Search for Pre-Existing Delta States at BLAST
from 2 H(e,e'A+ + )
by
Chana M. Greene
Submitted to the Department of Physics
in partial fulfillment of the requirements for the degree of
Bachelor of Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2006
© Chana M. Greene, MMVI. All rights reserved.
The author hereby grants to MIT permission to reproduce and
distribute publicly paper and electronic copies of this thesis document
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Richard G. Milner
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ARCHIVES
Search for Pre-Existing Delta States at BLAST from
2 H(e,e'A++)
by
Chana M. Greene
Submitted to the Department of Physics
on May 12, 2006, in partial fulfillment of the
requirements for the degree of
Bachelor of Science
Abstract
At the MIT-Bates Linear Accelerator Center a comprehensive study of low-Q2 spin-
dependent electron scattering from deuterium has been carried out using the Bates
Large Acceptance Spectrometer Toroid (BLAST). This experiment has employed an
850 MeV polarized electron beam from the MIT-Bates linear accelerator incident on
an internal polarized deuterium target and the BLAST detector. Deuterium's simple
composition is an important factor in understanding the structure of the inter-nucleon
potential. The pion production region has a resonant structure and is a promising
location to search for pre-existing delta particles in deuterium. While, theoretical
calculations predict that delta resonant states account for anywhere from 0.25 to
3.60% of the nuclear wave function, more realistic predictions for deuterium range
from 0.3 to 1.0%. This thesis presents the determination of the (e,e'++) event rate
from deuterium, the first of many steps towards a complete study of delta resonant
states.
Thesis Supervisor: Richard G. Milner
Title: Professor
2
Acknowledgments
I would like to thank everyone at MIT-Bates for their support and advice throughout
this process. I would especially like to thank Richard Milner for taking me into his
group and giving me this opportunity;
Michael Kohl, Kevin McIlhany and Renee
Fatimi for answering all of my questions whether it was about physics or ROOT and
taking soccer lunches. All of their passion for the pursuit of knowledge and the beauty
of physics has inspired me. Thank you.
3
Contents
1 Introduction
5
2 Experimental Arrangement
7
2.1
Electron
Beam
2.2
Toroid Magnet.
2.3
2H
. . . . . . . . . . .
Polarized Target .........
2.4 The BLAST Detector ........
2.4.1
Drift Chambers .......
2.4.2
Cerenkov Detectors .....
2.4.3
Time-of-Flight Scintillators.
2.4.4
Neutron Detectors .....
...................
...................
...................
...................
...................
...................
...................
...................
3 Resonant State Study
7
9
9
9
10
10
11
11
12
3.1 A Resonance ...............................
12
3.2 Kinematics
14
................................
3.3 (e,e'++) Event Rate ...........................
4 Discussion
4.1
15
23
Future Plans ................................
4
23
Chapter
1
Introduction
The simplest inter-nucleon potential is that of the proton-neutron interaction in the
deuterium nucleus. By considering the interactions in a many-bodied problem to
be the summation of all the inter-nucleon potentials between two nucleons, the deu-
terium wave function can be used to model these larger systems. For this reason,
among others, deuterium's simple composition is an important factor in understanding the many-bodied problem and therefore a system of great interest in nuclear
physics. Work carried out in the 1970s and 80s in laboratories worldwide have been
moderately successful in describing the strong interaction for few-body systems. De-
spite advancements made over the last few decades, accurate measurements at low-Q2
have not been possible and important questions about minor, though still important,
aspects of the system remain unanswered.
At the MIT-Bates Linear Accelerator Center a comprehensive study of low-Q2
spin-dependent electron scattering from deuterium has been carried out using the
Bates Large Acceptance Spectrometer Toroid(BLAST).
Not only does the large ac-
ceptance of the detector allow for a study over a large kinematic range, the experiment
also explores the spin-dependent electromagnetic response by employing a polarized
electron beam from the MIT-Bates linear accelerator incident on an internal polarized deuterium target. Among the questions that interest us we concern ourselves
here with the presence of pre-existing A states in 2 H. This study is possible through
r-nucleon decay channel.
5
Theoretical calculations predict that A resonant states account for anywhere from
0.25 to 3.60% of the nuclear wave function, the most realistic predictions for deuterium
range from 0.3 to 1.0%[6]. Using the data from the BLAST experiment we develop a
reasonable subset of candidate events for A resonant states focusing on the A++A channel.
6
Chapter 2
Experimental Arrangement
2.1
Electron Beam
The longitudinally polarized electron beam of the South Hall Ring (SHR) located
at the MIT-Bates Linear Accelerator Center is used in this experiment. Polarized
electrons were accelerated to an energy of up to 1 GeV. The 500 MeV beam from the
linear accelerator is recirculated into the linac in order to reach the energies up to
nearly 1 GeV.
A schematic of the SHR is shown in Fig. 2-1, and ring parameters are given in
Table 2.1.
Table 2.1: South Hall Ring parameters.[1]
Parameter
Value
Energy Range
300-1000
190.204
1.576
9.144
MeV
m
MHz
m
> 100
99
mA
%
1-1000
2.856
1812
kHz
GHz
Circumference
Revolution Frequency
Bend Radius
Stored Current
Internal Duty Factor
Injection Frequency
RF Frequency
Harmonic Number
7
A
'- ~. -- -------------- -s.-o.
- -.-
¾1
-IJ'
--
J
';'
't ;
·.
112
.I
,
If
r
SIBERIAN
SNAKE
,.-/
i
: I
I o
I
I:
if
P .,
.
.
"1\
.-
_ _
---
1.
=__
. ---
- -
_ :
S.!- -, ,1·
:---:-
Figure 2-1: Schematic of the South Hall Ring.[l]
8
::
.
.
2.2
Toroid Magnet
Eight copper conductor coils form the BLAST magnet, symmetrically arranged around
the beam axis. The curvature to the trajectories of charged particles produced by
the magnetic field contributes to precise momentum resolution and tracking. The
coils are made of 1.5 in2 copper hollow conductor with a 0.8 in inner diameter. There
are 26 turns in each coil and the DC current of a coil is 6731 A. This generates a
maximum field of 3.8 kG.
2.3
2H
Polarized Target
There are two types of polarized targets used in experiments today, solid and gaseous.
Solid polarized targets have a high density which contributes to a high luminosity.
However for deuterium
samples, which come in the form of deuterated
(ND 3) in solid targets, the target polarization
ammonia
is very low at around 25%. Also,
solid ammonia targets are not pure atomic species which introduces higher levels of
background events from scattering on other atomic species in the target.
For the purposes of the BLAST experiment the target cell consists of a thinwalled target chamber which is fed with a polarized atomic gas. The target thickness
is approximately 0.2x1016 atoms/cm2 . The polarization direction is determined by
the low holding field produced by 3 Helmholtz coil pairs. This means that the target
polarization can be reversed rapidly. This target type is advantageous for the purposes
of BLAST as it results in higher polarization, around 85%, and it is present as pure
atomic species reducing dramatically the effect of background events.
2.4
The BLAST Detector
The Bates Large Acceptance Spectrometer Toroid (BLAST) detector, shown in Fig. 2-
2, is instrumented in two of the eight sectors of the BLAST toroidal spectrometer
magnet. The detector packages consist of drift chambers, Cerenkov counters, scintillation detectors and neutron detectors.
9
Wire Chhmhprq -...
"'
.
^
"' ' 1rll-t
.
Tv Counters
LLU
TOF Scintillators '
Figure 2-2: Schematic of the BLAST detector.[1]
2.4.1
Drift Chambers
Drift, or wire, chambers are used to track charge particles through the magnetic field
in order to determine vector momenta and their points of origin. In both the left and
right sector there are three drift chambers which cover the angular range between
20° and 80° . The passage of a charged particle through the drift chambers causes
a local ionization, this in turn causes a discharge between the cathode and anode.
From this information one can determine the coordinate where the particle crossed
the chamber. Using the information from the three chambers, the path of the particle
can be reconstructed.
2.4.2
Cerenkov Detectors
Cerenkov detectors are used to discriminate
electrons from pions, r-, in BLAST.
There are four Cerenkov counters in each sector, only 3 are considered here. These
detectors are made of material with an index of refraction close to that of air, for
10
Table 2.2: TOF time separation between the positive particles[7].
Kinetic Energy
P-7r+
400
200
p- 2H
At
MeV
MeV
TOF Timing Resolution
6
8
ns
ns
750
ps
BLAST this is aerogel. A charged particle with velocities close to the speed of light
passing through this material will emit radiation which is used to discern what type
of particle it is. For angels forward of 40° the index of refraction is n = 1.020 while
for angles backward of 40° the index of refraction is n = 1.030
2.4.3 Time-of-Flight Scintillators
Time-of-Flight (TOF) scintillators provide timing signals for triggering and particle
identification. For identification between the pion and the proton, the timing separation at the TOFs are summarized in Table 2.2. As the time separations are well
above the timing resolution of the TOFs they provide a dependable source for particle
identification.
There are 14 TOFs with thickness of 2.5 cm per sector. The TOFs have coverage
between 15° and 85° from the center of the target. This coverage extends beyond the
drift chambers in order to include curved tracks.
2.4.4 Neutron Detectors
The neutron detectors have an angular coverage of 38° to 70° . The right sector is
instrumented with one OHIO wall and four LADS wallsl. The left sector is instrumented with one OHIO wall.2
1These walls are named accordingly because the first set were constructed by Ohio University
while the other set stands for Large Acceptance Detector System.
2In this work we focus on the (r+p) decay channel for the A++ resonance, therefore we will not
use the neutron detectors.
11
Chapter 3
Resonant State Study
3.1
A Resonance
There are four charge states of the A(1232) resonance: A++, A +, A° and A-. The
widths of these resonances are on the order of
rF
100MeV, which indicates that
these particles have a short lifetime according to
h
= r
6.6 x 10- 22 MeVs
1 M eV
100MeV
6.6
24
6.6 x 10-243.
(3.1)
The lifetime given in Eq. 3.1 makes physical sense as it is on the same time scale that
is typical for the strong interaction.
The deuterium wave function is dominated by the proton-neutron states but there
is a finite probability to find the deuterium nucleus in a AA state,
12H) = alpn)+/|IAA)
IAA) = aIA++-)+sIA+A
°)
Theoretical predictions for the contribution of AA states to the deuterium wave
equation range from 0.25 to 3.60%, with the most realistic range being from 0.3 to
1.0%[6].
The constituent A states result from a pion exchange between the proton and
12
A
P
7C
TA
n
A
Figure 3-1: Schematic of the pion exchange process that produces the A resonances
within the deuterium nuclei.
a)
b)
q
/,nx
A
A
,Si/_
/
'
intermediate
particles in
Figure 3-2: Feynman diagrams where a)A+ and b)A° are intermediate particles in
the excitation and pion production process of a nucleon.
neutron as shown schematically in Fig. 3-1. A resonances can also be produced in
excitations of the proton or neutron as shown in Fig. 3-2. Notice that Fig. 3-2 only
shows the excitation processes for A+ and A °. Due to the conservation of charge,
there is no way to excite the proton or the neutron to produce the A++ or A- state.
Data for the (A+A°) states will be dominated by the excited resonances while the
(A++A-) will not compete with other production sources. For this reason we focus
on the (++A-)
states in this work.
13
q
Figure 3-3: This is a schematic of electron scattering on a nuclear system.
3.2
Kinematics
Fig. 3-3 shows a schematic for electron scattering on a nuclear system in the Plane
Wave Impulse Approximation
(PWIA). In PWIA only one photon is exchanged and
it interacts with only one nucleon, other nucleons are not directly affected by the
scattering. For this work PA, the target nucleus, is deuterium; PR, residual system,
is A-; and PN the struck nucleon is A++.
The incident electron has initial four-momentum, K = (E, k)1, and final fourmomentum, K' = (E', k'). The four-momentum exchange with the nucleus is therefore the difference of the two four-momenta for the electron, q = (w, q) = K - K'.
In the lab frame the other four-momenta are; PA = (MA, 0), PN = (EN, P~N)and
PR = (ER, pR)2 . We also assign a separate four-momentum to the struck nucleon
before it was hit, Pm = (E,
p).
Working with the resulting equations at each vertex we can derive the following
1For the energy of the electron we take the relativistic approximation, E I pl1.
2
Here EA = mA because piA= 6 in the lab frame, that is we assume the target nuclei is at rest.
14
relations,
Em = w- (TN + TR) = (MN + MR) - IA , Missing Energy
IPmr
n PR I ,
,2 = E2_
Missing Momentum
IP
12
Missing Mass.
However, as mentioned before, the lifetime of the A particle is extremely small and
will decay into a pion and nucleon almost instantaneously.
Therefore we must find
qualified events in the pion channels to analyze further the kinematics of pre-existing
A states.
3.3
(e,e'++) Event Rate
In this work we are searching for 2 H(e,e'A++)A-
events. Looking at the pion channel
this translates to 2 H(e,e'7r+p)r-n. Therefore the subset of events from the BLAST
data that we are looking for must have these qualities:
1. Three track event with one negative track and two positive tracks corresponding
to the scattered electron, 7r+and proton.
2. A Cerenkov detector should be triggered in the sector that corresponds to the
negative track. This rules out other negative particles such as r-.
3. Another accepted cut for the electron track is 3 > 0.99. This removes nonsense
events.
4. Event originates from within the target cell. Though the cell size is 60 cm
(-30cm to +30cm) the accepted range for events is +20 cm from the origin. 3
5. Each track should originate from the same vertex. For our purposes we present
a 5 cm cut on Az. 4
3
The gas density falls linearly from the center of the cell, an ideal vertex profile is a triangle
centered about the origin.
4
Az = zi - zj for i j and i, j = 1, 2, 3 since there are three tracks.
15
Table 3.1: Three track event yield for 2004 BLAST data.
Run Number
Cut
(- ++)
7803-8691
8692-9295
9296-9850
9851-10496
115762
116220
114189
109423
Cerenkov
18527
19039
18921
18769
/ > 0.99
11550
8025
4489
11783
8415
5050
12038
8656
5345
11938
8722
5695
10497-11072
11073-11559
11560-12013
166236
29739
19065
13940
9128
177918
32843
20410
14246
8126
245571
40846
25503
17759
9830
z < 20cm
Az < 5cm
(- ++)
Cerenkov
/ > 0.99
z < 20cm
I Az 1< 5cm
Table 3.1 summarizes the event yield for the 2004 BLAST data with each of
the above cuts cumulatively applied. Figures 3-4, 3-5, 3-6 show the data for runs
11560-12013with only the condition that each event has three tracks, one of which
is negative.
As we can see from these plots there is a significant difference in the
quantity of data between right and left sectors. It is interesting to note that the
data already have very clean vertex distributions, including a concentration of the
data around Az = 0. In the p plot for the negative track we also see that there is a
high concentration
of relativistic particles which would be electrons while there are
also other negative particles with lower velocity. For the other two tracks we observe
irregular spikes in the 0 and
have a large distribution
4 distributions.
The P plots for the two positive tracks
of slower particles, these are good candidates for protons
and pions.
Figure 3-7 shows the same data for the negative track with all of the cuts from
above applied. The data after all cuts have been applied are very clean, the difference
in magnitude between right and left sector has been reduced greatly and anomalous
negative tracks have been removed for the most part. The Az2 distribution reveals an
interesting characteristic at Az = 0 which requires further investigation. In similar
plots for the other two tracks, the second track is shown in Fig. 3-8, we also se that
16
the irregularities between sectors are reduced and the irregular spikes are eliminated
aswell.
17
c-
I-
1
J
Figure 3-4: Data for the negative track from runs 11560-12013,left sector data is in
blue and right sector data is in red; a)O, b)O, here 180' is added to the left sector
data to provide a comparison, c)momentum, d)3 focused on the range of 0 < P < 1,
e)charge, f)vertex, g)Az l , h)Az2.
18
1,
11
t
S.
i
'
tP
II
-,
!Wlc
I I
...
I
,II 1111 11
1.
I
I
F
II
U.j
.
.
.
I1
II
I
l~ il-
l1
I
qI
0
i
I
i
I
i
IIi
via
data is in
Figure 3-5: Data for the second track from runs 11560-12013, left sector
the left sector
blue and right sector data is in red; a)9, b)O, here 1800 is added to
< 1,
data to provide a comparison, c)momentum, d)3 focused on the range of 0 < /
e)charge, f)vertex, g)Azl, h)Az3 .
19
,,
Lc
- z.I- ..- z. I
--3
I
.
-I
,
i
I
i -.IIIR
i
I
I
L
II
Figure 3-6: Data for the third track from runs 11560-12013, left sector data is in blue
and right sector data is in red; a)9, b)q, here 180° is added to the left sector data to
provide a comparison, c)momentum, d)/3 focused on the range of 0 < 3 < 1, e)charge,
f)vertex, g)AZ2 , h)Az 3 .
20
[1
I
z
a
q
q
!
I
i
[
Figure 3-7: Data for the negative track from runs 11560-12013with all cuts applied.
The left sector data is in blue and right sector data is in red; a)6, b)O, here 180 is
added to the left sector data to provide a comparison, c)momentum, d)/3 focused on
the range of 0 < p < 1, e)charge, f)vertex, g)Azl, h)Az2.
21
[1
Figure 3-8: Data for the second track from runs 11560-12013with all cuts applied.
The left sector data is in blue and right sector data is in red; a)O, b),
here 180 is
added to the left sector data to provide a comparison, c)momentum, d): focused on
the range of 0 < p < 1, e)charge, f)vertex, g)Azl, h)Az 3.
22
Chapter 4
Discussion
As summarized by run grouping in Table 3.1, the total number of candidate events
from the 2004 BLAST data is 47663 events. This is from 450 k-Coulombs of data,
resulting in approximately
106 events per k-Coulomb.
As shown in the previous
section this data is very clean, particularly in the negative track where we have placed
cuts to eliminate any particle that is not an electron. There are some irregularities
in the positive tracks which require further investigation such as the
which should be flat and the Az 2 and Az 3 distributions
distribution
which have irregular dips
around Az = 0.
4.1
Future Plans
In continuation of this study the next steps to follow will be:
1. Impose a particle identification on the two positive tracks for the 7r+ and proton. Using a two dimensional plot of AT =TOF(positive track)-TOF(electron
track) vs. Ionization Energyl we expect two clusters; where the pions will be a
tight cluster with low AT and low ionization energy while the protons will be
in a broader cluster with higher AT and higher ionization energy.
2. With an acceptable particle ID applied, we can then assign mass values to each
1
This is the energy deposited by the particle in the scintillator detector.
23
of the tracks. This in turn allows us to reconstruct the 4-vectors of the for the
(e,e'pir+) particles.
3. With well defined 4-vectors for (e,e'plr+), we can reconstruct
A++ and A-.
24
the 4-vectors of
Bibliography
[1] The BLAST Collaboration. Bates large acceptance spectrometer toroid. Technical
design report, MIT-Bates Linear Accelerator, Aug 1997.
[2] C. Crawford. Precision Measurement of the Proton Electric to Magnetic Form
Factor Ratio with BLAST. PhD dissertation, MIT, Department of Physics, May
2006.
[3] A. Fix et al. Photopion reactions on deltas preexisting in nuclei. July 2004.
[4] A.I. Fix et al. Search for the
++
component in
12
c ground state using
12
c(-y,7r+p)
reaction.
[5] B. Povh et al. Particles and Nuclei: An Introduction to the Physical Concepts.
Springer, Berlin, fourth edition, 2004.
[6] H. Arenhdvel H.J. Weber. Isobar configurations in nuclei. PHYSICS REPORTS
(Section C of Physics Letters), 36(4):277-348, 1978.
[7] V. Ziskin. Measurement of the Electric Form Factor of the Neutron at Low Momentum Transfers Using a Vector Polarized Deuterium Gas Target at BLAST.
PhD dissertation, MIT, Department of Physics, April 2005.
25