Master’s Project
Signal modelling and verification with a cosmic ray telescope for
a scintillating fibre tracker in the context of the LHCb upgrade
Nicolas Durussel
Supervised by:
Guido Haefeli, LPHE EPFL
Barinjaka Rakotomiaramanana, LPHE EPFL
21.06.2013
Contents
1 Introduction
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2 LHCb
2.1 LHCb Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 LHCb Upgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Description of the SciFi module
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3.1 Principal dimensional characteristics . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Scintillating fibres characterictics . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 Silicon Photomultipliers characteristics . . . . . . . . . . . . . . . . . . . . . . . 12
4 Description of the telescope
4.1 Cosmic rays . . . . . . . . . . . . . .
4.2 Telescope elements . . . . . . . . . .
4.3 Other configurations of the telescope
4.4 Data Monitoring . . . . . . . . . . .
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5 Simulation
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5.1 Overview of the simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.2 Parameters of the Landau distribution . . . . . . . . . . . . . . . . . . . . . . . 18
6 Angular distribution
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6.1 Angular distribution of cosmic rays . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.2 Angular distribution for the telescope . . . . . . . . . . . . . . . . . . . . . . . 20
6.3 Influence on the cluster size distribution . . . . . . . . . . . . . . . . . . . . . . 21
7 Epoxy layer
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7.1 Di↵usion of the photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
7.2 Cluster size distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
8 Efficiency
8.1 Computation of the efficiency . . . . . . . . . . .
8.2 Influence of the seed threshold and of the number
8.3 Study of the distribution of ADC per cluster . .
8.4 Inefficiency of dead regions . . . . . . . . . . . .
9 Conclusion
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of PE/MIP
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Introduction
The future upgrade of the LHCb detector will require the change of several of its components. For the tracking stations, a technology using scintillating fibre (SciFi) modules and
silicon photomultipliers (SiPMs) is currently investigated. This report presents studies realised with a cosmic muon telescope based on the same technology and with a simulation
of this system. The geometric acceptance of the telescope and the angular distribution of
cosmic muons were implemented in the existing simulation to give a better description of the
system. The main objective of this work is to study the detection efficiency of the system.
Several aspects are studied in this context, such as the inefficiencies due to dead regions in
the detector. Some limitations of the simulation are also revealed by the comparison with the
data taken with the telescope. It is shown that the target of 99% set for the detector can be
reached, with the adjustment of some parameters such as the cuts imposed on the data.
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LHCb
2.1
LHCb Detector
Figure 1: LHCb detector [12]
The LHCb detector is a single-arm spectrometer, this particular geometry is chosen because the b hadrons are mainly produced in the forward and backward cones with respect to
the beam pipe. Figure 1 shows the layout of the detector, the z axis is aligned with the beam
pipe. The main elements of the detector are described below.
1. Vertex Locator: The vertex locator (VELO) is part of the tracking system, it allows to
make high-precision position measurements in the region close to the interaction point.
The VELO is composed of silicon strip detectors.
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2. Magnet: The role of the dipole magnet is to bend the trajectory of charged particles.
This is used to determine the momentum of those charged particles.
3. Ring Imaging Cherenkov Detector: The ring imaging Cherenkov detectors (RICH) are
present both downstream and upstream of the magnet, they are used for particle identification.
4. Tracking stations: Together with the VELO, the tracking stations make up the tracking
system. The trigger tracker (TT) is situated upstream from the magnet and is based on
a silicon microstrip technology. The stations T1, T2 and T3 are situated downstream
of the magnet. They use silicon microstrip detectors in the central region, close to the
beam pipe, and straw tubes farther away from the beam pipe. These two distinct types
of detectors are called the inner tracker (IT) and the outer tracker (OT) respectively.
Di↵erent technologies are used because the occupancy is much higher in the central region. The tracking stations are shown in Figure 2, where the silicon microstrip detectors
are depicted in purple and the straw tubes in blue.
Figure 2: LHCb detector, tracking stations TT and T1-T3.[13]
5. Calorimeters: The electromagnetic calorimeter (ECAL) and the hadron calorimeter
(HCAL) permit to measure the energy of the particles as well as their position.
6. Muon Detectors: The muon detectors are situated downstream of the calorimeters and
are used for muon identification. This provides vital information for the di↵erent trigger
systems.
2.2
LHCb Upgrade
An upgrade of the LHCb detector is scheduled in the upcoming years[1]. This upgrade will
increase the readout capabilities of the detector. Currently, the amount of data collected by
the LHCb detector in one year is limited at about 1fb 1 . The aim of the upgrade is to gather
data at higher luminosity, thereby reaching 5 fb 1 per year. This implies a 40 MHz readout
for the detector vs. the 1 MHz limit today. Moreover, the higher luminosity will generate
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levels of radiation higher than those currently observed. Hardware and software changes will
therefore be implemented in the context of this upgrade.
2.2.1
Tracking stations upgrade
One possible solution for the upgrade of the tracking stations (IT and OT) is to replace
the silicon microstrips (IT) and straw tubes (OT) detector by a central tracker (CT) based
on a scintillating fibre (SciFi) technology and an outer tracker (OT), still composed of straw
tubes [2, 3]. The other solution is one similar to the existing detector but with a larger area
covered by the IT. A schematic of the two solutions is presented in Figure 3. In any case,
the upgrade of the tracking stations is necessary to address the issue of the occupancy in the
region close to the beam pipe, which will exceed the capacity of the straw tubes detector.
This increase in occupancy comes from the fact that the detector will operate at a higher
luminosity. The work presented in this report was realised in the context of the R&D towards
a scintillating fibre tracker.
Figure 3: Two solutions for the upgrade of the tracking stations. Left: Central tracker with
scintillating fibre detector and outer tracker with straw tubes detector. Right: Inner tracker
with silicon strip detector and outer tracker with straw tubes detector.[2]
The CT is composed of 2.5 m long scintillating fibre modules with a mirror at one end (at
the beam pipe) and the signal detection and readout at the other end, out of the acceptance
region. The scintillating fibres are laid out in layers stacked up on top of each other (Fig.4).
The upgrade of the tracking stations with a scintillating fibre tracker presents several
advantages as well as some disadvantages:
1. Advantages
(a) Homogeneous detector and homogeneous material in the acceptance
(b) Cooling system and electronics out of the acceptance
(c) Transport of the signal out of the acceptance by the fibres themselves
(d) Sufficiently small channels to keep the occupancy low across the acceptance
2. Disadvantages
(a) Radiation hardness of the fibres and detectors
(b) Alignment of large modules (2.5m) at the innermost region of the detector
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Principle of the scintillating fibre detector
1. Particle interaction and light production: When a particle traverses the layers of scintillating fibres (Fig.4), ionisation of the medium occurs and scintillating light is produced.
The longer the trajectory of the particle in the fibres, the more photons will be emitted,
on average.




Figure 4: Particle passing through 5 layers of scintillating fibres.
2. Signal propagation: Once photons are emitted, they will propagate in the fibre until
they reach the interface between the fibre and the cladding (Fig.5). Then the path of
the photons depends on the angle at which they reach the interface. Some photons will
be lost and others will propagate inside the fibre. At one end of the fibre, there is a
silicon photomultiplier (SiPM), where the signal is detected, and at the other end, a
mirror to increase the light on the side of the detector (Fig.6).
Figure 5: Particle traversing a fibre.[9]
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






Figure 6: View of the fibre layer in the plane orthogonal to z.
3. Signal detection: The photons that reach the end of the fibre are detected by a silicon photomultiplier (SiPM). One SiPM is composed of 128 channels and each channel
contains 88 pixels (width: 4 px, height: 22 px). Figure 7 illustrates the case of a particle traversing the layer of fibres. The separations between channels are represented by
vertical lines and the pixels fired by the photons are shown in red. Note that in some
cases, pixels are fired even though they do not directly face a fibre which was traversed
by the particle. This can be the result of several causes. One possible cause is the case
of a photon going into one of the neighbouring fibres (crosstalk between fibres). This
can also be the result of crosstalk between pixels. Moreover, a layer of epoxy is present
between the end of the fibres and the SiPM, where a di↵usion of the photons can occur.
x0= 29.345 mm, θ_x = -3.66317 °
Figure 7: In red: pixels fired by the photons reaching the SiPM.
The signal of each channel is then integrated and an algorithm is used to identify the
hits and their position. This is explained in more details below.
4. Clustering algorithm: Every recorded event provides a value of the signal detected by
each channel. An algorithm is used on the data to determine the position of clusters.
A cluster is the result of the signal of a particle traversing the layer, or thermal noise.
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The idea is to adjust the parameters to obtain a maximum of clusters coming from an
ionising particle and to reject the noise.
An example of an event is presented in Figure 8. The illustration is focused on a
restricted number of channels, where a cluster is identified. The vertical axis represents
the signal detected by each channel (ADC count). The main parameters of the clustering
are:
(a) Seed threshold: If the signal is above this value for a channel, there is potentially
a cluster at this position. In Figure 8, this is the case for channel 58.
(b) Neighbour threshold: When a seed is found (i.e. channel with ADC > seed threshold), the neighbouring channels are examined, if the value of the signal is above
the neighbour threshold, the channel is considered part of the cluster. This is the
case for channel 57 but not channel 59. If the neighbouring channel satisfies the
condition, the next channel is also considered, etc. Here channel 56 does not satisfy
the condition.
(c) Sum threshold: Finally, the sum of the signals of all channels that are part of the
potential cluster must be above the sum threshold for it to be considered a cluster.
In this example, the resulting cluster is represented in red and the noise in black.
Figure 8: Thresholds for the clustering algorithm.
5. Track reconstruction: The track reconstruction is made possible with the superposition
of layers aligned at di↵erent angles. Note that here a ‘layer’ designates the five layers
of fibres. In the stack up of five layers of fibres, the fibres are always aligned to each
other. This stack up of five layers constitutes what will henceforth also be referred to as
a layer. The meaning should be clear from the context. The usual layout of a module is
constructed as a bi-layer, which comprises one straight layer (0 ) and one inclined layer
(e.g. 5 ), this is illustrated in Figure 9. One layer gives two parameters:
(a) One position on the z axis. This is obvious since the layer is orthogonal to the z
axis.
(b) One position on the axis that is orthogonal to z and orthogonal to the fibres. In
Figure 9, we can see two layers on the left, the one on top gives a position on the
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x axis and the bottom layer gives a position on the v axis. On the right, the top
layer gives a position on the u axis and the bottom layer gives a position on the x
axis.
The information provided by four layers (each with a di↵erent z coordinate) is enough to
reconstruct the track of a traversing particle. Note that, as shown in Figure 9, although
one layer is tilted with respect to the other, the edges of both layers are parallel to the
x axis. So the SiPMs are aligned with the x axis for both layers.
Figure 9: Layers aligned with di↵erent angles give positions on di↵erent axes. Note that
axes x, y, u and v are all in the same plane.
Note that unless otherwise specified, the value of the thresholds used for the clustering algorithm are always as follows: Seed threshold = 2.5 PE, Sum threshold = Seed threshold
+ 2 PE, Neighbour threshold = 1.5 PE. Moreover, there is another version of the clustering
algorithm called ‘step 2’ (explained in Section 8.4.2) for which it is allowed to jump a channel
to form a cluster. The method ‘step 2’ is always used, unless in Section 8.4.
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Description of the SciFi module
To develop the scintillating fibre detector for the LHCb upgrade, test modules were produced in order to study the properties and behaviour of the di↵erent components. These
modules are thus based to a large extent on the same principles as the ones foreseen for the
LHCb upgrade.
The drawing of one module is presented in Figure 10. The basis of the structure is a
sandwich with one piece of Rohacell (in purple) between two sheets of carbon fibre, and at
the extremities, pieces of polycarbonate (in grey) which are used as fixation support for the
mirror at one end and the SiPMs and the cooling system at the other end. The scintillating
fibre layer (in blue) is glued on this structure. One module is constructed as a bi-layer with
two of these structures glued togethet, one is straight and one is tilted. Three SiPMs (in
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dark grey) are aligned side by side at the extremity of each layer. The signal detected by the
SiPMs is carried by a flat cable (in pink) to the readout electronics (in green).
For these test modules, the layer of fibres does not cover the full width of the module. In
Figure 11, the photograph of the extremity shows that no fibres are present on the left-hand
side on a small portion of the module. Consequently, two SiPMs per layer instead of three
are used for signal detection in the specific case of those test modules.
Figure 10: SciFi test module (Drawing: F. Bernard)
Figure 11: Side view of the structure of the module.
3.1
Principal dimensional characteristics
The dimensions of the module are listed below and are also prensented in Figure 12.
1. Layer lenght: 220 mm
2. Layer width (fibres): 82.5 mm
3. Layer width with signal detection (2 SiPMs): 66 mm
4. Layer thickness: 1.15 mm
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5. Angle between layers: 5
6. Distance between the two layers: 30.21 mm (center to center)
Figure 12: Dimensions of the layers (Drawing: F. Bernard)
3.2
Scintillating fibres characterictics
The type of fibre used is the SCSF-78MJ from Kuraray, its emission peak is in the blue
at 450 nm [14], which corresponds well to the sensitive region of the SiPM. It has a trapping
efficiency of 5.4% and a numerical aperture of 0.72. The main characteristics of the fibre are
presented in Table 1 and Figure 13.
Fibre component
Core
Inner cladding
Outer cladding
Material
Polystyrene (PS)
Polymethylmethacrylate (PMMA)
Fluorinated polymer (FP)
Table 1: Fibre characteristics [14]
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Refractive index
nD = 1.59
nD = 1.49
nD = 1.42
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


Figure 13: Dimensions of the fibre [14].
D = 250 µm, To = Ti = 3% of D
3.3
Silicon Photomultipliers characteristics
1. Channel width: 250 µm
2. Channel height: 1.32 mm
3. Pixels per channel: 4 ⇥ 22 = 88
4. Number of channels per SiPM: 128
4
Description of the telescope
4.1
Cosmic rays
The modules described in the previous section are tested in a setup built as a telescope
to detect cosmic rays. The particles detected by the telescope are the products of cosmic
rays interacting with the Earth’s atmosphere. The cosmic rays are mostly protons and alpha
particles, and also some heavier nuclei and electrons and positrons. They come from outer
space and interact with the atoms in the high atmosphere and subsequently create so called
air showers [5]. These showers are composed of the particles created by the cosmic ray’s
interaction and their further decay products. Some of those decay products (e.g. muons) can
then reach the ground and be detected by the telescope. The telescope is situated at EPFL,
in the laboratory of high-energy physics (LPHE), altitude: ⇠380 m.
4.2
Telescope elements
The setup for the telescope is presented in Figure 14.
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Figure 14: Telescope setup.
4.2.1
Trigger system
The SciFi modules have a sample and hold logic and are read only upon a trigger. The
trigger is constituted by two scintillators put in coincidence.
A layer of lead is placed above the bottom scintillator, to filter out the electrons, which
produce small showers. This avoids the triggering at the passage of electrons, the targeted
particles being minimum ionising particles (MIP), in this case cosmic muons.
Dimensions:
1. Top scintillator: width 220 mm; length 500 mm
2. Bottom scintillator: width 140 mm; length 320 mm
3. Thickness of lead: ⇠ 5 cm
4.2.2
SciFi modules
Three modules are used, there are two modules as presented in Section 3 and a third
module with di↵erent dimensions. The relative position of the three modules is shown in
Figure 15. Note that each module is encased in a box, this provides a light-tight environment
for the module as well as a way to fix the position in the setup (Fig.16).
Dimensions of the third module:
1. Layer lenght: 860 mm
2. Layer width (fibres): 62.94 mm
3. Layer width with signal detection (2 SiPMs): 62.94 mm
4. Layer thickness: 1.17 mm
5. Angle between layers: 1
6. Distance between the two layers: 19.25 mm (center to center)
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Figure 15: Relative positions of fibre modules (Drawing: F. Bernard)
Figure 16: Setup with three modules (Drawing: F. Bernard)
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Temperature control
The cooling system allows to keep the SiPMs at a stable temperature, they are operated
at T ' 15 C. A stable temperature is important because the photon detection efficiency and
the gain of the detector vary with temperature if the bias voltage is kept constant, which is
the case in our setup.
The temperature is monitored in the setup by two sensors at the position of the SiPMs in
each of module 1 and module 2. Figure 17 shows the temperature monitoring over a period
of 24 hours. The maximal variation observed is about 0.25 C.
Figure 17: Temperature monitoring over a period of 24 hours. Note that the o↵set of the
temperature was not calibrated, therefore only the variations of temperature must be
considered.
4.3
Other configurations of the telescope
In previous configurations of the telescope, only the two short modules were included (the
long module was not available at that time). The two-module configuration allowed us to
have a good understanding of the detector.
In Figure 18, we can see the distribution of the sum ADC per cluster for the four layers
of the telescope, in the two-module configuration. The horizontal axis represents the sum
of the signal contained in a cluster (in terms of ADC). If we divide this axis by the gain of
the detector, it gives the number of photoelectrons (PE) gathered by the detector, which is
proportional to the energy deposited by the particle. The peak of the distribution corresponds
to the most likely value for the energy deposited by a minimum ionising particle (MIP). We
observe in the figure that the distribution for the layers P1 L1 and P2 L1 is somewhat shifted
to the left. The shift of 150 ADC corresponds to a di↵erence of 2.5 PE between the lowest
and the highest light yield. Several causes were investigated to explain this shift:
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Figure 18: Data (two module configuation): Sum ADC/cluster distribution for the di↵erent
layers. Gain: 60 ADC/PE.
1. Since the two layers P1 L1 and P2 L1 were each the top layer of the bi-layer module,
it was conjectured that interactions in the top layer could create secondary particles,
resulting in more energy deposited in the bottom layer. This hypothesis was tested by
flipping the telescope, i.e. the order of the four layers on the z axis was reversed.
2. The individual response of each SiPM was not uniform, this could come from a bad
optical coupling between the SiPM and the fibre or from a deficient SiPM. This hypothesis was tested by verifying the optical coupling and by switching the position of some
SiPMs.
3. The light yield is not uniform across the width of the fibre mat, which could result in
a non-uniformity of the signal detected by each SiPM. This hypothesis was tested by
switching the position of some SiPMs.
None of the hypotheses mentioned above could explain the di↵erence and therefore a
statistical fluctuation has to be assumed to be the cause. However, these tests improved the
know-how to operate the detector and the understanding of the behaviour of the di↵erent
components. The third module was then added with the objective to measure the efficiency
of the detector. The data used and presented in what follows was taken with the 3 module
configuration.
4.4
Data Monitoring
Some problems associated with the equipment occurred during the data taking process,
such as intermittent shutdowns of the bias voltage power supply and a badly connected cable
for example .
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If the data acquired during a run where such problems happen is then used for analysis, the
results may lead to some inappropriate conclusions. It is therefore useful to implement a way
to monitor the acquired data. One good indicator of the ‘quality’ of the data is the proportion
of events where exactly one cluster per layer is detected, these are ‘good events’. These events
are interesting for further analysis because they can be used for track reconstruction for
example.
A monitoring system for the telescope was implemented. First of all, the data files should
be written frequently to avoid losing too much time and data in case of a problem (e.g. one file
should contain the data of one day rather than one week). The data can then be monitored
with the ratio of good events mentioned above. In Figure 19, we can see the example of a
file subdivided in ten parts. The horizontal axis represents the di↵erent parts of the file, it
can be assimilated with time, assuming events are recorded at constant rate. The ratio of
good events over all events remains fairly constant across the file at around 4.5%. However,
looking at Figure 20, we can see that at some point the ratio falls to zero, this was the case
of a power supply shutdown.
This type of monitoring is especially useful since we want to study the efficiency of the
detector. The loss of events due to a failure of power supply for example must not be mistaken
for a loss due to the inefficiency of the detector.
Figure 19: Data monitoring: 100,000 events
subdivided in 10 parts. Nominal behaviour.
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Figure 20: Data monitoring: 100,000 events
subdivided in 10 parts. Case of a power
supply shutdown.
Simulation
A simulation for the SciFi detector was developed [9, 10, 11]. This simulation was then
expanded with additional features and used to study di↵erent parameters and their influence
on the output of the simulation.
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Overview of the simulation
The simulation considers one layer and one SiPM. A particle traversing the layer is simulated at a random position, then the length of the trajectory of the particle in the fibre is
used for the emission of photons. The number of photons generated is distributed according
to a Landau distribution, with a mean proportional to the length of the path of the particle
through the fibre. The sigma of the Landau distribution is adjusted based on the measured
data (see Section 5.2). The photons are emitted in a random direction in the fibre, their
propagation is performed taking into account the refractive index of the fibre and claddings
as well as the attenuation. There is also a certain probability for cross talk between fibres,
when a photon goes into a neighbouring fibre. The photons then leave the fibre and traverse
the Epoxy layer before reaching the SiPM. The pixels of the SiPM are then fired by the photons. The signal is integrated for each channel of the SiPM, taking into account the electronic
noise, thermal random noise, cross talk between pixels and afterpulsing.
The output of the simulation is stored in a ROOT file. The analysis can then be performed
with the same tools on the simulated data and on the data from the telescope, which also
stores the data in ROOT files.
5.2
Parameters of the Landau distribution
The parameters defining the Landau distribution used for the creation of photons in the
fibre have a big impact on the output of the simulation. The Landau distribution is defined
by two parameters, one location parameter µ and one scale parameter .
In the simulation, the location parameter µ corresponds to the mean of the number of
photons created by millimetre of fibre traversed by the particle. This property was used to
artificially change the number of photoelectrons per minimum ionising particle (PE/MIP), in
reality for the telescope, the di↵erent values of PE/MIP can be obtained by modifying the
bias voltage of the SiPMs, and therefore changing the photon detection efficiency.
The value of the scale parameter was adjusted based on the data recorded with the
telescope. In Figures 21 and 22, one can see the distribution of ADC per cluster for the data
at 21.6 PE/MIP and for the simulation at 21.7 PE/MIP, respectively. The overall shape of the
distribution for the simulation is similar to the data. However, we notice several di↵erences,
which are emphasised in both figures with the dashed lines. The horizontal lines mark the
height of the peak of the distribution and the third of this value. The vertical in the centre
marks the position of the peak and the other two the intersection with the lower horizontal
line. The emphasis put on these points suggests a similarity to a gaussian distribution for the
data.
1. The construction with the dashed lines allows to calculate slopes on the left and on
the right for the top part of the distribution. This method provides a simple way to
evaluate the steepness of the distribution in this region. In this case, the slope on the
left is 1.61 [events/ADC] for the data and 1.75 [events/ADC] for the simulation. On the
right part of the distribution, the slope is 1.21 [events/ADC] for the data and 1.07
[events/ADC] for the simulation. We conclude that the simulated distribution is slightly
steeper on the left and less steep on the right, compared to the data.
2. If we look at the bottom right of the distribution, we observe that there are fewer events
in this region of high energy for the data than for the simulation. This might be due in
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part to the saturation of the readout electronics, which is not taken into account in the
simulation.
3. If we look at the bottom left of the distribution, we observe that there are more events
in this region of low energy for the data than for the simulation. This cause of this e↵ect
is not understood. We will see in Section 8 that this region is of particular importance
to compute the efficiency of the detector.
These observations show that the ADC/cluster distribution obtained with the simulation
is not totally satisfactory. Adjusting the parameters of the Landau distribution alone does not
suffice to achieve an accurate matching with the data, especially in the region of low energy,
which is important for the computation of the efficiency. The origin of this di↵erence has to
be determined, in order to have a simulation consistent with the real system.
P1_L1_sumAdcs_nodrs
Events
P1_L1_sumAdcs_nodrs
Entries
Mean
RMS
1400
34893
1421
510.8
1200
1000
800
600
400
200
0
0
500
1000
1500
2000
2500
3000
SUM Cluster ADC
Figure 21: Data: ADC/Cluster distribution.
21.6 PE/MIP, = 0.8, gain 60ADC/PE, seed
threshold 2.5 PE
6
Figure 22: Simulation: ADC/Cluster
distribution. 21.7 PE/MIP, = 0.8, gain
60ADC/PE, seed threshold 2.5 PE
Angular distribution
A new possibility for the angular distribution of the particles was implemented in the
simulation in order to give a better representation of the particles going through the telescope.
6.1
Angular distribution of cosmic rays
As mentioned previously, the telescope is used to detect cosmic rays, or more precisely
the particles that are the decay products of the air shower. These particles consist mainly
of muons. The angular distribution of cosmic muons at the ground was measured to be
proportional to cos2 ✓ [5], where ✓ is the zenith angle, i.e. the angle between the trajectory of
the particle and the vertical axis (Fig.23). The di↵erential flux has the form I(✓) = I0 cos2 ✓
[cm 2 s 1 sr 1 ], where I0 is the di↵erential flux for ✓ = 0.
This distribution for the zenith angle ✓ was implemented in the simulation and distribution
for the angle ' (see Fig.23) was assumed to be uniform in the interval [0, 2⇡].
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Taking the solid angle into account, the probability density f (✓, ') will respect:
f (✓, ') / cos2 ✓ sin ✓
6.2
(1)
Angular distribution for the telescope
The telescope has of course a limited acceptance. First of all, the position of the scintillators used for the trigger mechanism only allows a restricted range for the angles ✓ and ', for
a particle to go through both scintillators. Then, once the trigger condition is satisfied, the
position of the layers will also impose restrictions on angles ✓ and '.
6.2.1
Implementation in the simulation
The geometrical acceptance was taken into account in the simulation. For each particle, a
position is chosen randomly on the bottom scintillator, then the angles ✓ and ' are generated
according to the probability density mentioned above. If the trajectory of the particle goes
through all layers and scintillators, the event is kept, otherwise new angles ✓ and ' are
generated until this condition is satisfied.
Figure 23: Definition of the angles ✓ and ' for the trajectory of a particle.
6.2.2
Angular distributions for the data and for the simulation
In Figure 24, one can see the distribution of the angle ✓ in the data from the telescope.
In Figure 25, the angular distribution of the simulation is presented.
First, we observe that the range covered for the data is 0 to 35 and 0 to 33 for the
simulation. The di↵erence of 2 degrees can be explained by the uncertainty on the position
of the scintillators, which is not measured with a great accuracy. Second, the peak of the
distribution is situated in both cases around 7 degrees. Although the peak for the distribution
of the zenith angle is at 0 , the solid angle covered when ✓ is close to zero is suppressed by the
factor sin ✓ in equation (1). Third, we notice that there is a larger proportion of trajectories
with ‘large’ angles in the case of the data than in the case of the simulation. A possible
contribution to these large angles can be the scattering occurring in the building above and
around the telescope.
In Figures 26 and 27, we can see the distribution of the angle ✓x , for the data and the
simulation respectively. The angle ✓x is defined as the angle made with the z axis by track
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ThetaOfTheIntersection
Angle_before
90
htemp
Entries 20000
12.63
Mean
7.451
RMS
450
Angle_before
4618
Entries
14.97
Mean
8.505
RMS
400
80
350
70
300
60
250
50
200
40
150
30
100
20
50
10
0
0
5
10
15
20
25
30
Figure 24: Data: Distribution of the angle ✓
for the particles trajectories.
Horizontal axis: ✓ [ ], Vertical axis: number of
events
0
0
35
5
10
15
20
25
30
35
ThetaOfTheIntersection
Figure 25: Simulation: Distribution of the
angle ✓ for the particles trajectories.
Horizontal axis: ✓ [ ], Vertical axis: number of
events
projected in the xz plane. In this case, the possible range for the angle is very restricted since
the x axis is associated with the narrow edge of the layers. The distribution is not perfectly
symmetrical, this is again due to the fact that the scintillators are not perfectly aligned with
the three modules. We notice that number of events decreases linearly with the angle, this
comes from the fact that tan(✓x ) ⇡ ✓x and that cos2 ✓x ⇡ 1 for these small values of ✓x . We
can compare this with the distribution of the angle ✓x , in a situation when the geometry of
the telescope is not taken into account, with the angle ✓ in [0, ⇡2 ] and ' in [0, 2⇡] (Fig.28). In
this case, we find back the distribution proportional to cos2 ✓x .
In Figure 29, the distribution of the angle ' is presented for the simulation. We clearly
see peaks for ' ⇡ ⇡2 and ' ⇡ 3⇡
2 . This corresponds to the situation when the trajectory of
the particle is ‘aligned’ with the y axis, i.e. aligned with the length of the modules. The
acceptance of the telescope is of course larger in this case than when the trajectory of the
particle is aligned with the narrower edge of the modules (for ' ⇡ 0 and ' ⇡ ⇡).
6.3
Influence on the cluster size distribution
The influence of the angular distribution can be observed in the distribution of the cluster
size. The cluster size is defined as the number of channels included in the cluster. For example,
the cluster presented as an example of the clustering algorithm in Figure 8 is a cluster of size
two.
In Figures 30 and 31, the simulated cluster size distribution is presented in the case of an
angular distribution not restricted by the telescope geometry and in the case of the telescope,
respectively. Without geometrical restrictions on the angular distribution (Fig.30), the cluster
size ranges from 1 to 5, with a most likely size of 2. In the case of the angular distribution for
the telescope (Fig.31), we observe that 2 remains the most likely size, and even the majority
of the clusters are of size 2 (more than 70% here). However, we notice that almost all clusters
have a size ranging from 1 to 3. In that sense, the clusters are narrower in the second case.
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Theta_xOfTheIntersection
AngleX_before
AngleX_before
4618
Entries
-0.8279
Mean
3.49
RMS
100
htemp
Entries 100000
0.01404
Mean
3.894
RMS
2200
2000
1800
1600
80
1400
60
1200
1000
40
800
600
20
400
200
0
-8
-6
-4
-2
0
2
4
6
0
8
Figure 26: Data: Distribution of the angle ✓x
Horizontal axis: ✓x [ ], Vertical axis: number
of events
-10
-5
0
5
10
Theta_xOfTheIntersection
Figure 27: Simulation: Distribution of the
angle ✓x [ ]
This is expected since the particles can have trajectories with larger angles. This is especially
important for ✓x because this angle is closely linked with the number of fibres traversed by
the particle and more precisely, how widely spread they are on the x axis. A particle with
a large angle ✓x will result in a signal covering more channels of the SiPM, hence a larger
cluster size.
ClusterSize_8000
ClusterSize
Entries 19003
2.782
Mean
0.9645
RMS
0.9
Events
Events
ClusterSize_8000
1
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
1
2
3
4
5
0
6
Cluster Size
Figure 30: Simulation: Cluster size
distribution with the angle ✓ in [0, ⇡2 ] and ' in
[0, 2⇡]. Gain 60 ADC/PE, 14.2 PE/MIP
ClusterSize
Entries 19800
2.026
Mean
0.5226
RMS
1
0
1
2
3
4
5
6
Cluster Size
Figure 31: Simulation: Cluster size
distribution with the angle acceptance of the
telescope, Gain 60 ADC/PE, 11.7 PE/MIP
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Theta_xOfTheIntersection
htemp
Entries 100000
Mean -0.03012
RMS
32.58
2400
2200
2000
phiOfTheIntersection
htemp
Entries 100000
185.2
Mean
95.48
RMS
4500
4000
1800
3500
1600
3000
1400
1200
2500
1000
2000
800
1500
600
1000
400
500
200
0
-100
-50
0
Figure 28: Simulation: Distribution of the
angle ✓x , with the angle ✓ in [0, ⇡2 ] and ' in
[0, 2⇡]. Horizontal axis: ✓x [ ], vertical axis:
number of events
7
0
0
50
100
Theta_xOfTheIntersection
50
100
150
200
250
300
350
phiOfTheIntersection
Figure 29: Simulation: Distribution of the
angle ', vertical axis: number of events [ ]
Epoxy layer
As mentioned before, there is a layer of epoxy between the extremity of the fibres and the
SiPMs.
7.1
Di↵usion of the photons
The epoxy layer contributes to the di↵usion of the photons in two ways:
1. The photons exit the fibre with a certain angle. Therefore, the bigger the thickness of
the epoxy layer, the larger the lateral displacement.
2. The refractive index of the fibre (n=1.59) is larger that the refractive index of epoxy
(n=1.52). Therefore, the angle of the photon is amplified when it crosses the interface
between the fibre and the epoxy.
Both these e↵ects are illustrated in Figure 32. Here, the example shows the trajectory of
photon in the xy plane, which puts the emphasis on the displacement x, induced on the x
axis. The same phenomenon is of course also valid for the displacement on the z axis, however
we are more interested in the displacement on the x axis since this is the axis on which we
measure the position.
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Figure 32: The layer of Epoxy between the fibres and the SiPM.
In Figure 33, one can see the angular distribution of the photons when they leave the fibre
(the refraction at the interface fibre-epoxy is already taken into account). The angle ↵E is
the angle between the trajectory of the photon and the longitudinal axis of the fibre. There
is a clear drop at ↵E ⇡ 28 , this corresponds, this is due to the limit angle of reflexion of the
photon in the fibre, which is 26.7 . Taking into account the refraction at the interface of the
fibre and the epoxy, Snell’s law yields:
!
!
nF
1.59
↵E = arcsin
sin(↵F ) = arcsin
sin (26.7 ) ' 28.04
(2)
nE
1.52
where nF and nE are the refractive indices of the fibre and the epoxy, respectively, and ↵F is
the angle between the trajectory of the photon and the longitudinal axis of the fibre, in the
fibre. This corresponds to the value of the drop observed in Figure 33.
7.2
Cluster size distribution
To have a better understanding of the influence of the epoxy layer, a simulation was run
with di↵erent values for its thickness. One way to determine the influence of the epoxy layer on
the di↵usion of the photons is to look at the cluster size distribution for di↵erent thicknesses.
The thickness of the epoxy layer, in the case of the SciFi modules used for the telescope, is
120µm. The cluster size distribution in a data sample from the telescope is shown in Figure
34 for 13 PE/MIP. Let us now take a look at cluster size distribution for the simulation of
di↵erent thicknesses of epoxy. The distributions are presented in Figures 35 and 36, for 14
PE/MIP and 23 PE/MIP respectively. We can first compare the distributions for the data
and for the simulation. If we look at Figure 35, which is at approximately the same value
of PE/MIP, for a thickness of 120µm, the simulation is in good agreement with the data. In
both cases, we observe a dominance of clusters of size 2 (about 70%) and almost all remaining
clusters are of size 1 or 3 (about 10 to 20% each). At the higher value of 23 PE/MIP, we
observe a shift towards larger cluster sizes.
The influence of the epoxy thickness can be clearly observed in both Figures 35 and 36.
The increase in thickness results in bigger clusters. The main e↵ect is a decrease in the
number of clusters of size 1 and 2 and an increase in the number of clusters of size 3. We also
notice that a suppression of the epoxy layer (i.e. a thickness of zero), compared to the current
thickness of 120µm, would not have a very large impact, with roughly 5% of the clusters going
from size 3 to size 2. The inspection of the cluster size distribution is a first step towards an
analysis to be performed on the influence on the efficiency and the resolution of the detector,
which are the characteristics that matter ultimately.
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

































Figure 33: Simulation: Angle distribution of
the photons when they leave the fibre and
enter the Epoxy layer.
Figure 35: Cluster size distribution for
di↵erent thicknesses of Epoxy, 14 PE/MIP.
8
8.1
Figure 34: Data: Cluster size distribution, 13
PE/MIP.
Figure 36: Cluster size distribution for
di↵erent thicknesses of Epoxy, 23 PE/MIP.
Efficiency
Computation of the efficiency
The objective is to determine the efficiency of the detector. Here we will study the efficiency
of one layer. The efficiency is defined as the following ratio:
Efficiency =
number of reconstructed hits
number of particles that traversed the layer
(3)
In the simulation, the measure of the efficiency is straightforward. Each simulated event
corresponds to a particle traversing the layer, the efficiency is then the ratio of the number of
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events where a cluster is reconstructed over the number of all simulated events.
For the telescope, the measure of the efficiency is not as straightforward as for the simulation. First of all, the data must be processed and fulfill several conditions, first to reconstruct
tracks, then to determine the efficiency. The steps to process the data are explained below,
in the case of the study of the efficiency of layer P2 L1 (one of the two layers of the middle
module):
1. Track reconstruction: The top module of the telescope (module 3) and the bottom
module (module 1) are used for track reconstruction. The information provided by the
two layers of the top module and by the two layers of the bottom module allow to build
a track. Only events for which a track can be reconstructed are kept.
2. Intersection of the track with the middle module (module 2): One more condition must
be satisfied, there must be exactly one cluster on layer P2 L2 and its position must be
within 1 of the intersection of the track and the layer. The variable represents the
uncertainty on the position of the intersection, coming from the finite resolution of the
layers of module 1 and 3 used to build the track. The number of tracks that also satisfy
this condition is the denominator of equation (3).
3. Efficient vs. inefficient events: The final condition separates efficient events from inefficient events. Efficient events are those for which a cluster is found in layer P2 L1 within
a tolerance of 3 of the intersection of the track and the layer. The number of events
that satisfy this condition is the numerator of equation (3).
In this example we want to compute the efficiency the layer P2 L1, but the same process can
be used to determine the efficiency of the layer P2 L2, by switching P2 L1 and P2 L2 in the
steps above. Note that the computation of the efficiency is done for the ‘good’ regions of the
layer, if the intersection of the track falls within a dead region (dead channel of the SiPM,
gap between detectors, gap between fibres), the event is not taken into account.
8.2
Influence of the seed threshold and of the number of PE/MIP
The target efficiency for the detector is 99%. In what follows, we study the influence of
two parameters on the efficiency: the seed threshold and the number of PE/MIP. We want
to determine for which values of these parameters an efficiency of 99% can be reached.
8.2.1
Simulation
In Figure 37, one can see the efficiency for the simulation, plotted for di↵erent numbers
of PE/MIP and di↵erent values of the seed threshold (the neighbour threshold is always 1.5
PE and the sum threshold is 2 PE more than the seed threshold). We observe that for all
the curves, i.e. seed thresholds from 2 to 5.5, the efficiency increases with the number of
PE/MIP. This can be expected since a higher number of PE/MIP means a larger signal,
whereas a low number of PE/MIP corresponds to a lower signal, which might be too low to
identify a cluster. We also observe that the slope of the curves is large for low numbers of
PE/MIP and decreases until the plateau of an efficiency of 1.00 is reached. By definition of
the efficiency, the maximal value that can be reached is 1.00 (100%).
Figure 37 also shows that the value of the seed threshold has a clear e↵ect on the efficiency.
The bigger the threshold, the more clusters will be lost. For a seed threshold of 5.5 PE, the
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efficiency of 99% can only be reached at 20 PE/MIP. Whereas a seed threshold of 2 PE allows
to maintain an efficiency above 99% at values as low as 14 PE/MIP.
These observations show that, in the simulation, the target efficiency of 99% can be reached
with the appropriate values of the seed threshold and of the number of PE/MIP.
8.2.2
Telescope
The efficiency computed for the data of the telescope is presented in Figures 38 and 39,
for the layers P2 L1 and P2 L2, respectively. For the simulation, the computation of the
efficiency was performed on a sample of 100,000 events. For the data the samples are much
smaller, ranging from about 800 to 4600. These limited samples make it difficult to identify
the peak of the distribution of ADC per cluster, which corresponds to the number of PE/MIP.
For this reason, the computed values of the efficiency for the data do not yield clear curves,
as observed for the simulation. The efficiency presents some di↵erences from one layer to
another, which can also be explained by the limited sample. Two layers might present an
intrinsic di↵erence in efficiency but the data available does not allow to conclude on that
matter.
The same trends as for the simulation can be observed for both layers. However, we notice
that for a given number of PE/MIP, the efficiency is lower for the data. Di↵erences of 1 to
2% can be seen, depending on the region of the graph. An explanation about this di↵erence
is provided in the next section.
Figure 37: Simulation: Hit detection efficiency
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Figure 38: Data: Hit detection efficiency for
the data, layer P2 L1
8.3
N. Durussel
Figure 39: Data: Hit detection efficiency for
the data, layer P2 L2
Study of the distribution of ADC per cluster
Let us explain in more details the e↵ects of the seed threshold and of the number of
PE/MIP described in Section 8.2. For that purpose, we study the distribution of ADC per
cluster.
8.3.1
E↵ect of the seed threshold
Figure 40 shows the distribution of ADC per cluster for 14.8 PE/MIP and a seed threshold
of 2.5 PE. We observe a clear cut at the left of the distribution, which corresponds to the
sum threshold of 4.5 PE (the sum threshold is always 2 PE more than the seed threshold).
Indeed, with a gain of 60 ADC/PE, the sum threshold of 4.5 PE is equal to 270 ADC. This
is the value of the cut observed in Figure 40. The clusters rejected by this threshold, at the
left of the distribution, are the main contribution to the inefficiency. In Figure 41, the same
distribution is shown, but with a seed threshold of 5.5 PE. The cut of the sum threshold (7.5
PE), in this case, corresponds to 450 ADC, it is clearly visible on the left of the distribution.
The dashed line in Figure 40, marks the value of 450 ADC, the clusters situated on the left of
this dashed line are the main component to di↵erence in efficiency between a seed threshold
of 2.5 PE and 5.5 PE. This shows the direct impact of the thresholds used for the clustering
algorithm on the efficiency.
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Figure 40: Simulation: E↵ect of cuts - gain 60
- seed threshold 2.5 - 14.8 PE/MIP
8.3.2
Figure 41: Simulation: E↵ect of cuts - gain 60
- seed threshold 5.5 - 14.8 PE/MIP
E↵ect of the number of PE/MIP
Figure 42 shows the distribution of ADC per cluster for 24.2 PE/MIP and a seed threshold
of 2.5 PE. We observe that, compared with Figure 40, the cut corresponding to the sum
threshold of 270 ADC has almost no e↵ect. This comes from the fact that the distribution is
shifted at a higher value of PE/MIP. Figure 43 shows the same distribution but with a seed
threshold of 5.5 PE, we observe that even in this case, the corresponding sum threshold of 7.5
PE (450 ADC) has very little impact. More clusters are rejected than with a seed threshold of
2.5 PE but the di↵erence is small, compared with the di↵erence observed between Figures 40
and 41. This explains why the e↵ect of the seed threshold is much smaller at higher numbers
of PE/MIP, as it was observed in the efficiency plots presented in Figures 37, 38 and 39.
The observations made above also highlight that the left of the distribution of ADC per
cluster, i.e. the region at low numbers of PE/MIP, is a key component of the efficiency.
It was mentioned in Section 5.2 that the simulation does not provide a perfectly accurate
representation of the distribution in that region. This explains the di↵erence of efficiency
observed between the simulation and the data in Section 8.2. Indeed, if we look at Figures
21 and 22, the bottom left of the distribution has more clusters for the data than for the
simulation. Thus, more clusters will be rejected for the data, leading to a lower efficiency.
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Figure 42: Simulation: E↵ect of cuts - gain 60
- seed threshold 2.5 - 24.2 PE/MIP
8.4
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Figure 43: Simulation: E↵ect of cuts - gain 60
- seed threshold 5.5 - 24.2 PE/MIP
Inefficiency of dead regions
Types of dead regions
So called ‘dead regions’ are present in the detector along the x axis. These can be of
several types, listed below, and are illustrated in Figures 44 and 45.
1. Gap between two SiPMs: 0.41 mm
2. Gap in the middle of each SiPM: 0.25 mm
3. Edge of the SiPM, where there are no pixels: 0.17 mm on each side.
4. Gap in fibre: The fibre mat is an assembly of several ribbons. There is a gap between
the di↵erent ribbons (Fig.45).
5. Dead channels: Channels of an SiPM which detect no signal. One channel is 250 µm
wide.
We are interested in quantifying the portion of clusters lost due to the presence of such dead
regions. In Figure 44, we can clearly see that fewer clusters are found in the dead regions.
This plot shows what is defined as the ‘relative efficiency’ as a function of the position on the
x axis. The relative efficiency of a given channel is the number of clusters that are positioned
in this channel, normalised by the average number of clusters found in an active channel (as
opposed to dead channel). The position of a cluster is its centre of gravity, i.e. the weighted
average of the position of the channels included in the cluster, the weights being the ADC
count of each channel. The relative efficiency can be more than 1, as it can be seen in Figure
44, where the normalised average efficiency is marked with a red line.
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Figure 44: Relative efficiency as a function of the position on the x axis. Examples of dead
regions are indicated. Note that the bins have the same width as a channel and are aligned
with the channels.
Figure 45: Gap between two fibre ribbons.
8.4.2
Relative efficiency of dead channels
We study here the relative efficiency of 1, 2 and 3 dead channels in the simulation. Figure
46 shows the number of clusters per channel across an SiPM. Note that here the horizontal
axis is given in terms of channels, not in terms of the position x. However, no gaps are
implemented in the simulation, it is therefore equivalent to plot as a function of channels or
as a function of the x position. The width of a bin is the width of a channel. We observe
that the channels that are neighbours of the dead channels register a higher number of cluster
than the average, which is represented by the red line. This means that not all the clusters
that would be located in a dead channel are lost, there is a contribution to the neighbouring
channels.
It is important to remark that the choice for the binning is very important to notice this
contribution. The bins have the width of a channel and are centred on the channel number,
i.e. the bin for channel 30 covers the interval [29.5,30.5[. As stated before, the position (or
here, channel number) of a cluster is computed with a weighted average over the ADC count
of each channel included in the cluster. As a consequence, in the case of a dead channel at
position 30, there is absolutely no cluster with a position in the interval ]29,31[, because the
centre of gravity of a cluster of size one will be at 29 or 31 exactly and a cluster of size two
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or more, will necessarily have a centre of gravity < 29 or > 31. Then, for example, a bin
covering the interval [29,30[ would contain exclusively clusters of size one (those located at
29). The bin covering the interval [30,31[ would be empty and the bin covering [31,32[ would
contain the clusters of size one located at 31 plus some clusters of size two or more which
have a centre of gravity in the interval ]31,32[. This type of binning would always show more
events in the bin on the right of the dead channel than in the bin on the left of the dead
channel. This is why the binning is extremely important in this case.
























Figure 46: Simulation of 1, 2 and 3 dead channels. 21.4 PE/MIP, gain 50ADC/PE, seed
threshold = 2.5 PE
In Figure 47, the contribution from the dead channel to the neighbouring channels is
highlighted in green. The relative efficiency of the dead channel is defined as the ratio of
the number of clusters contained in this contribution and the average number of clusters per
active channel. In this case the relative efficiency of the dead channel is about 82%.
In Figure 48, a dead channel was also simulated but a di↵erent version of the clustering
algorithm (called ‘step 2’) was used. In this version, the clustering algorithm allows to jump
one channel to form a cluster. The centre of gravity of the clusters constructed in this way
can be located in the dead channel, which is what we observe in the figure. This additional
contribution from the dead channel is also represented in green. With this method, the relative
efficiency of the dead channel in that example is about 92%.
In the case of two or three dead channels, the relative efficiency is computed in a similar
way. For two dead channels, their relative efficiency is defined as the ratio of the contribution
to the neighbouring channels over twice the average of clusters/active channel. For three dead
channels, the contribution is divided by three times the average.
The relative efficiency was computed for one, two and three dead channels, at di↵erent
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N. Durussel




































Figure 47: Simulation of 1 dead channel.
Clustering with step 1. 21.4 PE/MIP, gain
50ADC/PE, seed threshold = 2.5PE





Figure 48: Simulation of 1 dead channel.
Clustering with step 2. 21.4 PE/MIP, gain
50ADC/PE, seed threshold = 2.5PE
numbers of PE/MIP. The results are presented, for a seed threshold of 2.5 PE, in Figures 49
and 50, for a clustering step of 1 and 2 respectively. We observe that the relative efficiency
increases with higher numbers of PE/MIP, the e↵ect is bigger for the case of one dead channel.
Comparing Figures 49 and 50, we also notice the improvement in relative efficiency produced
by the clustering step of 2. There is an improvement only for one dead channel. This is
expected, since allowing a jump of one channel is useless in the case of two or three dead
channels.
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Figure 49: Simulation: Relative efficiency in
the case of dead channels (seed threshold =
2.5PE, culstering step = 1)
N. Durussel
Figure 50: Simulation: Relative efficiency in
the case of dead channels (seed threshold =
2.5PE, culstering step = 2)
Figures 51 and 52 present the relative efficiency with a clustering step of 2 for a seed
threshold of 2.0 PE and 5.5 PE, respectively. There is a clear influence, the relative efficiency
is reduced for a higher threshold. This can be explained by the fact that the clusters present in
the neighbours of the dead channels will have a probability higher than average to be clusters
with a low ADC count, since part of the signal is lost in the dead channels. And we have seen
previously that the e↵ect of cuts is large for clusters at low ADCs.
The study of the simulated dead channels has shown that not all clusters are lost, there
is a contribution of the dead channels to the neighbouring channels. For one dead channel,
the clustering algorithm with a step 2 allows to recover some additional clusters.
A further improvement would be to study the relative efficiency for other types of dead
regions in the case of both the simulation and the data.
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Figure 51: Simulation: Relative efficiency in
the case of dead channels (seed threshold =
2.0, culstering step = 2)
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N. Durussel
Figure 52: Simulation: Relative efficiency in
the case of dead channels (seed threshold =
5.5, culstering step = 2)
Conclusion
The scintillating fibre (SciFi) modules associated with the silicon photomultipliers (SiPM)
is a technology being developed and studied for the future upgrade of the LHCb detector
tracking stations T1 to T3.
Two di↵erent ways to study the system are presented in this report: the use of the SciFi
modules and SiPM as a telescope for cosmic muons and the simulation of those elements. The
angular distribution of the simulation was adapted for a better description of the experimental
setup, by implementing the angular distribution of cosmic muons and the geometrical acceptance of the telescope. The study of the influence of the layer of epoxy between the fibres and
the SiPM showed that its suppression would not have a large impact. The relative efficiency
of the dead regions of the detector was studied in the case of dead channels in the simulation.
It was observed that the dead channels are not completely inefficient, as an increase in relative
efficiency is seen in the neighbouring channels. The efficiency of the detector was investigated
and we conclude that the target of 99% can be reached. The di↵erence in efficiency between
the simulation and the data is due to the imperfect representation of the energy distribution.
For a better description of the system, the e↵ects leading to this discrepancy have to be
identified in future work.
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N. Durussel
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