Observation of muon induced electromagnetic showers with the Antares detector
Version 5, Date: 23.09.2009
Abstract
The Antares collaboration aims to detect high energy neutrinos from extraterrestrial origin. Relativistic
muons emerging from charged-current muon neutrino interactions in the detector surroundings
produce a cone of Cerenkov light which allows the indirect detection of the original neutrino. Though
the primary aim is neutrino astronomy, the detector detects mainly down-going muons, which are the
decay products of cosmic-ray collisions in the Earth's atmosphere. This article presents an algorithm to
identify electromagnetic showers induced along atmospheric muons with the Antares detector,
applied on both simulated and real data. It is shown that this new tagging method can improve the
resolution on muon track energy and opens the possibility to make new analysis where shower
information is relevant.
1 Introduction
The Antares neutrino telescope is located on the bottom of the Mediterranean Sea, 40 km o# the
French coast. The main objective is the observation of extraterrestrial neutrinos using the sea water as
detection medium for the Cerenkov light emitted by relativistic charged particles induced by neutrino
interactions around the detector. This light is detected by an array of photomultipliers tubes, thus
allowing the muon direction and energy to be obtained from the arrival times and collected charges.
The detector is installed at a depth of 2475 m, and consists of twelve vertical lines # 450 m long
equipped with a total of 885 photomultipliers. The lines are separated from each other by about 65 m.
They are anchored at the sea floor by a dead weight and held taut by a buoy located at the top.. The
instrumented part of the line starts at 100 m above the sea floor. Every 14.5 m along the line, there are
three photo- multipliers pointing downward at an angle of 45 # with respect to the vertical direction, in
order to maximize the detection of upward-going tracks. Antares is operated in the so called
all-data-to-shore mode,namely all information is digitised off-shore and sent to shore to be treated by
a computer farm. These data are mainly due to background light caused by radiative decays of the 40 K
diluted in the salt water and the bioluminescence emitted by bacteria colonies and living species. The
data are filtered by processes dedicated to relevant physics events. A detailed description of the
Antares detector is given in [4].
Although Antares is optimized for upward going particle detection, the most abundant signal is due to
the atmospheric downward going muons produced by the interaction of primary cosmic-rays in the
atmosphere. The processes contributing to the energy loss of a muon in water include ionization, e + e
pair production, bremsstrahlung, and photonuclear interactions. Below 1 TeV, the muon energy loss is
dominated by the continuous ionization process. Above 1 TeV, the muon energy loss is dominated by
pair production and bremsstrahlung [2, 8], which are radiative processes characterized by large energy
fluctuations and discrete bursts along the muon track. The average muon energy loss due to these
electromagnetic showers increases linearly with the energy of the muon allowing the determination of
its energy.
The Antares detector has the capability to follow high energetic muons over a few hundred meters.
Distinguishing electromagnetic showers could improve the pointing accuracy of the detector using a
dedicated track fitting algorithm. A similar measurement technique as the one presented in this article
has been recently published by the Super-Kamiokande experiment [7].
The aim of this work is to show how electromagnetic showers induced by highly energetic atmospheric
muons can be observed with the Antares detector. Section 2 explain the phenomenology of
electromagnetic showers in Antares. Section 3 describes an electromagnetic shower reconstruction
algorithm, and its performance with monte Carlo simulations . The last section compares these results
with those obtained with data taken in 2007 when the detector comprised only 5 lines.
2 Phenomenology of muon electromagnetic showers in Antares
At low energies, Cerenkov photons are emitted continuously along the trajectory of a relativistic muon.
Above 1 TeV, the stochastic nature of discrete energy loss can produce also electromagnetic showers.
The purpose of the electromagnetic shower reconstruction is to distinguish Cerenkov photons
produced contiuously along the muon track, hereafter called muon Cerenkov photons, from the
Cerenkov photons induced by electromagnetic showers, hereafter called shower photons. Because of
the radiation length in water (X 0 = 35 cm), these showers never extend more than a few metres and
can be considered point-like in the Antares detector.
They can be identified from a localised increase of the number of photons along the track.
They are emitted almost isotropically whereas muon Cerenkov photons are emitted at the
characteristic Cerenkov angle (42 degrees) with respect to the muon direction. As a consequence, the
direct muon Cerenkov photons reaches usually the PMT photocathode earlier than the shower
photons, and, because the photomultipliers are oriented downward, their acceptance is higher for
shower light than for light emitted by the downward going muons.
In summary, the main differences between the shower light and the muon Cerenkov light are that the
shower light is produced on a small length scale on the muon path and it arrives, in general, delayed
compared to the muon Cerenkov light.
Figure 1 shows an event recorded in 2007 when the detector comprised only 5 lines. Each of the five
panels corresponds to the date obtained from one of the line in the detector. These data have been
reconstructed from an algorithm superimposing a muon track (pure Cherenkov light) and several
spherical emission. This results in a downward-going muon and two electromagnetic showers
identified. The result of the muon reconstruction algorithm and the results of the shower
reconstruction algorithm are displayed. As can be observed from figure 1, most but not all photons are
associated with the muon track fit. Using the fitted shower positions from the shower reconstruction
algorithm, a prediction is made for the arrival time of the shower light. In general, the shower light
curves are de- layed with respect to the muon Cerenkov light curve. The photons not associated with a
reconstructed tracks are mainly random background photons due to the radioactive 40 K decays or the
bioluminescence. The bottom right panel in figure 1 displays the number of detected photons along
the muon trajectory. The electromagnetic showers are identified by an excess of emitted photons
along a muon trajectory over the continuous baseline of photons emitted by a minimum ionizing
muon. Each peak indicates an identified shower position on the muon trajectory..
3 Algorithm for shower reconstruction
In what follows, a hit is a photomultiplier signal exceeding a threshold of 0.3 photoelectron. The
shower algorithm consists of three steps. The first step look for a downward-going muon track
candidate, and if found reconstruct it. In the second step Afterwards, hits originating from one distinct
shower are selected from these reconstructed muons. The last step consists in a # 2 -minimization
procedure yielding the space and time position of the shower within the selected hits is performed.
Muon events are selected by using an existing muon reconstruction algorithm [1, 6] which provides an
estimate of the direction and position of the muon at a given time. The measured hit times of all the
hits from a reconstructed muon track are considered relative to the expected arrival time of a direct
Cerenkov photon, calculated as (see figure 2):
t CK i = t 0 + 1 c # z i z r i tan # CK # + n c r i sin # CK , (1)
where t 0 is a time of reference, c is the speed of light in vacuum, n is the refraction index of water (n is
about1.35) , # CK is the Cerenkov angle t42°) and r i is the perpendicular distance between the muon
trajectory and the PMT. The direction perpendicular to the track (r-coordinate) is given by the photon
momentum vector in water. Hits too far in time from the expected muon hit time, -t min < t i t CK i < t
max, are expected to be background hits and are rejected (see figure 3). The value for t min=20ns is
given by the timing resolution of the PMT and the dispersion of light in water, whereas t max=200 ns is
defined by the value where the number of signal hits approaches the background level.
Figure 1: Event display of an atmospheric muon event with two electromagnetic showers. The first five
panels show, for each line, the height of the photomultiplier tubes for each associated detected photon
as a function of its arrival time. In these panels, the origin on z-axis corresponds to the middle of the
line and the time o#set is with respect to the time of the first photon compatible with the muon
trajectory. The crosses represent all photons detected by the detector. The first five diagrams show the
fitted (black line) arrival time from the Cerenkov light of the muon. The black square are photons which
are used for the reconstruction of the muon trajectory. The fitted (red line) arrival time of the showers
light are displayed. A red circle around a cross indicates that the photon is used for the shower
reconstruction. The bottom right plot shows the number of emitted photons projected along the muon
trajectory. The peaks indicate the shower positions on the muon trajectory, with the reconstructed
shower positions (red triangles)
Figure 2: Schematic view of the Cerenkov light detection and the isotropically emitted shower light. The
thick line represents the muon trajectory, the thin line the path of the Cerenkov light and the thin
dashed line the path of the shower light. The muon goes through point (x, y, z, t). The Cerenkov light is
emitted at an angle # CK with respect to the muon track at point # CK i and is detected by a PMT as a
hit in point (x i , y i , z i , t i ). The shower light is emitted at point # i and is detected by the same PMT,
but later in time.
This time interval is subdivided in two intervals. The earliest one contains mostly muon Cerenkov
photons and is given by |t i t CK i | < t min . The hit time is mainly given by :
# CK i = z i z r i tan # CK . (2)
Corresponding to the Cherenkov photon emission. The second interval is defined by t min < t i t CK i < t
max and contains mostly electromagnetic shower photons, and the hit time under our assumption of a
spherical emission is given by t i = t + # i z c + n c # r 2 i + (z i # i ) 2 , (3)
Equation (3) has two distinct solutions 2 represented by # + i and # i . All calculated # CK i , # + i and # i
positions are shown in a one-dimensional histogram Figure 4 shows the number of detected photons
along the muon trajectory, for the same event as presented in figure 1. The shower signature is
recognizable as a peak which indicates a shower position on the muon trajectory. A one-dimensional
peak finder algorithm (see section 4.3) selects peaks with amplitudes higher than a threshold
identifying only statistically relevant peaks. The peak finder takes into account that if the two solutions
# + i and # i are used in di#erent peaks, the solution in the smaller peak is eliminated.
Figure 3: Time residuals for the measured photon arrival times relative to the calculated arrival times
of Cerenkov photons coming from the selected muon tracks in the Monte Carlo sample (see section
4.1). Contributions are shown for the direct and scattered pho- tons originating from the muon as well
as from the showers. Also shown are background photons. The three vertical lines define the early
time interval (between -20 ns and 20 ns) and the late time interval (between 20 ns and 200 ns).
Figure 4: The number of emitted photons along the projected muon trajectory for the same
atmospheric muon event with two electromagnetic showers as shown in figure 1. The peaks indicate
the shower positions on the muon trajectory, with the reconstructed shower positions (red triangles).
The last step of the algorithm is to calculate the electromagnetic shower space-time position assuming
that the light is emitted from a single point as a spherical wavefor each peak. A first estimate of the
shower space-time position # x s = (x s , y s , z s , t s ) as explained in [9] is used. Then, for a peak with N
hits with # x # j = (x # j , y # j , z # j , t # j ) a # 2 can be introduced:
# 2 = N # j=1 1 # 2 · # t # j t s n c # (x # j x s ) 2 + (y # j y s ) 2 + (z # j z s ) 2 # 2 . (4)
The # 2 is calculated assuming a time resolution of # = 10 ns for all hits. Only fits with a # 2 -probability
larger than 1% were taken as shower candidates. If the value is below 1%, hits are removed, until
among all possible combinations of the remaining hits used to calculate the shower position, a
satisfactory # 2 -probability is found.
4 Simulation and selection
The electromagnetic shower reconstruction was validated using the Corsika simulation code [10]. The
performance of the reconstruction algorithm for muons with electromagnetic showers was studied in a
sample of simulated atmospheric multi-muons with background light. Analysis cuts were optimized
with the sample of simulated events. The results of the shower reconstruction algorithm were then
compared to the data.
4.1 Simulation
Cosmic ray interactions in the atmosphere, with energies between 1 and 105 TeV, inciodent angle
between zero (vertical) and 85 degeress, and further shower development were simulated with Corsika
The primary cosmic ray composition and flux model is a simplified version 3 of the H˜orandel model
[11]. The hadronic interaction model chosen is QGSJET [12]. The muon propagation through water, the
discrete energy losses at high energies, the Tcherenkov light production and propagation, including
scattering, and the response of the five line detector was simulated using the Antares KM3 code [5]..
KM3 uses tables simulated with GEANT 3 which parametrize the amount of light and the arrival time
detected by individual PMTs. The muon propagation uses the MUSIC [3] code.
4.2 Muon selection
The shower algorithm makes use of tracks reconstructed by the muon reconstruction algorithm
described in [1] with two additional criteria. These criteria require the tracks
Figure 5: E#ciency (a) and purity (b) as a function of shower energy for reconstructed showers.
to be traced for at least 125 m and to have a minimum of twelve hits used in the track reconstruction.
These selected tracks are referred to as `long well-measured tracks' and account for around 65% of all
reconstructed tracks. The advantage of the long well-measured tracks is not only that the direction of
the tracks is better reconstructed but also that the tracks are long enough to have the possibility to
emit showers.
4.3 Shower selection
All photon emission locations calculated in section 3 are collected into a one-dimensional histogram.
The parameters in the algorithm are the width and the height of the peak. For each selected peak the
number of hits is integrated in a ±5 m position interval around the peak center. Only peaks having at
least 10 hits over the muon-track Cerenkov photon pedestal hits in a position interval of 10 m are
selected. The number of pedestal hits is defined as the average number of hits per track length times
the interval width.
To suppress the background and in order to make a constrained space and time shower fit, at least
five hits from di#erent positions in the detector are required in one peak. Finally, for each selected
peak the algorithm does a # 2 -minimization calculating the shower space and time position under the
assumption of a point-like shower source (see equation 4).
4.4 Performance and limitation of the shower reconstruction method
The shower e#ciency is given by the ratio between the number of well reconstructed showers and the
number of generated showers. Only generated showers which produce at least hits in five di#erent
positions in the detector are taken as shower candidates.
Number of showers 0 1 2 3 4+
Sources Variation in [%]
Background rate 30 kHz -0.2 +1 +10 -18 0
Background rate 120 kHz 0.0 -2 +14 +15 0
Max. muon energy loss -50% -0.1 +1 +15 -3 0
Max. muon energy loss +50% +0.1 -3 +6 -11 +50
PMT acceptance -1.2 +18 +30 +1 -30
Absorption length -20% +1.2 -18 -40 -80 -60 Total ±1.7 ±25 ±54 ±82 ±83
Table 1: Systematic uncertainty as a function of the number of reconstructed showers. The systematic
uncertainty is estimated by varying the background rate, the energy threshold to produce photons from
electromagnetic shower light or photons from Cerenkov light, the PMT acceptance and the water
absorption length.
A well reconstructed shower is defined as a shower position #x found at less than 25 meters from the
generation point. Monte Carlo studies show that the shower reconstruction e#ciency ranges from 10%
at low muon energy (300 GeV) to 30% at high muon energy (30 TeV). The final shower reconstruction
e#ciency after cuts is around 5%. The shower purity is given by the ratio between the number of well
reconstructed showers and the number of all reconstructed showers, requesting that at least one hit
from the generated shower is present in the list of hits used for the shower reconstruction. The final
shower purity is 70%, with variation from 40% to 90% from below 300 GeV to 1 TeV.At higher muon
energies the purity decreases, and reaches 60% at 30 TeV. A these energies the density of showers
along the muon track becomes comparable to the position resolution of the detector and showers
become indigushable from the Cherenkov light emission. Figure 5 shows the evolution of efficiency and
purity as a function of energy.
Muons with at least one reconstructed shower have on average 2.5 times higher energy than muons
without a reconstructed shower.
The relatively low efficiency is essentially due to tha fact that the algorithm has di#culties to identify
showers with less than 300 GeV.
Another difficulty comes from the fact that the showers one a single reconstructed muons can
originate from a physical events with several muons passing through the detector..
Light scattering, which is not included in the algorithm, also contributes to the loss of efficiency.
4.5 Systematic Uncertainties
The systematic uncertainty on the number of reconstructed showers is shown in Tbale 1 and is
evaluated from varying the flowing parameters in the simulation :




Background rate : a variation from 30 to 120... The systematic error arising from the
uncertainty of the background rate is estimated by varying the contribution from the
background from 30 kHz to 120 kHz. The measured detector background rate is around 60 kHz.
.
The uncertainties arising from the energy threshold to produce hits from electromag- netic
showers or hits from muon Cerenkov light is estimated by varying the threshold ±50% from its
default value of 1 GeV. .
The uncertainty in the angular acceptance of the optical modules is estimated by taking a
di#erent PMT parametrization of the angular acceptance. .
The uncertainty resulting from the water properties is estimated by repeating the analysis with
a water absorption length of -20% from its default value.
All systematic errors are added in quadrature. The largest systematic errors are pro- duced by the
di#erent PMT acceptance and the 20% shorter absorption length. Table 1 shows that when decreasing
the absorption length, less showers are reconstructed. A shorter absorption length makes the
reconstruction of showers more di#cult, because the photons are absorbed in the water before they
can reach the PMTs. On the other hand, the systematic studies show evidence that the shower
algorithm is stable against large variations of the background.
5 Comparison between data and Monte Carlo simulation
A sample of data corresponding to 47.3 days of data taking with low bioluminescence conditions
between January and December 2007 has been selected. The Corsika simulation has to be scaled by a
factor 0.87 to normalize the simulated muon rate to the measured data muon rate for the long
well-measured tracks. Figure 6a shows the angular distribution of the photons whose hits have been
used in the shower fit with respect to the muon direction. This distribution is expected to be isotropic
and is here distorted due to detector e#ects and to the cuts used in the analysis. The peak at around 42
is a contamination ???? of photons emitted under the Cerenkov angle. Figure 6b shows the time
residuals of all the hits used by the shower algorithm. This time residual is calculated for each
measured photon arrival time relative to the calculated arrival time of the shower photon. The width
of the shower time residuals of 10 ns is similar to the width of the muon Cerenkov time residuals [1].
The distribution of figure 7a shows the hit multiplicity of the selected showers (note that a minimal
number of five hits is required by the reconstruction algorithm). With the final set of applied cuts, the
average number of hits is 12. Counting the number of hits in one shower provides a first order estimate
of the energy of the shower. Showers with 12 reconstructed hits have on average a generated energy
of 350 GeV. Figure 7b shows the distance of closest approach to the muon track for each selected
shower. It is noticeable, that even when the measured events could consist of multiple muons,
Figure 6: The photon emission angle (a) and the time residuals for the photons used in the shower fit (b)
in data and the Corsika Monte Carlo simulation.
Figure 7: The relative number of photons used in the shower reconstruction (a) and the distance of
closest approach of the shower position to the muon track (b) in data and the Corsika Monte Carlo
simulation.
Figure 8: The muon event rate as a function of the shower multiplicity for data (points) and the Corsika
simulation (line). This distribution compares data and simulation after reconstruction without
correcting for the reconstruction e#ciency. The systematic error for the simulation are given by the
height of the blue bands. Only statistical errors are given for the data points.
the showers are mostly reconstructed near the fitted muon track. The distribution of this variable
suggests that most likely the reconstructed showers are belonging to the reconstructed muon.
The Corsika simulation distributions agree reasonably well with the data distributions. The event rate
as a function of the number of reconstructed showers is presented in figure 8. The distribution shows
the results for data and the Corsika simulation without correcting for the reconstruction e#ciency. Also
shown is the systematic error for the simulation, which is estimated in section 4.5. For the data points
only the statistical errors are shown. For the described set of selection cuts, the one-shower muon
events constitute about 5% of all muon events. The agreement over five orders of magnitude between
data and simulation is remarkable.
6 Conclusion
A method to reconstruct showers emitted by atmospheric muons has been applied to the Antares
detector for the first time. The essential element of the algorithm is that the selection of shower
photons is reduced to a one-dimensional problem. The performance of the reconstruction algorithm
has been validated using a sample of simulated atmospheric muon events. Finally, a good agreement
between data and simulation was found in the number of reconstructed showers.
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