis is designed to search for small nuclear recoils in relatively
clean images, only single-a events are likely to be properly reconstructed. Alternative
methods will be needed to analyze the two-a events, while there are too few three-a
to obtain much information with any reasonable statistical uncertainty.
In CF 4 . the Bragg peak for a particles occurs at approximately 800 keV, so for
energies greater than approximately 2 MeV, the Bragg peak occurs toward the end
of the track [119].
Using this fact to distinguish the start and end of tracks, the
initial positions of o, decays may be determined. In particular, it is useful to classify
events in terms of their positions with respect to the field cage rings. In this section,
a distance of 870 or more pixels from the center of the anode will be defined as "near
the field cage." The outer radius of the central anode channel is 910 pixels, so this
is a fairly broad definition of edge events. Table 6.3 shows the number of a tracks
organized by the position of the start and end position with respect to the field cage.
While a large fraction of o tracks will be expected start or end at the field cage due
to the large energies and long ranges of most, a particles, it is striking that more than
50%/ of events are reconstructed as starting near the field cage while less than 20%
4 Defined
as having a range greater than 100 pixels. a CCD energy greater than -1 000 ADU. and
a maxiinnin pixel valie less than 1000.
143
Starts Near Edge
No
Yes
No
Yes
Ends Near Edge
No
No
Yes
Yes
Number
184
1036
308
296
Table 6.3: Number of tracks in single-a events with start and end positions having
the given relationship with respect to the field cage rings. Positions greater than 870
pixels (14 cm) from the center of the anode are defined as being near the edge of the
drift volume.
are reconstructing as ending there. This suggests that the field cage is a major source
of a backgrounds.
Starting with the hypothesis that the position with respect to the field cage is an
important metric to classify events, we may consider various reconstructed track parameters. Figure 6-8 shows the range as a function of reconstructed energy for events
starting near the field cage rings and for all events.
Even in the two-dimensional
(CCD only) reconstruction, a band of events with ranges near the SRIM prediction is measured, although many events have much smaller ranges than would be
expected.
By adding the PMT analysis and reconstructing an approximate three-
dimensional range, there is much less spread in reconstruction range compared to the
reconstructed energy. This shows that the Az reconstruction is obtaining results that
are approximately correct. In the 3D range reconstruction, the extrapolated energy
from the reconstructed range is generally somewhat larger than the reconstructed
anode energy. This is as expected due to the aforementioned issues with the a anode
signals. Much more spread is seen when all events are considered rather than just
ones originating near the field cage. This suggests that the events not originating
at. the field cage rings are primarily only partially contained within the detector, so
the reconstructed range will be longer than would be expected for an a losing all its
energy in the active volume. The favorable agreement of well-contained edge events
with SRIM predictions compared to other events bolsters the case that these events
are in fact associated with decays at the field cage.
If a decays are occurring on the field cage. then information about any sites with
144
-30
I
I
, I
25
25
0
N02
20
15
10
ill
5
~O
2 1
3
6
.
4
Energy MeV
&
1
1
2
3
-
4
5
6[
Energy IMeV]1
25
20
15
10
IN,
5
-'0
Figure 6-8:
1
2
3
5
Range versus energy for a events.
6 [
Energy (MaVJ
The top plots include only events
originating near the field cage and ending in the central region of the detector, while
the bottom plot includes all events. Top left: Two-dimensional range as measured
by the CCDs. Top right: Three-dimensional range determined from the CCD range
and the mean width of the three PMT pulses. Bottom: Three-dimensional range for
all events. The red curves are the SRIM prediction for the mean three-dimensional a
range.
145
higher contamination may be obtained from the positions on the field cage rings from
which decays appear to occur. Since the field cage is cylindrical, the position is most
easily understood from the angle of the end of the track. Considering only tracks with
a high (> 800 pixels) two-dimensional length with one but not both ends reaching
the edge region, the distribution of start and end points on the field cage is shown
in Figure 6-10.
These requirements help ensure that the tracks are generally fully
contained in the field cage. Rather than being uniform, four clear peaks are seen,
at
±450,
and ±1350. In the detector coordinate system used here, the spacers are
aligned along the 0' axis. High voltage wires connect to the anode and veto channels
at -90', while the outer electrode and mesh are connected to ground at +90.
The
positioning of peaks at values of 45' mod 900 are no accident, however. The four
acetal posts supporting the field cage are placed at those four positions. Additionally,
the cathode high voltage wire is located at -135'. This shows that, both the field cage
and the field cage support structure are significant sources of background a events.
Because there is an excess at all four posts, the source of the a particles at the posts
is likely to be 1) the copper washers between field cage rings 2) the acetal washers
preventing electrical contact between the copper washers and rings or 3) the leads
of the field cage resistors. A diagram of the different, parts attached to the support
posts is given in Figure 6-9
The energy spectra of different classes of events may provide clues about what
types of decays are being measured by the detector. The spectrum of events with
one end near a field cage ring shows a clear peak centered at about 4.6 MeVe, but
extending up to 5 MeVec. Many fewer events are seen at higher energies than at lower
energies. That events are seen at much higher energies tells us that, there are several
decays occurring, as would be expected from the long decay chains of uranium and
thorium, but a single large peak is not necessarily expected. The lower energy events
will be from a. combination of lower energy decays and partially-contained events.
The reconstructed ranges of these events suggests that the true energy is closer to
5 MeVe,, with the difference largely lost due to spacers. However, it is also likely that
this too is an underestimate. Decays occurring at the field cage do not necessarily
146
Support Post
Fie dCage Ring
Acetal Washer
Resistor
Cu Washers
--- m
Acetal Washer
Figure 6-9: Diagram of the different parts associated with the support post. Left is
the outer edge of the rings while right is the active volurne. Both leads of the field
cage resistor are wrapped around the post and connect to the rings. Acetal washers
are placed in between the rings to prevent electrical contact from being made between
the copper washers and the rings.
00
35
-
-
+1+
12520
.......i...
... . . . ..
...............
. ... ........ .....
....
-0
-980
-
-135
-90
135 180
45
90
0
-45
Starting Position on Field Cage Rings [0]
Figure 6-10: The position on the field cage of high-range events originating near the
field-shaping rings. In these coordinates, the field cage support, posts occur at ±45'
and ±1350. The anode and veto connections are at -90'
electrode connects at +900.
147
and the grounded outer
,70_
z
50
-
Energy [MeV
j
Figure 6-11: Energy spectrum of a events with one end occurring near the field cage
rings. A single prominent peak is seen at 4.6 MeVe. Considering that some energy is
lost due to spacers and some is lost before the a particles reach the volume measured
by the central anode channel, these are likely 210Po decays.
occur right at the edge of a ring, so some energy is often lost in inactive regions of
the detector. Furthermore, electrons left near the field cage rings often do not reach
the amplification region due to field nonuniformities at the outside edge of the drift
volume. Because this introduces an expanded inactive region comprising most of the
veto electrode, the CCD tracks typically only trace events to the edge of the central
anode rather than the inner edge of the field cage rings. All this suggests that the
true energy of these events is close to, but slightly larger than, 5 MeVee. This makes
the 5.3 MeV as from polonium-210 [1221 a likely candidate source of these events.
A clear peak is found in the energy spectrum of events where neither end is near
the field cage or where both ends are near the field cage. In this case, the peak is
near 4.9 MeVee (Figure 6-12). Further investigation shows that this peak is primarily
associated with events fully contained within the central region of the detector. These
events also typically have small widths at the start of the track, suggesting that the
source of these events is the amplification mesh and anode. These tracks are found
t~o have a range near 11.7 cm, corresponding to 5.33 MeV. This provides strong
evidence that these, as well as the peak in the edge event spectrum, are from decays
148
z
235
202 5
15
5
0
-
--
4
--
.
.....
-
..........
-
-
-
-
1
2
3
4
5
6
7
Energy [MeVe
Figure 6-12: Energy spectrum of events with either both ends or neither end occurring
near the field cage rings. The peak at 4.9 MeVe is associated with a decays in the
central region of the detector. The ranges of these events are consistent with
decays.
21 0
Po
of polonium-210. The difference in energy is simply because the central events are
fully contained, whereas the edge events lose several hundred keV in inactive regions.
However, this measurement is not definitive, as the PMT readout is not as well
understood as the CCD and charge data. The systematic uncertainties of the PMT
Az reconstruction are poorly understood, leaving room for considerable uncertainty
on the range and energy measurements. Further work will be necessary to understand
the PMT readout well enough to reduce the systematic uncertainties.
The energy spectrum of events starting in the edge region can be further separated
into events near the support posts and events away from the posts. Taking events
within 100 of a support post to be near the posts, the two spectra are plotted in 6-13.
The 4.6 MeVe, peak is seen in both data sets, but an additional peak near 4.1 MeVee
is seen in the data from near the posts. The 4.1 MeVe have measured ranges near
15 cm. Adding an extra ~1 cm to the range to account for energy losses in inactive
regions, these events have true energies near 4.75 MeV. As with the higher energy
peak, the limited energy resolution for long range tracks prevents us from making a
definitive statement as to what the origin of this might be. However, this energy is
149
10 Frm Postss
<100 Friom Posts
50 .
-
~40
-
-
-
-
---
- --
-
E
20
30
00
--
-
-
-
-
-mj
1
2
3
4
5
6
Energy [MeVJ
7
Figure 6-13: Blue line: Energy spectrum of a events originating near the field cage
within 10' of the field cage support posts. Red dotted line: Energy spectrum of a
events originating near the field cage more than 100 from the field cage support posts.
consistent with a number of a-emitting isotopes in the 238U decay chain such as 234u,
230
Th and
of
222Rn,
6.2.3
226
Ra. Contamination of these isotopes will also result in the production
which will then contaminate the gas and surfaces within the detector.
Decay Identification with Timing Information
While in the previous section we have determined several sources of contamination
within the detector but cannot make a definite statement as to what the contamination is, there are several isotopes that can be identified through timing information.
In. particular, isotopes leading to several a decays in quick succession can be identified
by measuring the lifetimes of the intermediate nuclei.
With an exposure time of 8 s, multi-a events allow us to look for isotopes with halflives of several seconds. The digitizer trigger is not arbitrarily fast and the pulses take
several hundred microseconds to return to baseline, so half-lives greater than several
milliseconds may be measured as well.
In the naturally-occurring decay chains of
2 38U, 235U,
and
2 32Th
there are two
types of events in particular that, we may hope to see within a single exposure. The
most easily identified is the decay of
223 Ra.
150
Radium-223 decays to radon-219 via a
emission with a half-life of 11.43 (lays. Radon-219 also undergoes o decay, but with
a half-life of only 3.96 s, short enough to be measured with a fairly high probability
in a single 8 second exposure. The resulting polonium-215 nucleus quickly decays to
lead-211 with a half-life of only 1.8 ms
[123]. The end result is three a particles being
emitted from approximately the same location over an average period of 4 seconds.
The second event type is from decays of
22 0
Rn. This isotope decays to
then decays to 2 "Pb with a half-life of 0.145 s
2 16
Po. which
[124]. Radon-220 events will show two
n tracks, likely stemming from near a common vertex. Because radon is a gas, these
events do not necessarily need to occur at surfaces.
Only a fraction of these events can be identified by the detector, particularly if they
occur at surfaces of solid materials rather than in the gas. For surface contamination,
only approximately 50% of a particles will be emitted in a direction allowing them
to be measured.
For radium-223, we can expect to measure all three a decays in
no more than 12.5% of events. Two of the a particles can be measured in at most
37.5% of events. The short half-life of
2 15
po combined with the long pulse lengths
may result in a reduced trigger efficiency for these events due to pileup. The half life
of 2"Ra
2 'Rn
is about 50% of the exposure time, so in a significant, fraction of events the
decay will occur in a different exposure than the initial
223
Ra decay.
Out of the five events with three high-energy charge signals, one is a clear
223
Rn
decay candidate. The stitched CCD image for this event is shown in 6-14. Only one
of the tracks appears to be fully contained within the detector. The second decay
occurs 1.47 s after the first, while the third occurs 3.20 ins later. consistent with the
lifetimes of
219
Rn and
2
Po. The three a tracks meet at a common vertex within
the central region of the detector. The diffusion near the vertex can be seen to be
quite small. suggesting that this event was from contamination in materials used to
construct the amplification region.
Radon-220 events and radiumn-223 events where one of the a decays is not measured may be tagged using events with two high energy charge triggers. Of the 135
such events. 60 events have a decays appearing to originate near a common vertex.
This number is consistent with our estimate that 67 events are expected from ran-
151
Z1000
x
200
500
150
0
100
50
-500
0
-1000
-1000
-500
0
500
100
5
-5
x [pixel]
Figure 6-14: A candidate 223 Ra -> 2 19 Rn - 2 15po _.> 2 Pb event. The decays occur
with time separations At 1 = 1.47 s and At 2 = 3.20 ms, consistent with what is
expected from the decays 2 19 RPn - 2 1 5 Po and 21 5 po _ 2 1 Pb. The low diffusion
of the tracks near the vertex suggests that this event originates at the amplification
region. The white dashed circle indicates the outer edge of the central anode electrode.
The left-most track appears to be fully contained and can be identified by its much
longer Az. It is the second a and has a measured energy of 6.2 MeVee and a range
corresponding to nearly 7 MeV, consistent with a 2 1 9 Rn decay.
152
dom uncorrelated decays. Figure 6-15 shows the distributions of the time separation
between the two decays for all 135 events and for the 60 event subset of events with
an apparent vertex. Of these 60 events, 55 have a time separation less than 1 s and
50 have a time separation less than 0.5 s. The vertices for each of the five events
with a time separation greater than one second occur near the field cage rings. These
events are likely candidates for a
2 3
Ra decay where either the
219
Rn or
2 15
Po decay is
missing. One event, with a time separation of At = 2.98 s is shown in Figure 6-15. A
fit to the expected distribution from a single decay, f(At) = A (2}
also shown
in Figure 6-15, yields a best-fit half-life for events with At < 0.5 s of 106 ± 27 ins.
While this is consistent with the 145 ms half-life of 2"1 Po, the quality of the fit is limited by the low statistics of the data set. Of the 50 events with At < 0.5 s, 18 have
an apparent vertex position greater than 870 pixels from the center of the anode.
Because the field cage extends to approximately 950 pixels, we would expect that
only 8 ± 2.6 events would occur in this region if the decays were uniformly distributed
throughout the detector. So, the field cage also appears to be a major contributor of
these events. The majority of events, however, fall within the central region of the
detector and have a variety of track widths, so many of the radon-220 decays occur
from radon floating in the gas. Figure 6-17 shows an example event near the edge of
the drift volume and one in the central region.
6.3
CCD Artifact Backgrounds
Various artifacts that can appear in CCD images and be mistakenly reconstructed as
nuclear recoils are extensively discussed in previous DMTPC theses such as
[94] and
[95]. Many of these events can be identified using just. the CCD analysis. and the lack
of a corresponding charge signal from CCD artifacts also allows them to be rejected
using combined CCD and charge data. Here., I provide a brief description of these
events. For a more detailed overview of CCDs, including these sorts of backgrounds.
see Ref. [125].
Pixels with unusually high amounts of light, (termed "hot pixels") often appear
in CCD images.
These can be persistent or transient.
153
Persistently hot pixels are
ICU
18
16
15
II I
I H'ifllTT
I
f
Ill
.4.
.....
14
+.
12
4I4
10
10
!T!
111!
I
111111
....
..
a
6
4
U
2
0
10.F2
10.1
1
0 0. 1
AT 1.1c?
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
AT (sec
1
Figure 6-15: The distribution of the time separation between the a decays in events
with two a-like charge signals. Left: Distribution of all events (blue) and events where
the two a particles originate near a common vertex (red). Right: The distribution of
events near a common vertex (blue) and the best fit to a histogram drawn from the
function f(t) = A (})
.
250
.11
200
150
100
3
1001
x [pixel]
-50
Figure 6-16: Two a decays with a separation in time of At = 2.98 s. These are a
2 11 Pb event
potential candidate 2 23Ra - 219Rn + 2 15 Po
where one of the three
a particles does not enter the active volume. This event, and several others like it,
appears to occur on one of the field cage rings.
154
250
25
2Z1000 -io
1000
200
;,200
500
500
ISO
150
0
-1000
-1000
0
100
50
50
0
0
.0
-500
0
Figure 6-17: Two candidate
500
220
-1000
1000
x [pixel)
Rn
-
100
-1000
-500
0
500
1000
5
x [pixel]
2 16 Po -
2 12 Pb
decay events. These decays
occur with a time separation of 142 ms (left) and 164 ms (right). The decays shown
on the left occur in the active gas volume, while the ones on the right occur near the
field shaping rings.
generally easily identified, as the same pixel is identified as a feature in many images.
Some of these are also identified in the image cleaning process. Transient hot, pixels
may be caused by things such as ionization occurring directly in the CCD chip from
radioactive decays or particles from cosmic ray showers. Such transient events are
typically referred to as "worms" by the DMTPC collaboration. An example of such
an event is shown in Figure 6-18.
Residual bulk images, or RBIs, are another common artifact seen in the Apogee
Alta U6 cameras typically used by the DMTPC collaboration. These features often
appear when a CCD measures a large amount of light, such as from a spark. With
a large amount of light, some ionization can occur the potential wells of the pixels.
Because electrons in the inactive region of the CCD are not removed by reading out
the CCD, these gradually diffuse into the pixels where they can then be removed.
The result is an afterimage of the initial bright event that fades away with time [125].
An example of such an event is shown in 6-19. The strength of the RBI signal is
proportional to the length of the exposure, so these become much more noticeable
when exposures of 5 seconds or more are taken. RBIs often resemble nuclear recoil
155
800
x
-
5000
780
4000
760
3000
740
2000
720
1000
700
220
240
260
280
300 0
x [pixel]
Figure 6-18: An example of a transient hot pixel event. Because this event includes
a number of pixels, it is likely that it is due to a charged particle causing ionization
within the CCD.
156
=900
0
0.
104
>,850
101
102
10
x [pixel]
x [pixel]
Figure 6-19: Left: A spark produces a great deal of light that is imaged by the
CCD. Right: Following the spark, the CCD still measures an afterimage (residual
bulk image) of the spark for some time. This effect becomes more noticeable as the
exposure length increases.
signals and are typically identified because of their constant location across several
events. Rejecting events for some set time after sparks also helps remove many of
the fainter RBIs, as they will have decayed away by the time the events are used for
analysis again.
A final class of CCD background events are events occurring during CCD readout.
When CCDs are read out, the charge in each pixel is shifted from pixel to pixel until
it reaches an amplifier to be digitized.
Because the shutters are not used during
running, the CCDs are still being exposed to light during the readout period. Events
happening during this period may be seen in the images but will be shifted from
their original position. Additionally, depending on when during readout the event
happened, it is possible for only a fraction of the track to appear in the image. This
introduces the possibility that a partial track, such as the end of an a track may be
misidentified as a nuclear recoil. These events are covered in more detail in [94].
157
158
Chapter 7
Searching for WIMPs with
DMTPC 4-shooter Surface Data
There have been several DMTPC WIIP analyses [89, 94] performed with data from
the earlier DMTPC 10L detector using only CCD readout. This chapter describes a
new WIMP analysis using data taken with the 4-shooter prototype during the summer
of 2013. In contrast. to the 10L. the 4-shooter was designed with several readout types
in mind, and the current (as of fall 2013) reconstruction and analysis utilizes both
charge and CCD readout to efficiently identify nuclear recoils. The analysis described
here builds upon previous analysis geared toward background rejection [109] and
neutron reconstruction [95]. It takes a very different approach toward nuclear recoil
identification than the previous WIMP dark matter analyses. Rather than focusing on
t he CCD analysis, where much effort is required to identify CCD-specific backgrounds,
nuclear recoils are largely identified using charge readout information.
The CCDs
provide confirmation that events are in fact nuclear recoils as well as directional
information. The use of charge readout for recoil identification allows for recoils to be
measured with a much higher efficiency than in many previous measurements. This
represents the first major WIMP run with the 4-shooter prototype and the first to
fully leverage the information taken with both charge and CCD readout.
159
7.1
Neutron and WIMP Data
The detector was run at 60 torr CF 4 at I 25'C with an anode bias voltage of 670 V
and a drift bias voltage of -5 kV. Each exposure (or event) was one second in duration.
The mesh, anode, and veto digitizer channels used voltage ranges of 400, 100, and
100 mV, respectively. The PMITs were run at a bias voltage of -925 V, and the PMT
digitizer channels used a range of ±200 mV. The charge and PMT readout were
triggered by the anode channel at a value of 10 mV (13 ADC above baseline) on the
rising edge of a pulse.
In addition to the calibrations described in Chapter 5, neutron calibration data is
used to develop a series of selection criteria to identify nuclear recoils and to estimate
the efficiency of the nuclear recoil identification process. An aiericium-beryllium or AmBe
neutron source emits a fairly broad spectrum of neutrons with energies
up to approximately 11 MeV [126]. Neutrons are created from "Am
a particles via
the 'Be(a, n) reaction. Elastic scattering of AmBe neutrons on CF 4 gas can result in
fluorine recoils with energies up to ~ 2.1 MeV and carbon recoils with energies up to
~ 3.1 MeV. The source, which contains 10 mCi of
24 1
Am and emits approximately
2.6 x 104 neutrons per second, is from a TIoxler Laboratories 3320 Series Depth
Moisture Gauge and is described in more detail in [95].
As in previous running, a
single two-inch thick lead brick is placed in front, of the bore hole in the source housing
to reduce the rate of '}-rays entering the detector. The source is further surrounded
by borated polyethylene except in the direction of the detector to reduce the number
of neutrons emitted away from the source. After removing events near sparks, 232 769
events, or 2.69 live days. of AmBe data was taken.
The WIMP search data consists of a series of runs taken with no sources in the
laboratory.
After spark removal, 595086 events., or 6.89 live days, of source free data is used
in the WIMP analysis.
160
Cut Title
B0
B1
B2
B3
B4
B5
B6
B7
B
Description
-2.14 mV < Mesh Baseline < -0.15 mV
-2 mV < Anode Baseline < 2.8 mV
-0.6 mV < Veto Baseline < 1.4 mV
Mesh RMS < 5.6 mV
Anode RMS < 1.3 mV
Veto RMS < 1.2 mV
Mesh Maximum < 395 mV
Anode Maximum < 99.1 mV
Veto Maximum < 99.1 mV
Table 7.1: List of basic charge quality cuts. Not included are cuts ensuring that pulse
rise and fall time information is properly reconstructed.
Nuclear Recoil Selection
7.2
The nuclear recoil analysis developed using the AmBe data is applied to this source
free data to search for any background or WIMP-induced nuclear recoils. This analysis
initially treats the charge and CCD data separately, building a lists of both charge
triggers and CCD tracks identified as possible nuclear recoil candidates. These are
then comlbined so that a nuclear recoil candidate consists of both a charge trigger and
a CCD track, which are both used for event characterization.
7.2.1
Charge Quality & Nuclear Recoil Selection Cuts
The charge readout analysis starts with a series of basic quality cuts, most of which
are summarized in Table 7.1. These initial cuts are set to ensure that, the waveforms
and pulses are properly reconstructed. These basic cuts include:
Baseline (BO to B 2 ) The baseline voltage of the three charge readout channels
the output voltage when there is no signal in the detector
is quite stable across
the different datasets (Figure 7-1). with typical variations of less than 1 mV.
However,. a small fraction of events has an unusually high voltage. With a total
event, rate of 0(50) Hz and with a typical pulse length of several hundred ps
for the anode and veto channels, we expect that as much as 1% of events could
be affected by pileup from events closely spaced in time. For these events, the
baseline. reconstructed at the beginning of the waveform. does not accurately
161
S..2
i0
7-7-
22'
22'
/
22'
{
7
1
j~tri~~I
/
K
I
Figure 7-1: Histograms of the anode, mesh, and veto channel baseline voltages.
I"
I'
Ie
S4
0
4
042
1
1
1
Figure 7-2: Histograms of the anode, mesh, and veto channel voltage baseline RMS.
describe the baseline immediately before the pulse. These events constitute the
bulk of the events removed by the baseline cut.
Noise (B 3 to B 5 ) The waveform noise, described by the rms of the bins used to
calculate the baseline, is also very stable (Figure 7-2). As with the reconstructed
baseline, the reconstructed noise is sensitive to pileup events. These and any
other events with an unusually large amount of noise are removed by placing a
cut on the maximum allowable noise rms.
Waveform Maximum (B6 to B 8 ) The digitizers are only capable of reconstructing a limited range of voltages.
When the signal from one of the channels
reaches the maximum voltage, it can no longer be certain that the pulse is
properly reconstructed, so such events are removed.
Pulse Rise and Fall Times Finally, the pulses must be well-contained within the
waveform. Because of the long decay time of the anode and veto channels, this
simply requires that the pulse rise time variables are properly reconstructed.
The mesh (current) pulses must be fully contained within the data trace, so all
162
Figure 7-3: Three different mesh pulse rise time variables versus energy using AmBe
neutron data. Left: 25% to 75%. Center: 10% to 90%. Right: 10% to 50%. The
bands extending up to high energy (peak height) are populated by nuclear recoils while
the remaining events represent backgrounds (muons, electrons, etc.). The center and
right plots are after several cuts have been applied so that the signal band is more
obvious.
rise and fall time variables must be properly reconstructed for these pulses in
order to ensure that the start and end of the pulse are found.
Once valid charge events passing the basic cuts are identified, a series of additional
cuts select only the nuclear-recoil-like events. Nuclear recoils are characterized by a
very short range, so the resulting Az gives nuclear recoils very different mesh p~ulse
shapes compared to other classes of events. The cuts are chosen to select tall, narrow
mesh pulses with very fast rising edges
-
the signature of low-Az events. The nuclear
recoil cuts also identify events occurring at the edge of the field cage, where backgrounds such as a decays may be expected. The nuclear recoil cuts are summarized
in Table 7.2 and include
Rise Time (N0 , N3 and N 4 ) Mesh pulses from short Az tracks have a very sharp
rising edge. Several cuts are placed on the duration of the rising edge between
the pulse start time and the initial pulse fast peak (Figure 7-3). The strongest
cuts are placed on the 25% to 75% rise time, with some additional discrimination
power coming from weaker cuts on the 10% to 50% rise time and 10% to 90%
rise time.
Mesh Peak Height (N 1 ) In addition to a fast rising edge, the heights of mesh
pulses of short Az events tend to be considerably larger than those of high Az
163
&.250
10
2ISO!-
I0F
F-.
20
00
50
s
0
s
10
Am%
P*
10
20
(A
30
40
50
60
TO
80
O
00 10
UM Peak (mVJ
Figure 7-4: Left: Anode peak height versus fast peak height of mesh pulse. Right:
Anode peak versus veto peak. In both cases, the signal band is the narrow band
extending to high energies.
events. A linear cut is placed on the two-dimensional space of the mesh fast
peak height versus the anode peak height (energy).
Veto Peak Height (N 2) As events occur closer and closer to the edge of the central
anode electrode, the pulse height of the veto signal as a fraction of the anode
signal increases. Events passing over the veto region are then identified by a cut
on the ratio of the anode peak height to veto channel peak height. This ratio
ranges from approximately VA/Vv ~ 7 at the center of the anode to VA /Vv ; 3
at the edge. For events passing directly over the veto channel, the veto pulse
may even be larger than the anode pulse.
Mesh and Veto Peak Time (N5 ) The peak times of the different channels should
be closely spaced in time. In a very small number of events, several pulses
may be present within a single waveform. If this happens, then pileup effects
could lead to the anode and veto channels measuring an incorrect value. A cut
ensuring that the veto peak occurs close to the mesh peak identifies many of
these events.
7.2.2
CCD Cuts and Charge/Light Matching
Because, as will be seen, the charge readout analysis is successful in reducing nuclear
recoil candidates to within a factor of two from the final number, few selection cuts
164
Cut Title
Noa
Description
Rf - Rf < 13.5 ns if 1/x < 25 mV
Rf - Rfa < 18 us
V[mV] > 2.22 mV + 2.593V74 if 4 < 60 mV
NOb
N1
N2
N3
N.1
I4 > 3.16V
Rfo - Ri* < 40 nis
Rf( - R&, < 18 ns
NTv
- Tf < 1.5 ps
Table 7.2: List of charge A: and fiducial cuts.
on CCD tracks are necessary. These cuts include:
RBI Cut CCD backgrounds such as resi(hal builk images and hot pixels tend to
persist in the same location for several events. Events appearig near the same
location within a given time winlow are idlentified as likely background events
and removed.
Range Because the range algorithm uses only a subset of pixels in calculating the
range, tracks with less than two pixels in that subset are assigned a range of
0. The reconstructe(l range is requlire(d to be nonzero, which ensures that, at
least two pixels in the track are above the higher threshold used for calculating
the range. The reconstructed range is also required to be less than 80 pixels
(13 mm). to ensure that events such as a tracks are not included in the analysis.
Maximum Pixel The peak pixel vahies from events such as persistently hot. (displaying an unusually large output value over several events) pixels and ionization
events in the CCI
tend to be much higher than those from legitimate ionization
events within the gas. The maximum pixel value of candilate CCD tracks is
requiredl to be less than 500 ADU.
Edge The image stitching routines used to combine the images of different cameras
into a single composite image are iot yet fully incorporate(d into the nuclear
recoil analysis.
As a result. CCD tracks reaching the edge of an image are
remove(l. as they likely are not properly reconstructed. However, few tracks at
energies useful for lark matter searches are removed dlue to overlap between the
165
images. A track appearing at the edge of one image is likely to be away from
the edge in the neighboring camera.
Each event contains one image for each camera but also a variable number of
charge triggers. As many as 30 triggers1 may be recorded for each event. The charge
and CCD analyses are used to independently identify nuclear recoil candidate charge
triggers and nuclear recoil candidate CCD tracks.
Once a list of candidate CCD
tracks and charge triggers is obtained for an event, the charge triggers are matched
to their corresponding tracks. This is done by placing a cut on the anode peak height
and gain-map-corrected CCD energy. Using data where only a single CCD track and
a single charge trigger pass all cuts, a best fit curve is obtained for each camera.
Because the curves deviate somewhat from a simple line 2 , a parabolic curve is used.
A symmetric acceptance region around the best fit curve is defined in three energy
regions: 0 to 40 mV, 40 to 60 mV, and 60 to 100 mV. The acceptance region is defined
so that no more than 1% of matching events fail the cut. Plots of the candidate events
in the AmnBe data and the resulting best fit. and acceptance region curves are shown
in Figure 7-5.
In the case that a single charge trigger can be matched to multiple CCD tracks (or
multiple charge triggers to a single CCD track), the closest energy match is chosen. If
multiple charge triggers and multiple CCD tracks pass all cuts, the analysis compares
all permutations of matching charge and CCD candidate event energies.
First, the
permutations containing the greatest, number of passing charge-CCD candidate pairs
are chosen. Second, if multiple such permutations exist, the permutation minimizing
the sum of the squared differences between charge and CCD energies of the passing
tracks is chosen. While this occurs for a small fraction of events in the AmBe data,
events with multiple candidate events are very rare in source free running.
'This number is set in software and can be increased if desired.
An effect introduced from the CCD reconstruction
2
166
I I'll - 11111.1
Camera 110121
t54000
4000
11 ,
1
1 11
1
Camera A80333
4
C
-
3500
00
z
3000:
03000-
2500
2500
2000 -
2000
1500-
1500
1000: -OD
0
-
500-
50010
30
40
50
60
10
90
100
70
80
Anode Energy [mV]
a500
Camera 100534
S4500
E4000
20
20
30
40
50
60
80
90 100
70
Anode Energy [mV]
40
50
60
90 100
70...810
Anode Energy ImVn
Camera 100439
4000 -
-
3500
03500
0 3000
3000
2500 _7
2500
2000:-
2000z
15007-
1500
10
20
30
40
50
60
90
70 80
Anode Energy
[mVI100
"O
10
20
30
Figure 7-5: Scatter plot: Anode peak voltage vs gain-mnap-corrected CCD energy for
each camera. Solid blue line: Parabolic fit. Dashed lines: Limits of acceptance region.
The cuts are chosen to be symmetric around the blue line, with a generous width in
three different energy bins.
167
7.2.3
Position Fiducialization
A final cut defining the fiducial volume of the detector is applied after pairing the
charge and CCD signals. There are two different fiducial cuts applied to data in each
camera:
Radial Cut The centroid of each track is required to be within 900 pixels (14.5 cm)
of the center of the anode.
This cut requires that events be located in the
central region of the anode.
Spacer Cut The track centroids must also be outside a twenty-pixel-wide region
surrounding each spacer.
Recoil candidates at the edge of the anode are much more likely to be from backgrounds such as a decays than events closer to the center, while candidates near
spacers are likely to be poorly reconstructed. The fiducial cuts will be treated here as
a reduction in fiducial mass, as these events tend to be reconstructed and identified
in the analysis. These cuts reduce the fiducial mass by 26%.
7.3
Expected Backgrounds
Neutrons are one of the most, pernicious backgrounds in dark matter searches. They
are able to create actual fluorine and carbon recoils throughout the detector. Because of the small size of DMTPC detectors, nuclear recoils from neutron scattering
events cannot, be distinguished from a WIMP signal on an event-by-event basis. Only
modeling and statistical methods can be used to identify neutron backgrounds, which
limits the sensitivity of the detectors to WIMP interactions.
At the surface, the principal source of neutron backgrounds is likely to be cosmic
rays and products of cosmic ray interactions with materials surrounding the detector.
The energy spectrum of neutrons from thermal energies to greater than 1 GeV has
been studied by a number of researchers (see. for example, [127], [128] and [129]).
The rate of cosmic ray induced neutrons at, sea level was found in [128] to vary
considerably from day to day. Using the spectrum for a typical day from [128).
168
an approximate estimate for the expected number of neutron events in the WIMP
data set is calculated using Geant4.
This estimate does not include the effects of
neutron and charged-particle interactions in detector materials or in the laboratory
and surrounding buildings. For a purely vertical flux of neutrons, around 120 events
are expected in this data set. This number of events, however, is highly dependent
on the angular distribution of events. For a cos 2 0 distribution, the typical rate will
increase to nearly 200 events. Even these are only rough estimates as the rate may
be considerably affected by interactions of neutrons in detector materials or in the
materials used to construct the laboratory and nearby buildings.
Additional fast
neutrons can even be generated by interactions of the various cosmic ray shower
remnants with these materials.
While cosmic rays are likely the most important source of neutron-induced recoils,
fast neutrons can also be created in the laboratory and in the detector due to contamination by heavy radioisotopes such as those found in the
238
u, 235U, and 32Th
decay chains. A small number of neutrons may be created from spontaneous fission,
while interactions of decay products with other nuclei, as in (a. n) reactions, can also
result in fast neutrons. Unlike cosmogenic neutrons, which can have energies well
above 1 GeV, these fast neutrons have much more modest energies and can be prevented from reaching the active volume of the detector by shielding [1301. Neutrons
generated in the detector can be reduced by using radiopure materials to construct
the detector. To (late, DMTPC detectors are not operated with neutron shielding, so
environmental neutrons may enter the detector and cause nuclear recoils.
Neutrons are not the only possible background in a DMTPC 'WIMP search. 'While
o decays involve much higher energies than 'WIMP-induced recoils, there are several
cases in which o events can mimic nuclear recoil events. In cases where only a small
fraction of the o track occurs within the active volume (as in the directionality study
described previously), the resulting "low-energy" a track measured in the detector
may look indistinguishable from a nuclear recoil. From basic kinematics. along with
each n particle from a decay, there is also a corresponding recoiling nucleus with
an energy of approximately 100 keV. A small fraction of these nuclear recoils will
169
reach the active volume. Unlike neutron-induced recoils, which occur throughout the
active volume, these a-related backgrounds are restricted to occurring close to the
edges of the active volume in order for only a small amount of energy to be deposited
in the detector. Events occurring near the field cage rings are easily identified with
the CCD analysis and with the veto channel charge signal. Because the 4-shooter
prototype lacks the ability to reconstruct the absolute position along the drift length,
it is susceptible to a backgrounds entering the drift volume through one of the meshes.
Due to the high rate of ionization events in the detector, the CCD readout may
also suffer problems from pileup of light from different events. If enough ionization
happens in a particular region of the detector, it may result in a region identified
as a possible nuclear recoil candidate track. Likewise, a nearly horizontal event may
lead to a charge signal that resembles a nuclear recoil. As a result, there is a small
probability that such a cluster and such a charge signal may be misidentified as a
nuclear recoil candidate. The rate of these events is estimated by combining the CCD
data, of an event with the charge data of the previous event and searching for nuclear
recoil candidates.
By introducing a time separation between the CCD and charge
data, there are no true nuclear recoil events that should pass all cuts. Performing
this analysis on the entire WIMP data set, four nuclear recoil candidate events are
identified in the 80 to 200 keVr. energy range. All four can be identified with the
charge signal from a nuclear recoil candidate and a CCD artifact. There are no cases
where both the charge signal and the CCD signal appear to have been misidentified.
Thus, the number of falsely identified nuclear recoils is less than 2.3 events at 90%
confidence level, although there is the possibility of a small number of nuclear recoil
charge signals being assigned to the wrong CCD track. This result and the known
ability of DMTPC detectors to reject electron recoils at the 10-'
level or better [109]
place significant constraints on the numbers of non-nuclear-recoil-like events that can
be identified as nuclear recoils. We can deterinine with high confidence that the vast
majority of nuclear recoil candidates are in fact nuclear recoils or similar events such
as low-energy a particles.
170
Cut
Basic
Nob
N1
N2
N:3
N4
No,
N,
CCD Track
Fiducial Cut
Er E [70, 200) keV,.
E7 E [80,200) keV,
AmBe
889363
24416
6186
6017
5993
5982
5955
5949
5551
4162
3493
3040
Rate [mHz]
3821
105
26.6
25.8
25.7
25.7
25.6
25.6
23.8
17.9
15.0
13.1
Change [%]
N/A
97.25
74.66
2.73
0.399
0.184
0.451
0.101
6.69
25.0
16.1
13.0
Table 7.3: The number of events (40 keVc. < E, < 200 keVee) passing each successive
cut in the AmBe neutron dataset and a WIMP (source free) dataset. The change
gives the fraction of of events passing the cut in each previous row but failing the cut
in that row. The first line shows the events passing all basic quality cuts.
7.4
Results from AmBe and WIMP Data
Table 7.3 and Table 7.4 summarize the number of events passing each cut, and the
equivalent event rate in the AmBe and source free data.
The rejection power of
the charge readout analysis stems largely from two cuts: Nob and N 1. These two cuts
alone reduce the two million charge triggers to less than one thousand. The remaining
cuts remove only a small fraction of the charge triggers passing Nob and N, in the
AmBe data set. but remove nearly 35% of those events in source free data. The CCD
analysis and matching of CCD tracks to charge triggers further reduces the number
of passing AmBe events by 6.69%, a small amount, but reduces the number of events
in the source free data set by 19.5%.
After applying all cuts. a total of 4 162 passing events is found in the AmBe
analysis with an energy between 40 and 200 keV((. In the WIMP analysis. 347 events
are found in the same energy range. Restricting the analysis to the 80 to 200 keV,
range used in previous DMTPC analyses. 3 040 events are found in the AmBe analysis.
an( 250 are found in the VIMP analysis.
Figure 7-6 shows the (listribution of AmBe and WIMP events on the anode. No
171
Cut
Basic
NOb
N1
N2
N3
N4
NOa
N5
CCD Track
Fiducial Cut
Er E [70, 200) keV,
Er E [80, 200) keV,.
Source Free
2166429
45100
886
682
628
603
575
575
463
347
283
250
Rate [mHzl
3641
75.8
1.49
1.15
1.06
1.01
0.966
0.966
0.778
0.583
0.476
0.420
Change [%]
N/A
97.92
98.04
23.02
7.92
3.98
4.64
0
19.5
25.3
18.4
11.7
Table 7.4: The number of events (40 keVee < E7. < 200 keV,,) passing each successive
cut in the WIMP (source free) dataset. The change gives the fraction of of events
passing the cut in each previous row but failing the cut in that row.
obvious hot spots are seen in the data, as would be expected for a data set populated by legitimate nuclear recoils. In the source free data, the distribution of event
distances from the center of the anode differs from the distribution for AmBe data
(Figure 7-7). In an approximately uniform distribution of event positions,. the number of events at each radial distance from the anode center is proportional to to the
radial distance. While the AmBe events are not quite uniformly distributed due to
geometric effects from the source, this behavior is displayed in the AmBe data. In
the WIMP data., however, a significant. excess of events is found at very large radii.
This suggests that some events associated with radioactive decays near the field cage
rings are leaking into the signal region. When the results for each camera are analyzed separately (see Table 7.5)., significant variation in the number of events is found
in both AmBe and WIMP data. Cameras 100534 and 100439 are located nearest
to the source in the AmBe data and thus experience a larger neutron flux than the
other cameras. In WIMP data., each camera should measure approximately the samne
number of events. Much of the variation in event rate in the WIMP data is due to
the excess high-radius events. Because of field non-uniformities. electrons are unable
to reach much of the veto electrode at some points on the readout plane. Because
much of the veto region is effectively inactive, the veto and default fiducial cuts are
172
1010
- 11
1
11
-
1
-100
Figue
rac
Te
rcontruced
76:
65'
pasn
.o
postios
5-
5 101521
x [cm]
1
evnt.
aa
Let.m.
x [cm]
Figure 7-6: The reconstructed track positions of passing events. Left: AmBe data.
Gray points are passing events not including the fiducial cuts. Red points are events
6
1043
Right: Source free data.
passing
all cuts. 81102
Camera
110121
A80333
100534
100439
AmBe Data
650
712
867
811
WIMP Data WIMP Data, Stricter Radius Cut
51
48
58
64
56
52
70
72
Table 7.5: Number of passing events in each camera in the 80 to 200 keVr range in
both AmBe and WIMP data.
not as effective as would otherwise be expected. The excess events can be removed
by using a more stringent radial cut requiring events to have a, centroid less than
870 pixels. This more stringent cut reduces the fiducial volume to 68.7% of the total active volume above the central anode. This leaves a total of 221 nuclear recoil
candidate events in the WIMP data set.
The energy distributions of nuclear recoil candidate events in AmBe and source
free running are shown in Figure 7-8. The source free data is seen to agree well with
the shape of the expected spectrum of recoils due to cosmnic-ray neutrons calculated
from the spectrum found in [128] using Geant4. While there is significant, uncertainty
as to the normalization of the background spectrumn, the measured number of events
is not inconsistent with what, might be expected. A single energy bin, between 140
173
300
-
E45Z 40
250-
~35:
2003
150-
25
20 100
15-
50
10
5
0
2
4
6
8
10
12
14
Radius [cm]
0
2
4
6
8
10
12
14
Radius [cm]
Figure 7-7: Histograms of the distance from the center of the anode of passing events.
Left: AmBe data. Fiducial cuts are not included in the AmBe data used here. The
linear increase in event rate with radius indicates that the events are approximately
uniformly distributed in radius. Right: Source free data. A noticeable excess of
events is seen at high radii, near the field cage rings.
and 150 keV,, falls far below the background curve. A similar drop in event rate
does not appear in the AmBe data, so this appears to simply be an unusual statistical fluctuation rather than an analysis or digitization effect. The expected AmBe
spectrum, which attempts to model the effects of detector and shielding materials,
matches the spectrum well between 70 and 160 keV, but falls approximately 20%
below the curve for energies up to 250 keV. This deficit is not necessarily a cause of
concern. The estimate is based on a benchmark spectrum because the exact spectrum
of neutrons emitted by this particular source has not been measured. The estimated
spectrum includes both elastic and inelastic events, and the shape of the measured
AmBe spectrum is in fact very close to the spectrum of elastic scattering events.
Reference [76] provides several methods to analyze two-dimensional angular (i.e.
circular) data. In particular, the modified Rayleigh statistic R.* described there is distributed as a x2 distribution with two degrees of freedom. In the laboratory frame,
the angles of the passing events have a Rayleigh statistic of R* = 1.86, with N = 221.
R* will be larger than this for uniformly distributed data in 39% of data sets, so this is
consistent with a uniform distribution in the laboratory frame. A WIMP signal is expected to preferentially point away from the direction of Cygnus. Considering instead
the track directions with respect to the direction of the WIMP wind, the modified
174
4
-60
>
0
--
-
400
30-
I
Z 300
I
40
20
230200
100
10
-
+4
00
50
100
150
200
250
300
E [keVJ
0
50
100
150
+
200
2
300
E fkeV,)
Figure 7-8: Energy distributions for nuclear recoil candidates. Left: AmBe data. The
blue points with V'N error bars are the data. The red dashed line is the expected
spectrum from a Geant4 AmBe Monte Carlo program. Right: Source free data.
Again, the blue points with error bars are the data. The red dashed line is the
estimated spectrum of cosmic ray neutrons calculated using Geant4 and neglecting
the effects of shielding. In both cases the normalization of the model spectrum is
arbitrary.
Rayleigh statistic is W* = 4.65. Only 9% of values drawn from a uniform distribution will have a Rayleigh statistic exceeding this. However, the Rayleigh statistic
decreases substantially if only higher energy events, where the angular resolution is
better, are considered, so this too is consistent with uniformity. The Rayleigh statistic not sensitive to a preferred axis rather than vector direction. Because axial data
has a period of 1800 rather than 360', the Rayleigh statistic may be calculated to
test for a preferred axis by mapping the axial direction onto a full circle. In both
laboratory coordinates and coordinates with respect to the WIMP wind, this axial
Rayleigh statistic is also consistent with uniformity.
The projected track ranges for the AmBe and WIMP data are plotted in Figure
7-10 along with estimates for the three-dimensional range from SRIM [119]. Because
the range measurement only uses a two-dimensional projection, the measured ranges
ought to fall in a band lower than and extending up to the predicted 3D range.
The reconstructed range typically includes diffusion in addition to the true track
length.
The transverse track width provides an estimate of the half-width of the
broadening due to diffusion. After subtracting twice the transverse track width to
account for diffusion, the measured values primarily fall near but generally below
175
Zb.
.
20
20E
Z
E
Z 15-
15
10
10
5
5150
-100
-5
0
50
100
150
-150
-100
-50
0
50
1J_
150
Figure 7-9: Left: Distribution of measured angles directions in laboratory coordinates
from the source free run. Right: Distribution of measured angles with respect to the
direction of the WIMP wind. Both plots use the two-dimensional projected angle.
the predicted range curves for fluorine and carbon, as expected. Two events in each
data set have ranges falling far above the expected values for carbon and fluorine.
These events cannot be from fast neutrons, as the rate would be much higher in
the AmBe run. Further investigation shows that these events are long tracks with
little diffusion, indicating that they originate near the anode (Figure 7-11). The long
ranges of these events suggests that these may in fact be from a decays occurring
in the anode or amplification mesh where only a small amount of energy reaches
the active volume. If this is the case, these would represent the first hints of what
would be a significant background in an underground WIMP run, where neutron
backgrounds will be negligible.
An additional class of nuclear recoil candidates has an unusually long 0% to 50%
mesh rise time. There are three events in the WIMP data set with a, 0% to 50%
rise time greater than 400 ps, and two in the AmBe data set. Again, the similar
rate of such events precludes these from being generated from fast neutrons. These
events have an electron-like pulse followed immediately by a nuclear recoil pulse. The
energies are well above the energy threshold, so a clear nuclear-recoil-like pulse is
seen. Additionally, the CCD tracks are seen with a variety of track widths, indicating
that these happen throughout the detector rather than just at the field cage rings or
the meshes. With a total rate of ionization events of ~50 Hz, we do not expect to see
any nuclear recoils occurring nearly simultaneously with electron recoils. As a result,
176
E
1'r,
AmBe Data
Source Free Dal
Fluorine, SRIM
-- Carbon, SRIM
------- Helium, SRIM
-.-.-.- Hydrogen, S"Rl10I.
10
8
0
6
4
2
0
20
-
40
60
80 100 120 140 160 180 200 220
Energy [keV.]
Figure 7-10: Reconstructed range vs. energy for AmBe (gray) and WIMP (red)
events. The value shown is the standard reconstructed range with twice the track
width ( 2 uT) subtracted to account for diffusion. A small number of events fall well
above the expected range for fluorine and carbon.
=800
200
780
150
=56015
540
50
760
520
100
0.
00
740
50
500
720
0
480
7
bo
520
540
560
580
4
600
x [pixel]
620
640
660
680
700
x [pixel]
Figure 7-11: CCD images of the WIMP run events with unusually large reconstructed
ranges. These events are seen with very little diffusion, indicating that they occur
very near the anode.
177
5.300-
E
a 250 ---
1 00 CD
150 -
c
--
-
+
-
-
-
-
-
50
-3
-L
-2
2A
A A,
Time [ps]
Figure 7-12: An example mesh trace of an event with a long mesh baseline to 50% or
veto rise time. Two pulses are seen: a small electron-like pulse immediately followed
by a nuclear recoil signal.
it is almost certain that these events are correlated in some way.
7.5
Detection & Reconstruction Efficiency
The nuclear recoil analysis is designed to identify ionization events with a high stopping power and a short projected range in all three dimensions. The CCD analysis
provides information about the range along the two-dimensional readout plane, but
provides minimal information about the range along the drift axis. In contrast, the
charge analysis constrains the range along the drift axis without providing information
about the range along the readout plane. Because the charge and CCD measurements
are sensitive to different event geometries, the detector efficiency may be estimated
by treating the charge and CCD data as two independent measurements.
The efficiency of the CCD analysis is estimated by determining the fraction of
nuclear recoil candidates identified just by the charge readout that ultimately pass
all cuts.
Using the AmBe data, this fraction is found to be approximately 95%
across the entire 80 to 200 keV, energy range used in the analysis.
Some fraction
of the passing charge triggers are not nuclear recoils, so this provides a somewhat
178
conservative estimate of the efficiency. This value is imuich higher than the efficiency
seen in the recent nuclear recoil analyses found in [94] and [95] lue to the greatly
relaxed cuts applied to the CCD data. This CCD efficiency includes the CCD-charge
readout matching cut. which is defined to have a > 99% efficiency, but does not
include the fiducial cuts. The fraction of events passing the fiducial cuts does not
display any energy dependence.
The efficiency of the charge cuts is similarly estimated from the fraction of CCD
tracks ultimately identified as nuclear recoil candidates. While the digitizers collect
triggers for one second per event, the average total elapsed time per event, including readout time, is 1.63 s.,3 As the CCD shutters are not used, the CCDs collect
light for this entire period, though some light may be shifted from its true position
if it is collected as the CCD is being read.
If the charge readout analysis were to
identify nuclear recoils with 100% efficiency, 62% of recoils measured by the CCDs
would also be measured by the charge readout. In the AmBe data, the fraction of
CCD tracks with a matching nuclear-recoil-like charge signal reaches a value consistent with this for measured gain-ma)p corrected energies of 800 to 1600 ADU for
each camera. roughly corresponding to the energy range considered in this analysis.
Furthermore, few of the nuclear recoil candidates in either AmBe or WIMP data have
reconstructed charge analysis parameters near the cut, values (Figure 7-13). The cut
on the mesh fast peak as a function of anode peak is clearly seen to be closest to
the main band of nuclear recoils. However, this cut (as well as the others) may be
weakened substantially without the total number of events changing by more than a
few percent at any energy in the range used here. Ths., we estimate that the charge
rea(ldot efficiency is approximately 90X or better in this energy range.
Assuming a CCD efficiency of 95% and a charge readout efficiency of 90% for all
energies, the overall detection efficiency is then 85.5% and is not dependent on energy.
This is in contrast to previous detectors, where the CCD event selection introduces
strong energy-dcpendent effects to the efficiency.
3
An extended discussion of this can be found in [94].
179
20
57350
~z18
E
[.
14
TA:*
C.
M 250
ae 12
-
200
10
j
4
300
A.
...
p,-
6
4
2
0
20
40
60
80
100
120
14
0
160
ii
180
200
Energy [keV.
150
100
-.
s0
220
-0
...
..
20
40
60
80
160
180
200
220
100
120
140
160
180
.-..
200
220
Energy [keVe]
30
25
0.
0
S20-
UC
_0
20
40
60
80
100
120
140
Energy [keV.]
Figure 7-13: Plots of the three most powerful cut variables for nuclear recoil candidates. AmBe data is plotted in gray while source free (WIMP) data is plotted in red.
The cut limits are shown as blue lines.
180
7.6
WIMP Direct Detection Limits
Given an expected number of background nuclear recoils b, expected number of signal
recoils s and a detector efficiency e, the probability of observing nols total nuclear
recoils is 4
P0oSss +-b, e)
-"'(1
nos!(n
-
)
--
n0os)!
"(s+.
n!
(7.1)
The source free data taken here can be used to set an upper limit on the rate of
WIMP-induced nuclear recoils. While a small detector such as the DMTPC 4-shooter
prototype is not large enough to be competitive with the world-leading experiments.
such limits are useful in comparing to previous DMTPC results and evaluating the
likely reach of future, much larger, detectors. Following the CL, upper limit procedure
[131], if N events are actually observed, we let
N
>3
P8 +b
and
,+
p(Pobs
b, E)
(7.2)
N
A =
Values of s may be rejected at, (1
-
P (IlobsIb, E).
(7.3)
x) confidence level when
CL's = P,+b
Pb
<
(7.4)
The denominator is intended to penalize the limiting power of measurements generally
consistent, with backgrounds in order to avoid setting excessively stringent limits if a
large downward fluctuation in the background is seen.
In this measurement. the efficiency is i = 85.5% and the number of measured
nuclear recoil candidates is N = 221. Since there is considerable uncertainty about
the expected number of background events. I will consider three benchmark scenarios:
1. Zero-background (signal-only) case. The most conservative measurement will
assume that all events may be signal events by setting b = 0. It is expected
4 This equat ion
is vahid
as
long
as the efficiencv is the same for bot h signal and background events.
181
that a significant fraction, if not all, of the events are due to backgrounds, so
this provides a worst-case benchmark that will generally lead to weaker limits
than is expected.
2. Simple cosmic ray neutron estimate. A simple estimate using the neutron spectrum from
[128] suggests that b ~ 140 (with large incertainties) is a reasonable,
though likely somewhat low, estimate for the number of cosmic ray neutron
events.
3. Ideal background case.
The upper limit will generally be best when the ex-
pected number of events is equal to the number of measured events, N = Eb.
This approximates the best that can be achieved if the backgrounds are fully
understood.
Using these values, we find that the 90% confidence level upper limit on the
number of signal events is SUL = 283 in scenario (1), SUL = 143 in scenario (2), and
SUL = 30.2 in scenario (3).
The expected number of events for a, given halo model
may be written s = aAhtS where MT is the target mass, I is the total live time and
S is a constant dependent on the halo parameters, (lark matter mass, and detector
energy range. Thus, the upper limit on the number of signal events is equivalent to
an upper limit on the cross section defined by
JUL(-F +
F+X)=
SUL±.
(7.5)
Ah'tS
Fluorine is primarily sensitive to spin-dependent WIMP-proton interactions.
Fol-
lowing [132], a WIMP-fluorine cross section can be converted to an equivalent spindependent, WIMP-proton cross section by
2
(SD N, __
__
/L
1
p12 CFIC
9
F + g
-19
F+
).
(7.6)
/, is the reduced mass of a WIMIP andl proton while pIF is the same for a WIMP and a
fluorine nucleus. C/OC, = 0.778 [132] characterizes the spin and angular momentum
of the nucleons in the fluorine-19 nucleus. The upper limit on the number of signal
182
events is then
u"j±-
(1)+
x
2
-)
p + X)
=2,
p
1
1,
SUL
.
(7.7)
Including the reduction in efiective nass due to the fiducial cuts, the total exposure of the source-free data set is 20.5 g-days. The dark matter calculation package
MicrOMEGAS v3.2 [133] is used to calculate S at different WIMP masses.
The
results from MicrOMEGAS have been validated from a WIMP event Monte Carlo
program generating WIMP events (listributed according to Equation 2.19. Limits for
the three background scenarios are shown in 7-14. The limits show a broad minimum
centered near a mass of 125 GeV. In the conservative (0 background) estimate, the
limit reaches a minimum of approximately 7 x 10-32 cm 2, while the optimistic scenario improves upon this by about an order of magnitude. The optimistic scenario is
statistics-limited by the background rate, so the limit can be improved by increasing
the exposure.
The results of this run are comparable to the surface limit set with the DMTPC
lOL detector in [89], which used data taken in a baseinent laboratory in a different
building at MIT and had a somewhat larger exposure.
The background rate in
the 4-shooter can be expected to decrease markedly in an underground run.
An
underground data set of the same exposure that contains no background events and
no signal events can set a limit approximately an order of magnitude lower than
the optimistic background scenario considered here. Whether or not the 4-shooter is
capable of obtaining a background-free measurement in a, more favorable environment
such as an underground laboratory remains to be seen.
183
0
44.4,
io-345
I
a I
3
i10
WIMP Mass [GeY9
Figure 7-14: 90% confidence level upper limits for WIMP masses between 30 GeV
and 10 TeV for the three background scenarios: zero background/signal only (dotted
blue), simple background estimate (dashed red), and background equal to measured
value (solid green). The dashed and dotted gray curve shows the equivalent limit for
this exposure with no backgrounds and no measured events, as might be expected in
an underground run.
184
Chapter 8
Conclusions
This wvork has presented the first significant nuclear recoil search with the DMTPC
4-shooter prototype.
Previous work [95] has shown that a small detector such as
the 4-shooter is not yet large enough to constrain WIMP-nucleon interaction cross
sections as well as world-leading experiments, but this work allows us to evaluate
how well the detector operates compared to ideal conditions. Our ability to constrain
dark matter cross sections from surface data is presently limited by uncertainties on
the expected rate of background events. Depending on assumptions, the limit at, the
optimal WIMP mass ranges from 8 x 10-32 C2
to 8 x
10-
cm 2 . This is comparable
to previous limits set with the earlier DMTPC lOL prototype [89, 94].
Dedicated
measurements of the neutron and muon energy and directional distributions would
help resolve this uncertainty and allow the results from surface running to be better
underst-ood.
However, even in the ideal case where the background rate is fully understood.
this result would be limited by the statistics of the number of background events. In
this statistics-limited regime., the limit will scale with the square root of the exposure,
so to attain another order of magnitude improvement, the exposure must be increased
by a factor of 100. Since even that is not sufficient to reach the current best limits on
\VIMP-nucleon spin-dependent interactions. it is clear that only marginal improveinents can be achieved by conti nuig to operate the detector in an environment with
significant numbers of background events and by working to better understand the
expected rate of neutron-induced recoils in the detector.
185
To achieve better sensitivity to dark matter interactions, the DMTPC collabora-
tion is designing a much larger detector with a cubic meter fiducial volume. This increases the fiducial mass by nearly two orders of magnitude. The detector is expected
to be commissioned at the surface, as with the 4-shooter, and installed underground
in the DMTPC laboratory at the Waste Isolation Pilot Plant near Carlsbad, New
Mexico. A detector of this size run background free for one year will greatly improve
upon the best limits set by a directional experiment and will start to be competitive with the present best direct detection limits for spin-dependent WIMP-proton
interactions.
The studies presented in this thesis raise a number of issues for operating such
a large detector, particularly for surface commissioning.
The considerable rate of
ionization events in the 4-shooter may pose several problems for a cubic meter detector. While MIPs, which likely comprise a large fraction of these events, are typically
restricted to lower energies than are used for nuclear recoil analyses in the 4-shooter,
the same will not be true for MIPs in a cubic meter detector. Because a m 3 detector
is much larger and is expected to be oriented with the drift axis pointing horizontally rather than vertically, typical cosmic ray muon events may deposit energies of
40 keVe, rather than 10 keV,,.
A horizontal drift field means that muons from cosmic rays, which travel mostly
vertically, will be preferentially oriented parallel to the readout plane. The vertical
field cage of the 4-shooter causes muon tracks to have large Az values. The nuclear
recoil selection cuts choose events with short Az, so muons are easily removed provided they deposit enough energy for the pulse shape properties to be reconstructed
properly. In contrast, the horizontal field cage of a cubic meter detector will result in
many muon tracks with short A: values. This will generally reduce the efficacy of the
pulse shape cuts for removing background events. The weakening of the background
rejection cuts for muons can be mitigated by a segmented anode., such as the two
anode channels of the 4-shooter. However, the excess of events found near the edge
of the field cage in the analysis in Chapter 7 shows that anode segmentation may not
be sufficient to reject all events crossing between two readout regions. To bolster the
186
other cuts, the introduction of an active muon veto system can be a key component
in identifying background events at the surface. A small scale version of such a system was used as the nmon trigger to search for cosmic ray events in Chapter 6, and
can be trivially adapted into a muon veto. A muon veto system for the cubic meter
detector would require a much larger and more robust setup to veto a significant
fraction of muons, but the basic design
plastic scintillator read out with PMTs
would work well. The ability to trigger the charge and PMT channels on muons also
raises the possibility of using the muon spectrum to monitor detector performance
without using any radioactive sources.
The muon rate will also increase by approximately an order of magnitude, likely to
hundreds of events per second. In the 4-shooter, the raw data from a 1000 event run
with one second exposures and a charge trigger rate of 10 Hz uses 600 Mb on disk.
The reconstructed files require even more storage space, so well over 1 Gb of disk
space is needed per 1000 s of live time. In a m2 detector with 8 cameras, more charge
channels, and a much higher trigger rate, digitizing all the data will not be feasible.
The data acquisition process for a large detector will need to be overhauled to handle
the large data, rate. In particular. software triggers can be used to record only charge
triggers and CCD images that, might contain nuclear recoils.
In the nuclear recoil
analysis here, two cuts were able to reduce the event rate by more than a factor of
10' (Table 7.4).
By adding some form of the nuclear recoil cuts to the DAQ, the
amount of data can likely be reduced to a small fraction of what it would be in the
current "witness" mode DAQ, where everything is recorded. Additional changes can
be made to reduce the dead time. In the WIMP runs described here, each 1 s exposure
takes approximately 1.63 s. Gas refilling. CCD dark frame taking, and file transfer
cause even more (lead time. leaving an overall duty cycle less than 50%. This can
be improved by reducing the data rate through software triggering and by organizing
the different pieces of the DAQ process' in a smarter way.
Vhile muons are a major problem at the surface, the muon rate at an undergrO~nd facility such as WIPP is quite low. A mion veto would easily identify the
'Data taking. reading. triggering, writing, etc.
187
small number of through-going muon events without introducing any significant dead
time. The a backgrounds in the 4-shooter may be problematic for conducting WIMP
searches with a dark matter detector. Despite taking precautions to use clean materials and avoid contaminating the detector, a decays have been determined to originate
at most of the surfaces near the active volume of the detector. The rate of a events
has improved by well over an order of magnitude compared to previous detectors
such as the lOL prototype, but in a long underground run, this rate may still be too
high to be able to run with no background events. While decays near the field cage
structure are generally easy to identify, the appearance of a clear peak in the a energy
spectrum that may be associated with 2" Po decays at the amplification region could
pose a serious problem for operating the detector with no backgrounds.
Already,
several events possibly associated with a decays near the amplification region have
been identified in this short, WIMP run. Without the ability to reconstruct the absolute positions of events along the drift length, such events cannot be rejected and
instead will often be identified as nuclear recoil candidates. Fortunately, the cubic
meter design may be less sensitive to this class of events. It is planned to have meshonly amplification regions, reducing the surface area and the total amount of material
needed to construct the anode. Multiple drift regions are expected to be read out by
the same anode, so many of these events may instead appear as two coincident tracks
found in multiple drift volumes. Any contamination at the cathode, however, may
still be difficult to identify. Because of these possible backgrounds it is imperative
that the DMTPC collaboration enact more rigorous materials screening and handling
processes to minimize any contamination inside the detector.
While this work has determined some areas for concern with respect to the design
and operation of future detectors, it has also described useful tools for calibrating
DNTPC detectors and evaluating detector performance. While calibration with xray sources has been used previously by the collaboration, the use of several sources
with known energies has allowed us to better understand the systematic uncertainties
in the energy calibration than in previous detectors. For a cubic meter detector, a
particles from reasonable calibration sources such as
188
241
Am and
2 10
Po will only be
able to sample a tiny fraction of the readout plane for each drift, volume. In contrast,
x-ray sources allow for much of the detector to be sampled at once and allow for a
much simpler measurement.
The much larger size will also allow for much higher
energy electrons to be contained, possibly allowing for measurements of -y-ray lines
such as the 60 keV line of
241
Am to test the detector response at energies used for
nuclear recoil analyses.
The use of low-energy a events has provided us with extremely useful information
regarding the quality of the angular reconstruction.
While those results are not
directly applicable to nuclear recoils, they show that the reconstruction is fully capable
of accurately determining the directions of low energy tracks. The a results provide
a stark contrast to the directional results from AmBe neutron runs in [95], where
only fairly weak directionality was found.
Because the response of the directional
reconstruction for nuclear recoils is needed in order to understand WIMP search data
with a directional detector, it is clear that more work is needed to understand how to
extract the resolution from neutron data. Significant improvement is needed in both
the directional reconstruction and our understanding of directional sources in order
to achieve the final goal of a directional (lark matter detector.
Perhaps the most important result from the WIMP analysis presented here is not
the final dark matter limit curves, but rather the success of the analysis technique,
which is quite different from previous DMTPC WIMP results. The full integration of
the charge readout with the more established CCD reconstruction and analysis allows
for the analysis process to be greatly streamlined. Few CCD cuts are needed to obtain
a result with very few backgrounds. even given the less-than-optimal conditions of
an unshielded surface laboratory with no overburden.
By relaxing the CCD cuts
and using charge cuts that remove few nuclear recoil events, the analysis is able to
identify nuclear recoils with a much higher efficiency than in previous results and with
an efficiency that is nearly flat in energy over the energy range used here. To increase
sensitivity to WIMPs, the collaboration should consider working to reduce the energy
threshold.
The gain of the 4-shooter and the noise of the readout electronics will
prevent the 4-shooter from accurately (list inguishing nuclear recoils from backgrounds
189
at energies much lower than the 80 keV threshold used here. To lower the threshold,
improvements must be made to the detector design to either achieve higher gains
or reduce the noise. The group is currently investigating new amplification region
designs and is likely to use different cameras, preamplifiers, and digitizers in future
experiments.
While the 4-shooter PMT channels have not been particularly useful in analyzing
nuclear recoils dcue to poor signal to noise and suboptimal digitizers for the fast PMT
pulses, they have proved to be an invaluable tool in the a analysis. With a combined
CCD and PMT analysis, the full three-dimensional range may be reconstructed. The
PIT Az analysis presented here relies on the assumption that the field is uniform so
that the electron drift velocity is constant and well-known. To obtain more accurate
results, calibration procedures for PMT readout must be developed. These include
energy calibrations, spatially-dependent optical gain maps, and even electron velocity
measurements to calibrate the Az reconstruction. This work has shown that for a
particles, even approximate estimates of the projected range along the drift axis will
result in reasonably accurate measurements of the full range of the tracks. Future
detectors are planned to have much larger PMTs, allowing for much lower energies to
be measured. Given the success of the PMT analysis to reconstruct the full ranges of a
particles, we can hope that future DMTPC directional detector analyses will utilize
CCD, charge, and PMT data to reconstruct the directions of low energy fluorine
recoils in all three dimension. The creation of a true directional nuclear recoil detector
sensitive to WIMP dark matter would be a major development for the entire field of
dark matter detection.
190
Chapter 9
Bibliography
[1] F. Zwicky. On the Masses of Nebulae and of Clusters of Nebulae.
86:217 246, 1937.
[2] R. Gavazzi et al.
A weak lensing study of the Coma cluster.
Ap. J..
Astronomy &
Astrophysics, 498:L33 L36, 2009.
[3] NASA, ESA, and Hubble Heritage. Inside the Coma Cluster of Galaxies.
http://apod.nasa.gov/apod/ap080616.html. Accessed 18 Jan. 2013.
[4] V.C. Rubin et al. Rotational Properties of 21 Sc Galaxies with a Large Range
of Luminosities and Radii, From NGC 4605 (R = 4 kpc) to UGC 2885 (R
122 kpc). Ap. J., 238:471 487, 1980.
[5] P. Tisserand et al. Limits on the Macho Content of the Galactic Halo from the
EROS-2 Survey of the Magellanic Clouds.
2007.
Astron. Astrophys., 469:387 404,
[6] K. Jedamzik and M. Pospelov. Particle Dark Matter, chapter Particle dark
matter and Big Bang nucleosynthesis. Cambridge University Press, 2010.
[7] D. Clowe et al. A Direct Empirical Proof of the Existence of Dark Matter. Ap.
J.. 648:L109 113 2006.
[8] M. Markevitch et al. Direct Constraints on the Dark Matter Self-Interaction
Cross-Section From the Merging Galaxy Cluster 1E0657-56. Ap. J., 606:819,
2004.
[9] D. Clowe et al. On Dark Peaks and Missing Mass: A Weak-Lensing Mass
Reconstruction of the Merging Cluster System A520. Ap. J., 758:128, 2012.
Bullet
et
al.
The
Matter
of
the
[10] NASA
http://apod.nasa.go/apo/ap060824.htiml. Accessed 18 Jan. 2013.
[11] J.C. Mather et al.
Cluster.
Calibrator Design for the COBE Far Infrared Absolute
Spectrophotometer (FIRAS) . Ap. J., 512:511, 1999.
191
[12] ESA
and
the
Planck
Collaboration.
http://spaeinimages.esa.int/Inages/2013/03/PlanckCMB.
June 2013.
Planck
CMB.
Accessed 17
[13] M. Longair. Galaxy Formation. Springer, second edition, 2008.
[14] ESA and the Planck Collaboration.
Planck Power Spectrum.
http://spaceinimages.esa.int/Images/2013/03/PlanckPowerSpectriin.
Accessed 17 June 2013.
[15] Planck Collaboration. Planck 2013 results. XVI. Cosmological Parameters.
2013. Submitted to Astronomy & Astrophysics. arXiv:1303.5076.
[16] G. Hinshaw et al. Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP)
Observations: Cosmological Parameter Results. Ap. J. Suppl., 208:19, 2013.
[17] G. Bertone. editor. Particle Dark Matter. Cambridge University Press, 2010.
[18] R. Catena and P. Ullio. A novel determination of the local dark matter density.
JCAP, 08:004, 2010.
[19] J. Edsj6 and P. Gondolo. Neutralino Relic Density including Coannihilations.
Phys. Rev. D, 56:1879 1894, 1997.
[20] J. Ellis et al. Supersymmetric Relics from the Big Bang. Nucl. Phys. B, 238:453476, 1984.
[21] H. Goldberg. Constraint on the Photino Mass from Cosmology.
Lett., 50:1419 1422, 1983.
Phys. Rev.
[22] B.W. Lee and S. Weinberg. Cosmological Lower Bound on Heavy-Neutrino
Masses. Phys. Rev. Lett., 39:165- 168, 1977.
[23] S. Dodelson. Modern Cosmology. Academic Press, 2003.
[24] G. Jungman, M. Kamionkowski, and K. Griest. Supersymmetric Dark Matter.
Phys. Rep., 267:195-373, 1996.
[25] D. Hooper and S. Profumo. Dark matter and collider phenomenology of universal extra dimensions. Phys. Rep., 453:29 115. 2007.
[26] H.-C. Cheng. J. Feng, and K. Matchev. Kaluza-Klein Dark Matter. Phys. Rev.
Lett., 89:21, 2002.
[27] J.L. Feng. A. Rajamaran, and F. Takayama. Superweakly-interacting massive
particles. Phys. Rev. Lett., 91:011302., 2003.
[28] J.L. Feng. A. Rajamaran, and F. Takayama. SuperWIMP dark matter signals
from the early universe. Phys. Rev. D.. 68:063504, 2003.
192
[29] R.D. Peccei and H.R. Quinn. CP Conservation in the Presence of Pseudoparticles. Phys. Rev. Lett.. 38:1440 1443, 1977.
[30] S. Weinberg. A New Light Boson? Phys. Rev. Lett., 40:223 226, 1978.
[31] M. Hertzberg, M. Tegmark, and F. Wilezek. Axion Cosmology and the Energy
Scale of Inflation. Phys. Rev. D, 78:83507, 2008.
[32] S.J. Asztalos et al. A SQUID-based microwave cavity search for dark-matter
axions. Phys. Rev. Lett., 104:041301, 2010.
[33] 0. Adriani et al. Observation of an anomalous positron abundance in the cosmic
radiation. Nature. 458:607 609. 2009.
[34] A.A. Abdo et al. Measurement of the Cosmic Ray e++e- Spectrum from 20 GeV
to 1 TeV with the Fermi Large Area Telescope. Phys. Rev. Lett., 102:181101,
2009.
[35] M. Aguilar et al. First Result from the Alpha Magnetic Spectrometer on the
International Space Station: PRecision measurement of the Positron Fraction
in Primary Cosmic Rays of 0.5-350 GeV. Phys. Rev. Lett., 110:141102, 2013.
[36] A. Abramowski et al. Search for Photon Line-like Signaturs from Dark Matter
Annihilations with HESS. Phys. Rev. Lett., 110:041301, 2013.
[37] T. Arlen et al. Constraints on Cosmic Rays, Magnetic Fields, and Dark Matter
from Gamma-Ray Observations of the Coma Cluster of Galaxies with VERITAS
and Fermi. Ap. J., 757:123, 2012.
[38] A. Abdo et al. Constraints on Cosmological Dark Matter Annihilation from the
Fermi-LAT Isotropic Diffuse Gamma-Ray Measurement. JCAP, 04:014, 2010.
[39] 0. Adriani et al. PAMELA results on the cosmic-ray antiproton flux from 60
MeV to 180 GeV in kinetic energy. Phys. Rev. Left., 105:121101, 2010.
[40] R. Abbasi. Multi-year search for dark matter annihilations in the Sun with the
Amanda-I and IceCube detectors. Phys. Rev. D, 85:042002. 2012.
[41] S.A.I. Mognet et al.
The Prototype GAPS (pGAPS) Experiment.
2013.
arXiv: 1303.1615.
[42] ATLAS Collaboration. Search for (lark matter candidates and large extra dimensions in events with a photon and missing transverse momentum in pp
collision data at V/s = 7 TeV with the ATLAS detector. Phys. Rev. Lett.,
110:011802. 2013.
[43] CMS Collaboration. Search for Dark Matter and Large Extra Dimensions in
pp Collisions Yielding a Photon an d Missing Transverse Energy. Phys. Rev.
Lett.. 108:261803. 2012.
193
[44] ATLAS Collaboration. Search for dark matter candidates and large extra dimensions in events with a jet and missing transverse momentum with the AT-
LAS detector. JHEP, 1304:075, 2013.
[45] CMS Collaboration. Search for dark matter and large extra dimensions in
monojet events in pp collisions at /s - 7 TeV. JHEP, 09:094, 2012.
[46] M.W. Goodman and E. Witten. Detectabiliy of certain dark-matter candidates.
Phys. Rev. D, pages 3059 3063, 1985.
[47] A.K. Drukier, K. Freese, and D.N. Spergel. Detecting cold dark-matter candi-
dates. Phys. Rev. D, 33:3495 3508, 1986.
[48] J. Engel, S. Pittel, and P. Vogel. Nuclear Physics of Dark Matter Detection.
Int. J. Mod. Phys. E, 1:1 37, 1992.
[49] G. Bertone et al. Particle Dark Matter: Evidence, Candidates and Constraints.
Phys. Rep., 405:279 390, 2005.
[50] J.D. Lewin and P.F. Smith. Review of mathematics, numerical factors, and corrections for dark matter experiments based on elastic nuclear recoil. Astropart.
Phys., 6:87 112, 1996.
[51] M. Srednicki. Quantum Field Theory. Cambridge University Press, 2007.
[52] E. Aprile et al. Dark Matter Results from 225 Live Days of XENON100 Data.
Phys. Rev. Lett., 109:181301, 2012.
[53] D. Akerib et al. The Large Underground Xenon (LUX) Experiment.
IJstrum. Meth. A, 704:111 126, 2013.
Nucl.
[54] T. Alexander et al. Light yield in DarkSide-10: a prototype two-phase liquid
argon TPC for dark matter searches. Astropart. Phys., 49:44 51, 2013.
[55] A. Badertscher. ArDM: first results from underground commissioning. JINST,
8:C09005, 2013.
[56] A. Hime. The MiniCLEAN Dark Matter Experiment. Presented at the 2011
meeting of the American Physical Society Division of Particles and Fields, 2011.
[57] M.G. Boulay. DEAP-3600 Dark Matter Search at SNOLAB. Proceedings for
the 12th International Conference on Topics in Astroparticle and Underground
Physics, 2012.
[58] Z. Ahmed et al. Dark Matter Search Results from the CDMS II Experiment.
Science. 327:1619 1621. 2010.
[59] M. Felizardo et al. Final Analysis and Results of the Phase II SIMPLE Dark
Matter Search. Phys. Rev. Lett., 108:201302, 2012.
194
[60] S. Archambault et al.
Constraints on Low-Mass
VIMP Interactions on 19 F
from PICASSO. Phys. Lett. B., 711:153 161, 2012.
[61] E. Behnke et al. First dark matter search results from a 4-kg CF 3 I bubble
chamber operated in a deep underground site. Phys. Rev. D, 86:052001. 2012.
[62] E. Aprile et al. Dark Matter Results from 100 Live Days of XENON100 Data.
Phys. Rev. Lett., 107:131302., 2011.
[63] G. Angloher et al. Results from 730 kg days of the CRESST-II Dark Matter
Search. Eur. Phys. J. C, 72:1971, 2012.
[64] R. Agnese et al.
Dark Matter Search Results Using the Silicon Detectors of
CDMS II. 2013. arXiv:1304.4279. Submitted to PRL.
[65] R. Bernabei et al. New Results from DAMA/LIBRA. Eur. Phys. J. C, 67:39 49.
2010.
[66] P. Belli et al. Observations of annual modulation in direct detection of relic
particles and light neutrinos. Phys. Rev. D. 84:055014, 2011.
[67] C.E. Aalseth et al. Search for an Annual Modulation in a P-type Point Contact
Germanium Dark Matter Detector. Phys. Rev. Lett., 107:141301, 2011.
[68] Z. Ahmed et al. Results from a Low-Energy Analysis of the CDMS II Gerina-
nium Data. Phys. Rev. Lett., 106:131302, 2011.
[69] Z. Ahmed et al.
Search for annual modulation in low-energy CDMS-II data.
2012. arXiv:1203.1309.
[70] E. Aprile. New Results from the XENON100 Experiment.
DarkAttack 2012 conference in Asconia, Switzerland, 2012.
Presented at the
[71] R. Bernabei et al. First Results with DAMA/LIBRA and the combined results
with DAMA/NAI. Eur. Phys. J. C, 56:333 355, 2008.
[72] C. Savage et. al. Compatability of DAMA/LIBRA dark matter detection with
other searches. JCAP. 04:010, 2009.
[73] R. Gaitskell. V. Mandic. and J. Filippini. DMTools. http://dmtools.brown.edu.
[74] D.N. Spergel.
Motion of the Earth and the detection of weakly interacting
massive particles. Phys. Rev. D, pages 1353 1355, 1988.
[75] B. Morgan. A.M. Green. and N.J.C. Spooner. Directional statistics for WIMP
direct detection. Phys. Rev. D. 71:103507. 2005.
[76] B. Morgan, A.M. Green. and N.J.C. Spooner. Directional statistics for WIMP
direct detection 11: 2-d read-out. Phys. Rep. D. 72:123501, 2005.
195
[77] A.M. Green and B. Morgan. Optimizing WIMP directional detectors. Astropart.
Phys., 27:142 149, 2007.
[78]
S. Henderson, J. Monroe, and P. Fisher. The Maximum Patch Method for
Directional Dark Matter Detection. Phys. Rev. D, 78:015020, 2008.
[79] J. Billard, F. Mayet, and D. Santos. A Markov chain Monte Carlo analysis
to constrain dark matter properties with directional detection. Phys. Rev. D,
83:075002, 2011.
[80] J. Billard, F. Mayet, and D. Santos. Assessing the discovery potential of directional detection of Dark Matter. Phys. Rev. D, 85:035006, 2012.
[81] J. Billard, F. Mayet, J.F. Mafas-P6rez, and D. Santos. Directional detection as
a strategy to discover galactic dark matter. Phys. Lett. B, 691:156 162, 2010.
[82] K. Freese, J. Frieman, and A. Gould. Signal modulation in cold-dark-matter
detection. Phys. Rev. D, 37:3388 3405, 1988.
[83] S. Ahlen et al. The case for a directional dark matter detector and the status
of current experimental efforts. Int. J. Mod. Phys., 25:1 51, 2010.
[84] K.N. Buckland et al. Low pressure gaseous detector for particle dark matter.
Phys. Rev. Lett., 73:1067-1070, 1994.
[85] E. Daw et al. Spin-Dependent Limits from the DRIFT-lId Directional Dark
Matter Detector. Astropart. Phys., 35:397 401, 2012.
[86] F.J. Iguaz. Micromnegas detector developments for Dark Matter directional
detection with MIMAC. JINST 6:P07002, 2011.
[87] S.E. Vahsen et al. The Directional Dark Matter Detector. Proceedings of the
3rd international conference on directional detection of dark matter (CYGNUS
2011), 2011. arXiv:1110.3401.
[88] K. Miuchi et al. First underground results with NEWAGE-0.3a directionsensitive dark matter detector. Phys. Lett. B, 686:11 17, 2010.
[89] S. Ahlen et al. First (lark matter search results from a surface run of the 10-L
DMTPC directional dark matter detector. Phys. Lett. B, 695:124 129. 2011.
[90] T. Naka et al. Development of emulsion track expansion techniques for opticalmicroscopy-observation of low-velocity ion tracks with ranges below the optical
resolution limit. Nucl. Instrum. Meth. A. 581:761 764, 2007.
[91] NJ. Kimura and T. Naka. Submicron track readout in fine-grained nuclear
emulsions using optical microscopy. Nucl. Instrum. Meth. A., 680:12 17, 2012.
196
[92] D. Nygren. High-pressure Xenon Gas Electroluminescent TPC Concept for
Simultaneous Searches for Neutrino-less Double Beta Decay & WIMP Dark
Matter. Presented at the American Physical Society 2013 April Meeting in
Denver, Colorado, 2013.
[93] A. Drukier et al. New Dark Matter Detectors using DNA for Nanometer Tracking. arXiv:1206.6809, 2012.
[94] A. Kaboth. Detecting the Invisible Universe with Neutrinos and Dark Matter.
PhD thesis, Massachusetts Institute of Technology, 2012.
[95] S. Henderson. An Assessment of the Sensitivity of a Low Pressure Time Projection Chamber to the Direction of WIMP-Induced Nuclear Recoils. PhD thesis,
Massachusetts Institute of Technology, 2013.
[96] G. Charpak et al. Studies of light emission by continuously sensitive avalanche
chambers. Nucl. Instrum. Meth. A. 269:142 148, 1988.
[97] G.F. Reinking, L.G. Christophorou, and S.R. Hunter. Studies of total ionization
in gases/mixtures of interest to pulsed power applications. J. Appl. Phys.
60:499, 1986.
[98] S.G. Lias, J.E. Bartmess, J.F. Liebman, J.L. Holmes, R.D. Levin, and W.G.
Mallard, "Ion Energetics Data* in NIST Chemistry WebBook, NIST Standard Reference Database Number 69. Eds. P.J. Linstrom and W.G. Mallard,
National Institute of Standards and Technology, Gaithersburg MD, 20899.
http://webbook.nist.gov. Accessed 10 August 2013.
[99] L.G. Christophorou, J.K. Olthoff, and M.V.V.S. Rao. Electron Interactions
with CF4. J. Phys. Chem. Ref Data, 25:1341 1388, 1996.
[100] L.G. Christophorou and J.K. Olthoff. Electron Interactions With Plasma Processing Gases: An Update for CF 4 , CHF 3 , C 2F6 , and C 3 F 8 . J. Phys. Chem.
Ref. Data, 28:967 982, 1999.
[101] E. Basurto and J. de Urquijo. Mobility of CF' in CF4 . CHF
in CHF 4. and
C+ in Ar. J. Appl. Phys.. 91:36, 2002.
[102] G.F. Knoll. Radiation Detection and Measurement. Wiley, fourth edition, 2010.
[103] A. Hitachi. Bragg-like curve for (lark matter searches: binary gases. Rad. Phys.
Chem., 77:1311 1317, 2008.
[104] 0. Guillaudin et al. Quenching factor measurement in low pressure gas detector
for directional dark matter search. EAS Publication Series, 53:119 127, 2012.
Proceedings of the 3rd International conference on Directional Detection of
Dark Matter (CYGNUS 2011).
197
[105] A. Kaboth et al. A Measurement of Photon Production in Electron Avalanches
in CF4. Nucl. Instrum. Meth. A, 592:63 72, 2008.
[106] A. Pansky et al. The scintillation of CF 4 and its relevance to detection science.
Nucl. Instrum. Meth. A, 354:262-269, 1995.
[107] C. Broggini. Detection of the scintillation light induced by a particles in pure
CF 4 . Nucl. Instrum. Meth. A, 361:543 547, 1995.
[108] J.F.M. Aarts. Ion and Electron Impact lonisation of CF 4 Studied via UV
Emission. Chem. Phys. Lett., 114:114 120, 1985.
[109] J.P. Lopez et al. Background Rejection in the DMTPC Dark Matter Search
Using Charge Signals. Nucl. Instrum. Aleth. A, 696:121 128, 2012.
[110] J. Lopez et al. Prototype of a Detector for Directional Measurement of the
Cosmogenic Neutron Flux. Nucl. Instrum. Meth. A, 673:22 31, 2012.
[111] H. Junde. Nuclear Data Sheets for A = 55. Nuclear Data Sheets, 109:787 942,
2008.
[112] Berger, M.J., Hubbell, J.H., Seltzer, S.M., Chang, J., Coursey, J.S., Sukumar,
R., Zucker, D.S., and Olsen, K. (2010), XCOM: Photon Cross Section Database
(version 1.5). National Institute of Standards and Technology, Gaithersburg,
MD. http://physics.nist.gov/xcom. Accessed 10 August 2013.
[113] A. C. Thompson and D. Vaughan, editors. X-ray Data Booklet. Lawrence
Berkeley National Laboratory, University of California, third edition, September 2009.
[114] Berger, M.J., Coursey, J.S., Zucker, M.A., and Chang, J. (2005), ESTAR, PSTAR, and ASTAR: Computer Programs for Calculating StoppingPower and Range Tables for Electrons, Protons, and Helium Ions (version
1.2.3). National Institute of Standards and Technology, Gaithersburg. MD.
http://physics.nist.gov/Star. Accessed 10 August 2013.
[115] M.S. Basunia. Nuclear Data Sheets for A = 237. Nuclear Data Sheets, 107:2323
2422, 2006.
[116] P.P. Day. Electromagnetic Spectrum of Am 24 1 . Phys. Rev., 97:689, 1955.
[117] D.D. Cohen. X-Rays From an 24 Am Source and Their Relative Intensities.
Nucl. Instrum. Meth. A, 267:492 498, 1988.
[118] D. Ballard. Generalizing the Hough Ransform to Detect Arbitrary Shapes.
Pattern Recognition. 13:111 -122, 1981.
[119] J.F. Ziegler, J.P. Biersack., and U. Littmark. The Stopping and Range of
Ions in Matter. Pergamon Press, 1985. SRIM and TRIM code available at
http://www.sriim.org.
198
[120] J. Beringer and others (Particle Data Group). 2012 Review of Particle Physics.
Phys. Rev. D, 86:010001. 2012. @26. Cosmic Rays. http://pdg.lbl.gov.
[121] Ashok K. Jain and Balraj Singh. Nuclear data sheets for a = 218. Nuclear Data
Sheets, 107(4):1027
1074. 2006.
[122] F.G. Kondev. Nuclear data sheets for a = 206. Nuclear Data Sheets, 109(6):1527
1654. 2008.
[123] E. Browne. Nuclear data sheets for a = 215,219,223,227.231.
Sheets. 93(4):763
1061. 2001.
Nuclear Data
[124] S.-C. Wu. Nuclear data sheets for a = 216. Nuclear Data Sheets, 108(5):1057
1092, 2007.
[125] James R. Janesick. Scientific Charge-Coupled Devices. SPIE, Bellingham. WA.,
2001.
[126] Reference neutron radiations Part 1: Characteristics and methods of production. Technical Report ISO 8529-1, 2001.
[127] W.N. Hess et, al. Cosmic-Ray Neutron Energy Spectrum. Phys. Rev.. 116:445
457, 1959.
[128] T. Nakamura et al. Sequential Measurements of Cosmic-Ray Neutron Spectrum
and Dose Rate at Sea Level in Sendai, Japan. Journal of Nuclear Science and
Technoloy., 42:843 853, 2005.
[129] P. Goldhagen et al. Measurement of the energy spectrum of cosmic-ray induced neutrons aboard an ER-2 high-altitude airplane. Nuci. Instrum. Meth.
A, 476:42 51, 2002.
[130] D.-M. Mei and A. Hime. Muon-Induced Background Study for Underground
Laboratories. Phys. Rev. D. 73:053004, 2006.
[131] T. Junk. Confidence level computation for combining searches with small statistics. Nucl. Instruim. Meth. A. 434:435 443, 1999.
[132] D.M. Tovey et al. A New Model-Independent Method for Extracting SpinDependent Cross Section Limits from Dark Matter Searches. Phys. Lett. B,
488:17 26. 2000.
[133] G. Blanger et al.
micrOM EG A s3.1 :
a prograin for calculating dark matter observables.
a rXiv:1305.0237. Code available at
http://lapti.cirs.fr/microimegas/.. 2013.
199