# Development and application of CATCH: A cylindrical active tracker and
calorimeter system for hyperon–proton scattering experiments

Y. Akazawa1 N. Chiga2 N. Fujioka2 S.H. Hayakawa3 R. Honda1 M. Ikeda2 K.
Matsuda2 K. Miwa2<EMAIL_ADDRESS>Y. Nakada4 T. Nanamura3,5 S.
Ozawa2 T. Shiozaki2 H. Tamura2,3 H. Umetsu2 1 High Energy Accelerator Research
Organization (KEK), Japan  2 Department of Physics, Tohoku University, Japan
3 Japan Atomic Energy Agency (JAEA), Japan  4 Department of Physics, Osaka
University, Japan  5 Department of Physics, Kyoto University, Japan

###### Abstract

In this study, we developed a new proton detector system called CATCH, which
was designed for a scattering experiment involving a $\Sigma$ hyperon and a
proton (J-PARC E40). CATCH is a cylindrical detector system covering an inner
target that can be used to measure the trajectory and energy of a proton
emitted from the target for the kinematic identification of a $\Sigma p$
scattering event. It comprises a cylindrical fiber tracker (CFT), a bismuth
germanate (BGO) calorimeter, and a plastic scintillator hodoscope (PiID),
which are coaxially arranged from the inner to the outer sides. The CFT is a
tracking detector consisting of 5,000 scintillation fibers, and it has two
types of cylindrical layers in which the fibers are arranged in straight and
spiral configurations. 24 BGO crystals are placed around the CFT to measure
the kinetic energy of the recoil proton. The PiID is used to determine whether
the recoil proton is stopped in the BGO calorimeter . We performed proton–
proton ($pp$) and proton–carbon ($p$C) scattering experiments using an 80 MeV
proton beam to evaluate the performance of CATCH. The total energy resolution
for the recoil proton was 2.8 MeV in $\sigma$ for the entire angular region
after the energy calibrations of the BGO calorimeter and the CFT. The angular
resolution of the CFT was 1.27 degrees in $\sigma$ for the proton, and the
time resolution was more than 1.8 ns in $\sigma$. We also developed an
analysis method for deriving the cross section of the $pp$ scattering using
CATCH. The obtained relative differential cross section for the $pp$ elastic
scattering was consistent with that obtained by reliable partial wave
analysis, and the systematic error was maintained at below 10%. These
performance results satisfy our requirements for a reliable detection system
for the $\Sigma p$ scattering experiment conducted at J-PARC.

###### keywords:

cylindrical detector , scintillation fiber tracking detector , bismuth
germanate (BGO) calorimeter , $\Sigma$-$proton$ scattering

###### MSC:

[2010] 00-01, 99-00

††journal: Journal of LaTeX Templates

##  1 Introduction

Scattering experiments involving a hyperon and a proton are the most effective
methods for investigating two-body hyperon–nucleon ($YN$) interactions, as is
the case in various intensive studies on $pp$ and $np$ scattering , which are
aimed at understanding nucleon–nucleon ($NN$) interactions. Scattering
observables, such as differential cross sections and spin observables, are
essential experimental inputs for constructing theoretical frameworks of $YN$
interactions based on the one-boson-exchange model assuming a broken flavor
SU(3) symmetry [1, 2, 3, 4]. The introduction of strange quarks is essential
for studying the role of quarks in the short-range region, where two baryons
overlap with each other. This is because the spin-flavor SU(6) quark model
predict significantly characteristic potentials in the short-range region,
such as significantly repulsive cores or attractive interactions depending on
the spin and flavor configuration of the quarks in the system [5, 6, 7].
However, regarding hyperon-proton scattering experiments, no experimental
progress has been made from the experiments conducted throughout the 1970s in
which hydrogen bubble chambers were employed [8, 9, 10, 11, 12, 13, 14]. This
is owing to the experimental difficulties stemming from the low intensity of
the hyperon beam and its short lifetime.

A new hyperon–proton scattering experiment, dubbed J-PARC E40, was proposed to
measure differential cross sections of the $\Sigma^{+}p$, $\Sigma^{-}p$ [15]
elastic scatterings and the $\Sigma^{-}p\to\Lambda n$ scattering [16] by
detecting more than 10,000 scattering events in the $\Sigma$ momentum region
ranging from 0.4 to 0.8 GeV/$c$. This experiment consists of two detector
components. The first component is the magnetic spectrometers for identifying
$\Sigma$ production. Because the $\Sigma$ hyperon’s lifetime is too short to
be delivered through a normal beam line, the $\Sigma$ hyperon is produced
inside a liquid hydrogen (LH2) target through $\pi^{\pm}p\to
K^{+}\Sigma^{\pm}$ reactions, and the momentum vector of the produced $\Sigma$
is tagged from the missing momentum in the $\pi^{\pm}p\to K^{+}X$ reaction
measured using the magnetic spectrometers. We regard such a $\Sigma$ hyperon
running in the LH2 target as a $\Sigma$ hyperon beam. The $\Sigma$ hyperon
interacts with a proton in the LH2 target with a probability that depends on
the interaction cross section between a $\Sigma$ hyperon and a proton. The
second component comprises a detector system that is placed around the LH2
target to identify the $\Sigma p$ scattering by detecting the recoil proton
and the decay products resulting from the $\Sigma$ decay. To identify the
$\Sigma p$ scattering events, the kinetic energy and the recoil angle of the
recoil proton should be measured to determine whether the detected proton is
consistent with the $\Sigma p$ scattering kinematics. For this purpose, we
developed a dedicated detector system called CATCH, which comprises a
cylindrical fiber tracker (CFT) for tracking, a BGO calorimeter for kinetic
energy measurement, and a plastic scintillator hodoscope (PiID) for providing
additional information regarding particle differentiation between a proton and
$\pi$ by verifying whether the particle is stopped in the BGO calorimeter.

In this paper, we describe the development and performance evaluation of the
newly constructed system called CATCH, including basic points, such as the
design concept, experimental requirements, and the fabrication of the detector
system.

##  2 Overview of CATCH for a $\Sigma p$ scattering experiment

CATCH is a cylindrical detector system for detecting recoil protons and decay
products from $\Sigma$ hyperons in $\Sigma p$ scattering experiments. It is
designed for the new hyperon–proton scattering experiment conducted at J-PARC.
One critical reason behind the low statistics associated with hyperon–proton
scattering experiments is the limited number of hyperon beams. For example, in
previous $\Sigma p$ scattering experiments conducted at KEK [17, 18], the
number of tagged $\Sigma^{-}$ beams was only 1.8 $\times$ $10^{5}$; this
limited number of beams resulted in poor statistical results regarding
approximately 40 scattering events [17]. In the J-PARC experiment, we shall
significantly improve the yield of the $\Sigma$ beam up to $8\times 10^{7}$
using high-intensity $\pi^{\pm}$ beams of 20 M/spill in which the spill
represents a beam cycle of 5.2 s with a beam extraction period of 2 s. In such
experimental conditions, CATCH is expected to operate stably under a high
singles count rate of approximately 2 MHz and have a sufficiently fast time
response to separate the scattering events from the accidental background. In
addition, a wider angular acceptance of the recoil proton is a crucial aspect
for maximizing the $\Sigma p$ scattering yield and the angular coverage.
Because the recoil proton is kinematically emitted to the forward angle in the
laboratory frame, a longer structure toward the direction of the $\pi$ beam is
desirable. Conversely, to ensure that the magnetic spectrometer is placed as
close as possible to the LH2 target, CATCH must be reasonably short in the
same direction to obtain a large acceptance of the scattered $K^{+}$, thereby
maximizing the yield of the $\Sigma$ beam. To satisfy both requirements for
the $\Sigma$ production and the $\Sigma p$ scattering, CATCH must be set up in
a significantly compact manner in the radial direction. We selected a detector
combination involving a cylindrical scintillation fiber tracker and a
calorimeter, as shown in Figure 1 to resolve both requirements.

Figure 1:  Proposed detector system called CATCH. CATCH comprises a
cylindrical fiber tracker (CFT) and a BGO calorimeter for measuring the
trajectory and energy of the protons emitted from the target installed inside
CATCH. The PiID is used to determine whether the recoil proton is stopped in
the BGO calorimeter. The upper half of the BGO calorimeter and the PiID is
omitted in this figure.

The CFT , which reconstructs the trajectories of charged particles, is a main
component of CATCH. It comprises eight cylindrical layers of scintillation
fibers. Each layer is placed coaxially from 49 mm to 84 mm in radius with a 5
mm interval in between the layers; the length of each layer in the direction
of the beam is 400 mm. The LH2 target, stored in a cylindrical target vessel
of diameter 40 mm and length 300 mm in the direction of the beam, is installed
in the inner center of the CFT. Owing to the flexibility of the arrangement of
the fibers, the required compact setup is realized by placing eight fiber
layers within a space of 35 mm in the radial direction. The CFT has two
different fiber configurations: the $\phi$ and $uv$ layers. In the $\phi$
layers, the fibers are placed parallel to the direction of the beam around
each layer’s cylinder surface; these $\phi$ layers are used to measure the
azimuthal angle ($\phi$). Conversely, in the $uv$ layers, scintillation fibers
are arranged in a spiral configuration along the surface of the cylinder. The
$u$\- and $v$-layers have opposite tilt angles to the direction of the beam.
The $uv$ layers are used to measure the zenith angle ($\theta$) of the track.
The trajectory of the charged particle obtained from the LH2 target is then
reconstructed three-dimensionally. To identify the $\Sigma p$ scattering
event, the angular resolution ($\sigma_{\theta}$) for the recoil proton
measurement should satisfy $\sigma_{\theta}<2^{\circ}$. In addition, the total
amount of the fiber material must be as small as possible to ensure the
detection of the low-energy protons down to approximately 20 MeV. Considering
the aforementioned requirements, the diameter of the scintillation fibers was
set to 0.75 mm. The necessary fast time response can be achieved by adopting
the CFT. To distinguish triggered events from accidental coincidences of
background events, the timing gate of the CFT must be narrower than 12 ns.
Therefore, a time resolution ($\sigma_{time}$) is required to be less than 2
ns in $\sigma$.

The kinetic energy of the recoil proton is measured using the calorimeter
around the CFT. The energy resolution must be higher than 3% in the $\sigma$
for 80 MeV protons to enable the identification of $\Sigma p$ scattering. The
crystal length should be 400 mm to cover the active region of the CFT in the
beam direction. A high-density calorimeter is also preferable to stop protons
up to 150 MeV. In addition, a non-deliquescent crystal is essential for
minimizing the material surrounding the crystal. Considering the points
presented above, we adopted a BGO-based scintillator as the calorimeter. 24
BGO crystals with a size of 30 (width) $\times$ 25 (thickness) $\times$ 400
(length) mm3 were placed at the outer circumference of the CFT. One concern
involving the BGO calorimeter is its relatively longer decay time of
approximately 300 ns. The singles rate for one BGO crystal is estimated to be
40–-400 kHz for charged particles depending on the condition of the $\pi$
beam. Under such a high singles rate, the pulse from the BGO calorimeter piles
up with a specific probability. Therefore, in the offline analysis, we adopted
a waveform readout using a flash ADC to decompose the accumulated signals.

We placed a PiID around the BGO calorimeter as the final component of CATCH.
In the $\Sigma p$ scattering experiment, both the protons and $\pi^{\pm}$
particles from $\Sigma$ decay are detected using CATCH. While the BGO
calorimeter was designed to be sufficiently thick for stopping recoil protons
of up to 150 MeV, many of swift pions penetrate the BGO calorimeter.
Therefore, the PiID provides additional information for identifying particles
by determining whether charged particles are stopped at the BGO calorimeter.

##  3 Structure and Development of CATCH

In this section, we describe each component of CATCH in detail.

###  3.1 Cylindrical Fiber Tracker (CFT)

A scintillation fiber is a fiber-shaped plastic scintillator; scintillation
photons are transmitted to the edge of the fiber through a total reflection
that occurs at the boundary between the inner core and the outer cladding with
different refractive indexes. Detecting the scintillation light at a fiber’s
edge face provides the hit information at the respective fiber’s position.
Therefore, a multi-layered fiber tracker can facilitate the reconstruction of
particle trajectories. A scintillation fiber tracker comprises many
scintillation fibers whose positions are well determined. Therefore, the
position information can be obtained by determining the correspondence between
the fiber segment hit by the particle and its fiber position. Trajectories are
reconstructed using multiple layers of arranged fibers.

The requisite characteristics of the scintillating fiber tracker employed in
our proposed application are as follows: First, the fiber can be arranged
flexibly with regard to shape. Second, its time response is sufficiently fast
to achieve better time resolution than 2 ns. Finally, the energy deposited on
the fiber can be measured. In our application of the CFT, fibers are arranged
alternately in a staggered manner along the cylindrical surface, and such
fiber-based cylindrical layers are stacked coaxially in eight layers. For
layer configuration, we introduce two types of fiber arrangements, i.e., a
straight $\phi$ layer and a spiral $uv$ layer in which fibers are arranged in
parallel and spiral configurations based on the direction of the beam, as
shown in Figure 2. By combining the hit information regarding different fiber
configurations, the trajectory of the charged particle can be reconstructed
three-dimensionally.

Figure 2:  Two types of fiber arrangements. The $\phi$ layer comprises fibers
that are arranged parallel to the beam axis. The $uv$ layer comprises fibers
arranged along the surface of the cylinder that is centered on the beam axis.

####  3.1.1 Design of the CFT

In this subsection, the coordinate axes defined in Figure 2 are used to
determine the cylindrical shape of the CFT. The $xy$ plane is defined as the
plane that is perpendicular to the central axis of the cylinder at the
upstream edge of the active region of the CFT; the azimuthal angle along the
circular direction in the $xy$ plane is referred to as $\phi$. The $z$ axis is
also defined as the central axis of the cylinder, and its origin is set to be
the upstream edge. Therefore, the center of the circle at the upstream edge is
defined as the origin of the coordinate, i.e., ($x,y,z$) = (0, 0, 0). The
active region of the CFT, where the fibers are placed in the desired location,
is designed to be 400 mm in the $z$ direction to cover the LH2 target. In the
spiral $uv$ layers, fibers are arranged at a tilt angle to ensure that they
rotate 360 degrees in the azimuthal angle $\phi$ from $z=0$ mm to $z=400$ mm
in one turn, as shown in Figure 2. Therefore there exists a correspondence
between $\phi$ and $z$ for each fiber in the $uv$ layers. Because the $\phi$
information regarding the $uv$ layer can be obtained through the tracking of
four $\phi$ layers, the position information associated with the $z$ direction
can be obtained, as demonstrated in Figure 3. We adopted a scintillation fiber
of diameter 0.75 mm from the Kuraray company (Kuraray SCSF-78M) by considering
the angular resolution, the number of readout channels, and the ease of
fabricating the CFT. The radial distance and the number of fibers for each
installed layer are listed in Table 1.

Figure 3:  Three-dimensional hit position of two fiber structures. The hit position in the direction of $\phi$ is obtained from the $\phi$ layers. The hit position in the $z$ direction is then obtained by combining the hits of the $uv$ layers with the $\phi$ information.  Table 1:  Radial distance and number of fibers for each installed layer. $\phi$ Layer |  $\phi$1 |  $\phi$2 |  $\phi$3 |  $\phi$4
---|---|---|---|---
Radial distance [mm] | 54 | 64 | 74 | 84
Number of fibers | 584 | 692 | 800 | 910
$uv$ Layer |  $u$1 |  $v$2 |  $u$3 |  $v$4
Radial distance [mm] | 49 | 59 | 69 | 79
Number of fibers | 426 | 472 | 510 | 538
Tilt angle [degree] | 37.6 | 42.8 | 47.3 | 51.1

####  3.1.2 Fabrication of the CFT

From the fabrication perspective, developing such cylindrical structures is
very difficult because of the narrow spacing between layers. To address this
difficulty, we fabricated four components containing one $u$ or $v$ layer and
one $\phi$ layer, separately. In each component, fibers with two different
layer configurations were attached to the detector frame, as shown in the
figure on the right side of Figure 4.

Figure 4:  Design of the CFT frame. The CFT comprises $4$ frames, including
one $\phi$ layer and one $u$ or $v$ layer for each frame to realize a compact
layer structure.

The actual fabrication procedure for the straight $\phi$ layer is as follows.
In the $\phi$ layer, the fibers must maintain their position over the entire
active area of 400 mm in the $z$ direction. The misalignment of the fibers
results in lower efficiency and worsens the angular resolution compared to
that of the ideal conditions. One technique for maintaining the position of
fibers involves ensuring that the neighboring fibers are attached to one other
using an adhesive to form a cylindrical shape. However, this method increases
the need for an adhesive material. This is not suitable for our proposed
application, because the detection efficiency for lower-energy protons
decreases due to the additional material. To address the difficulty of fiber
alignment, we prepared frames and position sheets to determine the fiber
position. The fiber positions at both edges of the active region were
determined using the fiber-fixing frame in which holes with a diameter of 0.80
mm were drilled along the fiber position, as shown in the enlarged figure of
Figure 5. As can be seen in the figure, fibers are arranged in a staggered
structure to minimize the ineffective area owing to the gap between the
fibers. To maintain the position over the active region, thin Mylar sheets of
0.1 mm in thickness, with holes corresponding to the fiber position, were
inserted at intervals of 50 mm, as shown in Figure 6. If the fibers are
stretched correctly with the appropriate tension, they are placed in the
desired position. For this purpose, we also added a function for adjusting the
fiber tensions to the frame structure, as shown in Figure 7. The fiber-fixing
frame at the downstream ($z=400$ mm), as shown in Figure 7, is used only to
determine the fiber position; the fibers are not attached to this hole.
Alternatively, the fibers are attached to the tension-adjustment frame, as
shown in Figure 7, whereas fibers on the other side ($z=0$ mm) are attached to
the fiber-fixing frame. Optical cement was used as the adhesive material for
attaching fibers to frames. Fiber tension can be adjusted by adjusting the
screws connected to the tension-adjustment frame.

Figure 5:  Fiber-fixing frames with holes for fiber to fiber attachment. These
were placed at both ends of the active region.  Figure 6:  Photo of a thin
Mylar sheet of 0.1 mm thickness with holes corresponding to the fiber
position.  Figure 7:  Fiber-fixing frame at the downstream to determine fiber
positioning. The fiber tension can be adjusted by adjusting the screws
connected to the tension-adjustment frame (Reflection edge).

The fabrication procedure for the spiral $uv$ layer is as follows. The fibers
in the $uv$ layer have to be arranged in a specific tilt angle along the
cylindrical surface. To realize the fabrication of such a challenging
structure, we decided to introduce fiber-positioning pillars at eight circular
positions set at 45∘ intervals, as shown in Figure 8. The pillar is made of an
acrylic bar of 1 mm thickness, and it has position pins of 400 $\mu$m diameter
to determine the fiber position, as shown in the enlarged figure of Figure 8.
The fibers are sandwiched by pairs of positioning pillars with position pins;
they have a zigzag configuration to minimize the ineffective area. Considering
the thickness of the material, it is better to remove these pillars as much as
possible. Positioning pillars were used throughout the fabrication process.
After placing all the fibers, a thin layer of epoxy glue was pasted to a
limitted region along the pillars to maintain the spiral shape. Finally, half
of the positioning pillars were removed, thereby leaving four of them at 90∘
intervals. Figure 9 shows the fabricated spiral layers in which fibers are
arranged in the desired spiral configuration.

Figure 8:  Fiber-positioning pillars at eight circular positions set at 45∘
intervals. The $z$ position of each fiber at the pillar location was
determined. The pillar comprises two acrylic bars and position pins.

Figure 9:  Fabricated spiral layers observed from the outside (top) and the
inside (bottom), respectively.

In one component, one spiral $u$ or $v$ layer and one straight $\phi$ layer
are placed at the inner and outer sides in the common detector frame,
respectively. These fiber edges at the downstream side ($z>400$ mm) are
attached to the detector frame, as shown in Figure 7. To increase the light
yield by reflecting the photon transmitted to this edge, an enhanced specular
reflector (ESR) sheet was attached to this surface as the reflector. The other
edge ($z<0$ mm) of the fiber is the readout side of the photon. This readout
edge of the fiber is guided to a hole in the readout frame, as shown in Figure
10. The fiber position at the readout frame corresponds to the position of
each photon sensor, which will be described in Section 3.1.3. To obtain a flat
surface for improved light transmission, the readout surface was polished
mechanically through diamond polishing.

Figure 10:  Photo of the fibers attached to the readout frame after passing
through the holes of the fixed frame.

These four CFT components were fabricated separately. Finally, the most inner
component was inserted into the neighboring outer component, and these two
components were attached to one another. This process was repeated until all
the four components were connected, as shown in Figure 11.

Figure 11:  Photo of the CFT after combining all the layers.

####  3.1.3 MPPC readout system using the EASIROC board

The scintillation lights in each CFT fiber are read out one after the other
using an multi-pixel photon counter (MPPC) (Hamamatsu S10362-11-050P) whose
active area is 1$\times$1 mm2 with 400 pixels of the avalanche photo diode
(APD). Because approximately 5,000 fibers are used for the CFT, the same
amount of MPPCs should be read out. We developed a printed circuit board (MPPC
PCB) on which 32 MPPCs are mounted in 2.54 mm pitch, as shown in Figure 12. To
ensure satisfactory contact between the fibers and the MPPCs, the MPPCs are
placed with a precision of more than 100 $\mu$m on the MPPC PCB. The fibers
are attached to the holes on the readout frame, where the positions of the
holes correspond to the MPPC position on the PCB. Using screws to attach the
MPPC PCB to the readout frame, the contact between the fibers and the MPPCs is
ensured. In total, 157 PCBs are used for the readout of the fibers in the CFT.

Figure 12:  Readout circuit board on which 32 MPPCs are mounted. Bottom
picture shows contact between the fibers and the MPPCs.  Figure 13:  Block
diagram and photo of VME-EASIROC. Two EASIROC chips are mounted on the board,
and these chips are controlled using the Xilinx FPGA Artix7. The red and blue
lines show the analog and digital lines, respectively, and the bold blue line
shows the digital bus line. Trigger signals are input from the front connector
and the VME J0 connector in the backplane. The communication between the PC
and VME-EASIROC is performed via Ethernet with a throughput of 100 Mbps.

To handle such a large amount of MPPCs, we developed a dedicated readout board
using an application specific integrated circuit (ASIC) of the extended
analogue silicon photomultipliers integrated readout chip (EASIROC) [19],
which was developed by Omega/IN2P3 to handle the multi-pixelated photon
detector (PPD). MPPC is a PPD produced by Hamamatsu photonics. The EASIROC has
preamplifiers, shapers, and a discriminator for each of the 32 channel inputs.
We developed a readout board designed for the CFT using the EASIROC, called
VME-EASIROC. The block diagram and photo of VME-EASIROC are shown in Figure
13. In the VME-EASIROC board, 64 channels of MPPCs can be read out by mounting
two EASIROC chips on the board. The control of the EASIROC chips and the
processing of the digital signals are handled by the Xilinx FPGA Artix7
(XC7A100-2FGG676) mounted on the VME-EASIROC board. A common voltage from an
external power supply is applied to the MPPC cathodes, whereas the anode
voltage can be adjusted using the digital-to-analog converter (DAC) in the
EASIROC chip with a precision of approximately 20 mV per channel. In the
EASIROC chip, two analog lines with different amplification gain settings
exist; both analog lines are followed by a charge preamplifier, a slow shaper,
and a switched capacitor for a charge measurement. The analog line with a high
gain setting (HG line) is optimized to measure small amounts of photo-
electrons, whereas that with a low gain setting (LG line) is suitable for
measuring large amounts of photo-electrons. The shaping time of the slow
shaper is adjustable from 25 ns to 175 ns. By inputting a trigger signal
(HOLD), the pulse height of the slow shaper is maintained in the switched
capacitor. In our application, we used the slowest shaping time of 175 ns to
ensure that the slow shaper pulse became the peak at the timing of the HOLD
trigger. The 32 channels of the switched capacitor for each analog line make
up an analog multiplexer and two analog multiplexers for the HG and LG lines,
respectively, which are connected to external ADC chips (AD9220). The A/D
converted 12-bit binary data are sent to FPGA , and thus, the charge
information of both the HG and LG lines for all channels are obtained
simultaneously. To suppress the huge amount of data, the pedestal suppression
function is also implemented in FPGA. For the timing measurement, the HG line
is also followed by a fast shaper with a shaping time of 15 ns. The fast
shaper signal is distinguished through the update type discriminator with a
common threshold for all 32 channels in one EASIROC chip; the threshold is set
by the register value of the threshold DAC. The logic signals from the
discriminators are fed into FPGA in parallel to measure its timing and time
over threshold (TOT) using FPGA-based multi-hit TDC (MHTDC). This MHTDC
measures the timing of leading and trailing edges of signals with a timing
precision of one ns. Data communication between the PC and the VME-EASIROC
board is performed via Ethernet with a throughput of 100 Mbps using a function
of a hardware-based TCP processor (SiTCP) implemented in FPGA [20]. The
detector data, including the charge and time measurements are transmitted
through SiTCP by generating Ethernet frames from the detector data.
Conversely, the slow control for setting the register of the EASIROC chip is
performed through a user datagram protocol (UDP) in the SiTCP function.

In total, 79 VME-EASIROC boards are used for the CFT readout.

###  3.2 BGO calorimeter

Figure 14:  Photo of the BGO crystal, whose size is $30\times 25\times 400$
mm3, for the scintillation calorimeter.

The BGO calorimeter comprises 24 BGO crystals whose size is 30 (width)
$\times$ 25 (thickness) $\times$ 400 (length) mm3; it is placed outside of the
CFT. Figure 14 shows the photograph of the BGO crystal used as the
calorimeter. Photomultiplier tubes (PMT) (Hamamatsu H11934-100) are used as
the readout sensors. The BGO calorimeter must have an energy resolution higher
than 3% ($\sigma$) for 80 MeV protons under the expected high singles rate of
40 to 400 kHz in the $\Sigma p$ scattering experiment. Under such a singles
rate, the pulse from the BGO calorimeter frequently accumulates owing to the
relatively long decay time of 300 ns. To decompose the accumulation events, we
selected the waveform readout using a flash ADC. If we consider the waveform
data of the raw BGO signal, a high sampling rate is necessary to detect the
fast leading edge of the signal. Because the BGO signal is significantly long
($\sim$1 $\mu$s ) in total, the data size becomes very large. To reduce the
data size, the BGO signal is filtered using an integral circuit and the shaped
signal is sampled at a low sampling rate of a few 10 ns. Because the sampling
points are coarse, the original pulse shape is reproduced by fitting the
sampled waveform data with a template function to maintain the energy
resolution. One more concern under the high singles rate is the stability of
PMT under the high current at the dynode. If the rated voltage of 900 V is
applied for PMT under such high rate conditions, the gain of PMT fluctuates
significantly owing to the voltage drop at the final dynode in PMT as a result
of the large dynode current. The instability of the PMT gain results in the
deterioration of the energy resolution of the BGO calorimeter. To suppress the
instability, PMT should be operated at a lower HV of approximately 600 V. We
developed a shaping amplifier circuit, which has the shaping circuit of the
integral filter, and an amplifier circuit to compensate for the lower gain of
PMT under the lower voltage operation. Figure 15 shows the circuit diagram of
the developed shaping amplifier. The first component is the integral circuit
whose time constant is set to 39.6 ns followed by the pole zero cancellation
circuit to shorten the falling time. The second component involves the two
stages of the non-inverting amplifier circuit, where the operational amplifier
AD811 is used. The typical amplification factors are 11 and 6.6 for each
stage, respectively. The final stage is a signal reset function, which forces
the output signal to be almost grand level by inputting a reset signal in the
Transistor-Transistor Logic (TTL) level. This function is prepared for data
suppression by combining the pedestal suppression function in a flash ADC
module (CAEN V1724). However, it was not used in the experiment. Figure 16
shows the waveform of the output signal of the shaping amplifier circuit. The
rising time is approximately 100 ns, and the falling time from the peak to the
10% level of the pulse peak is 370 ns. The minimum sampling points at the
leading region are three points, which are used to obtain the required energy
resolution by reconstructing the original pulse shape and by fitting it with
the template function of the waveform. Therefore, the sampling frequency of
the flash ADC was adopted to be 33 MHz. Through this readout method, the
energy resolution was 1.3% at 80 MeV with the proton intensity of up to 550
kHz in the test experiment.

Figure 15:  Circuit diagram of the developed shaping amplifier, which has the
shaping circuit of the integral filter and an amplifier circuit to compensate
for the lower gain of PMT under the lower voltage operation.  Figure 16:
Typical waveform of the BGO calorimeter after the shaping amplifier circuit.
The black points show the flash ADC data with a sampling rate of 33 MHz. The
blue line shows the reconstructed pulse shape by fitting the data point with a
template waveform.

###  3.3 PiID counter

For satisfactory particle identification, we also install a PiID counter,
which is a plastic scintillator located at the outside of the BGO calorimeter.
Basically, the particle identification is performed using the partial and
total energy deposit information ($\Delta E$-$E$) in the CFT fibers ($\Delta
E$) and the BGO ($E$) calorimeter. Because almost all $\pi$ particles
penetrate the BGO calorimeter, the hit information of the PiID counter helps
in the particle differentiation between $\pi$ and the proton. We adopted
plastic scintillators with a wavelength shifting fiber for a MPPC readout. The
PiID counter comprises 34 plastic scintillators whose size is 30 (width)
$\times$ 15 (thickness) $\times$ 400 (length) mm3. A wavelength shifting fiber
(WLS) of 1.0 mm diameter from the Kuraray company (Kuraray Y-11(200)M) is
mounted in a groove dug in the scintillator, as shown in Figure 17. Photons of
the WLS are read out using an MPPC (Hamamatsu S10362-11-100P) attached to the
scintillator with screws. The VME-EASIROC board is also used for the readout
of the PiID counter.

Figure 17:  Photo of the PiID counter. It comprises a scintillator of 30
(width) $\times$ 15 (thickness) $\times$ 400 (length) mm3 and a wavelength
shifting fiber 1.0 mm in diameter mounted in a groove dug in the scintillator.

##  4 Commissioning of the CFT using cosmic rays

The CFT was fabricated by placing fibers one after the other, as described in
Section 3. We focused on the fiber’s position and its tension to maintain the
desired position. However, there was a limit on the accurate placement of
fibers. In the experimental setup, where the CFT is placed horizontally, the
fibers are also deflected under its weight. Therefore, the actual fiber
position should be estimated in other ways. For this purpose, we performed the
CFT operation with cosmic ray measurement to collect calibration data for the
CFT fiber positions. In this section, we focus on the correction of the fiber
position with the cosmic ray data.

###  4.1 Cosmic ray measurement using the CFT

We accumulated cosmic ray data using the full setup of CATCH for approximately
10 days. In the entire operation of the CFT, 22 segments of fibers were
missing owing to problems in the MPPC and the scintillation fiber itself, out
of 4,932 fibers. These missing channels affected the detection efficiency of
the CFT; the efficiency will be discussed later. For data acquisition, the
coincidence between the two inner fiber layers ($\phi 1$ and $\phi 2$) was
used as the trigger. The ADC and TDC data of the CFT were read out using the
VME-EASIROC board for each fiber to reconstruct the trajectories of the cosmic
rays. To identify the hits in the fibers, the hit timing obtained from the TDC
was required to be within $\pm$20 ns from the triggered timing, as discussed
in the following analysis. Figure 18 shows an example of the cosmic ray event
detected using CATCH. As can be seen in this figure, the track of the cosmic
ray can be reconstructed from hits in all the 16 layers in combination with
the top eight layers and the bottom eight layers. Therefore the actual
trajectory can be estimated with improved accuracy even if the fiber position
used in the tracking is different from the actual position resulting from the
misalignment. To obtain trajectories using the CFT, two stages of tracking are
performed, as shown in Figure 19. First, a tracking in the $xy$ plane is
performed using the $\phi$ layers. By fitting the hit points of each $\phi$
layer with a straight line, the trajectory in the $xy$ plane can be obtained.
Next, straight tracking in the $zx$ or $zy$ plane is performed using the hit
information in the $uv$ layer. The $z$ positions in the $uv$ layers can be
estimated from the one-to-one correspondence between the $z$ position and the
azimuthal angle ($\phi$), which is obtained from the intersection between the
straight track in the $xy$ plane and the circle with the radius of each $uv$
layer. The trajectory in the $zx$ or $zy$ plane is then obtained by fitting
the hit points of each spiral layer. Therefore, the trajectory can be
reconstructed three-dimensionally using the CFT. For position calibration, the
deviation between the predicted position from the tracking and the used fiber
position was verified for all the fibers one after the other; the fiber
position was corrected to ensure that the deviation was small. We iterated the
tracking using the corrected fiber position and the correction of the fiber
position after the tracking until the deviation was negligible.

Figure 18:  Example of the cosmic ray event detected using CATCH. The tracks
of the cosmic ray reconstructed from the 16 layers and eight layers are also
shown using red solid lines and blue dashed lines, respectively.  Figure 19:
Tracking procedure of the CFT with two stages. To reproduce the actual fiber
position, the position correction was iterated because the tracking of the
$\phi$ and $uv$ layers is related.

We then describe the analysis for the fiber position correction in detail. The
$\phi$ layer determines the azimuthal angle $\phi$. To represent the deviation
of the fiber position, the difference in the azimuthal angle ($d\phi$) between
the original designed value and the reconstructed value from the tracking is
introduced, as shown in Figure 20. If the fiber position in the analysis
matches the actual fiber position, $d\phi$ should be 0. The top figure in
Figure 21 shows the $z$ dependence of $d\phi$ in the $\phi 3$ layer, where the
$z$ position is obtained from the tracking process. The deviation is small at
both edges of the active region ($z=0$ and 400 mm), where the fibers are
attached to the fiber-fixing frames, whereas the deviation increases at the
center region. This is consistent with the characteristics of the CFT
structure. The position deviation was corrected according to $d\phi$ as a
function of the $z$ position. Because the $z$ dependence of the deviation is
different from fiber to fiber even in the same layer, the position correction
for each 10 fibers was performed. A fifth-order polynomial function was
adopted to reproduce the $z$ dependence of $d\phi$ reasonably. After the
correction, the deviation was well suppressed, as shown in the bottom figure
of Figure 21. Next, the deviation in the radial direction ($dr$), as shown in
Figure 22, was also verified to obtain improved fiber position. Figure 23
shows the $dr$ distribution of the $\phi$ layer after correcting the position
of $d\phi$. This deviation was also corrected to remove this correlation. For
the evaluation of the $\phi$ deviation, cosmic ray events passing near the
central axis ($z$ axis) of the CFT cylinder were used because such
trajectories were sensitive to the deviation of $\phi$, as shown in Figure 20.
Conversely, for the evaluation of the $r$ deviation, tracks, apart from those
in the central axis were used, as shown in Figure 22. Such a separation
analysis was valid for circular-shaped detectors, such as the CFT.

Figure 20:  Definition of the deviation in $\phi$ ($d\phi$) in the $xy$ plane.
$d\phi$ represents the difference in the azimuthal angle $\phi$ between the
desired position and the estimated position from the tracking process.

Figure 21:  $z$ dependence of $d\phi$ in the $\phi 3$ layer. The $z$ position
is obtained from the tracking before (top) and after (bottom) the fiber
position correction.  Figure 22:  Definition of the deviation of the radial
position ($dr$) in the $xy$ plane. $dr$ represents the difference between the
desired position and the estimated position obtained through tracking in the
radial direction.  Figure 23:  $dr$ distribution of a specific layer after
position correction in the $d\phi$ direction.

The fiber position correction was performed similarly for the $uv$ layer,
where the correlation between the $\phi$ and $z$ positions was calibrated
using the tracking information fiber by fiber. The deviation of the radial
direction was also verified. We iterated the tracking using the corrected
fiber position and the correction of the fiber position after the tracking
until the deviation became negligible.

###  4.2 Angular resolution for the cosmic ray

The angular resolution of the CFT for the cosmic ray was evaluated after
completing the fiber position correction. The zenith angular ($\theta$)
distribution was obtained using the CFT, where 90o in $\theta$ corresponding
to the vertical direction in the laboratory frame because the $z$ axis was the
central axis of the CFT. For the evaluation of the angular resolution of the
CFT, we used the summation of both zenith angles ($\theta_{1}+\theta_{2}$),
where $\theta_{1}$ and $\theta_{2}$ were obtained through the top eight layers
and the bottom eight layers of the CFT, respectively. This
$\theta_{1}+\theta_{2}$ should be 180o for the same straight track, as shown
in Figure 24. The spread of $\theta_{1}+\theta_{2}$
($\sigma_{\theta_{1}+\theta_{2}}$) was obtained as 1.84o in $\sigma$. The
angular resolution ($\sigma_{\theta}$) obtained through the eight-layer
tracking was 1.30$\pm$ 0.01o assuming that the spread in
$\theta_{1}+\theta_{2}$ was expressed as follows:
$\sigma_{\theta_{1}+\theta_{2}}=\sqrt{2}\sigma_{\theta}$. This result
satisfied the requirement of 2o in $\sigma$ for the $\Sigma p$ scattering
experiment. The mean value of the $\theta_{1}+\theta_{2}$ peak was 179.99$\pm$
0.01o, as expected.

Figure 24:  The $\theta_{1}+\theta_{2}$ distribution measured using the CFT
for cosmic rays.

##  5 Performance evaluation of CATCH using a proton beam

To evaluate the performance of CATCH, proton–proton ($pp$) and proton–carbon
($p$C) scattering experiments were performed in January 2017 at the Cyclotron
Radio Isotope Center (CYRIC) in Tohoku University. An 80 MeV proton beam was
irradiated on a polyethylene (CH2) target of 800 $\mu$m thickness installed
inside CATCH. The experimental setup is shown in Figure 25. The scattered
protons were detected using CATCH. The target position was changed to three
different positions ($z$=54, 126, and 208 mm) to determine the $z$ dependence
of the performance along the sensitive area of 400 mm in the $z$ direction.
The trigger for the data acquisition was the coincidence between the inner two
$\phi$ layers and the RF signal of 50 MHz synchronized with the beam incident
timing from the accelerator. The experimental conditions are listed in Table
2.

Figure 25:  Setup for the $pp$ and $p$C scattering experiments with a CH2 target and CATCH. Table 2: Experimental condition of the CATCH test with a CH2 target in CYRIC. setup and conditions |  Polyethylene (CH2) target
---|---
Target Position |  |  $z$ = $54,126,208$ mm
---
change position with one target
Target thickness |  $800\mu$m
Beam particle | proton
Beam energy |  $78.5$ MeV
Beam size |  About $5(x)\times 10(y)$ mm2
Beam intensity |  About $0.05$ nA
Trigger |  CFT ($\phi$1 $\times$ $\phi$2) $\times$ RF
Beam time |  $3.5$ days

###  5.1 Overview of the performance evaluation of CATCH

We first describe the procedure for evaluating the performance of CATCH as a
system for measuring differential cross sections.

To identify the $pp$ and $p$C elastic scattering events, we require
information regarding both the scattering angle and the kinetic energy of the
scattered proton. The scattering angle of the proton is obtained using the
CFT, as explained in Section 4. The energy calibrations of the CFT and the BGO
calorimeter are performed by comparing the energy of the scattered proton
calculated from the scattering angle $\theta$ and the measured energy deposits
on each detector for the $pp$ and $p$C scattering events. For this purpose,
the CFT is necessary; it also affects the accuracy of the calibration
directly. Therefore, the tracking performance of the CFT is evaluated first.
After the energy calibration, the energy resolutions of the BGO calorimeter
and the CFT are evaluated.

To identify the $pp$ elastic scattering, we require that the relationship
between the kinetic energy and the scattering angle is consistent with the
scattering kinematics. Here, we define an index $\Delta E_{kin}$, which
represents the consistency in the $pp$ elastic scattering defined as follows:

$\Delta E_{kin}=E_{measure}-E_{calc}(\theta),$ (1)

where $E_{measure}$ represents the energy measured using the BGO calorimeter
and the CFT, and $E_{calc}(\theta)$ represents the calculated energy for the
scattering angle $\theta$ based on the $pp$ elastic scattering kinematics.
This index can be applied to other scattering reactions, such as the $p$C and
$\Sigma p$ scatterings using each kinematical relation between the energy and
the scattering angle. To identify the $\Sigma p$ scattering event from the
background reaction, the resolution of $\Delta E_{kin}$ is required to be
higher than 7 MeV in $\sigma$. The $\Delta E_{kin}$ resolution is evaluated
through the $pp$ scattering events. Finally, the differential cross section is
derived as the total performance of CATCH.

###  5.2 Angular resolution in the CFT

In the analysis, the fiber position correction explained in Section 4 has
already been applied. In the $pp$ scattering event, two protons are emitted
from the target. The opening angle between the two protons is slightly smaller
than 90o owing to the relativistic effect. Figure 26 shows the opening angle
distribution obtained by adding both scattering angles, $\theta_{1}$ and
$\theta_{2}$, for two protons. Assuming that the angular resolution is similar
for both tracks, i.e., the same assumption for the cosmic ray measurement, the
spread of the opening angle ($\theta_{1}+\theta_{2}$) should be
$\sqrt{2}\sigma_{\theta}$, where $\sigma_{\theta}$ represents the angular
resolution of the single track. The angular resolution $\sigma_{\theta}$ was
1.27$\pm$ 0.01∘. It is also crucial to verify the uniformity of the angular
resolution for all the azimuthal ($\phi$) regions. This uniformity was
confirmed by determining the $\phi$ dependence of $\sigma_{\theta}$, as shown
in Figure 27. From a simulation in which the misalignment of fiber positions
is not considered, the angular resolution was estimated as
$\sigma_{\theta}=1.04$∘ as a result of similar evaluations. Although there is
an insignificant difference between the angular resolution data and the
simulation data, the obtained angular resolution satisfies the requirement of
2∘.

Figure 26: The opening angle for the $pp$ scattering events. It was obtained
by adding the two scattering angles $\theta_{1}$ and $\theta_{2}$ for two
protons.  Figure 27: The $\phi$ dependence of the CFT angular resolution
($\sigma_{\theta}$). The angular resolution was obtained uniformly over the
$\phi$ direction.

###  5.3 Time resolution of the CFT

The time resolution of the CFT should be evaluated as one of the most crucial
performance evaluations of the CFT. This is because the time resolution
determines the minimum time gate for the truly triggered event under the high
counting rate in the $\Sigma p$ scattering experiment. As a result of the
analysis, the transmission time of the scintillation photon in the
scintillation fiber affects the timing resolution in the CFT. Figure 28 shows
the correlation between the time response of the CFT and the $z$ position of
the charged particle obtained from the CFT. There is a clear correlation
between these values corresponding to the propagation time of the light in the
fiber. This $z$ dependence in the time measurement was corrected using a
linear function. The results of the time resolutions without and with the $z$
position correction are listed in Table 3. The time resolution higher than 1.8
ns in $\sigma$ was achieved in all the layers.

Figure 28:  $z$ position dependence of the CFT time distribution of the $v$4
layer. The correlation corresponds to the propagation time of the light in the
fiber.  Table 3: Summary of the CFT time resolution ($\sigma$) for each layer
in ns.

$\sigma_{time}$ ns |  $u$1 |  $v$2 | $u3$ |  $v$4 |  $\phi$1 |  $\phi$2 |  $\phi$3 |  $\phi$4
---|---|---|---|---|---|---|---|---
not corrected | 2.02 | 2.24 | 2.39 | 2.47 | 1.98 | 1.98 | 1.86 | 1.83
z corrected | 1.57 | 1.68 | 1.63 | 1.68 | 1.76 | 1.72 | 1.54 | 1.56

###  5.4 Energy calibration of the BGO calorimeter

In this section, we describe the energy calibration of the BGO calorimeter
using the kinematic relation for the $pp$ and $p$C scattering experiments. As
explained in Section 3.2, the waveform data of the shaped signal with an
integral circuit were recorded using a flash ADC with a sampling frequency of
33 MHz. The pulse height and the timing of each waveform were obtained through
the template fitting method.

The energy of protons incident on the BGO calorimeter has a one-to-one
correlation with the scattering angle $\theta$ because the $pp$ and $p$C
elastic scatterings are two-body reactions. However, protons pass through the
CFT before they arrive at the BGO calorimeter. Therefore it is necessary to
consider the energy loss in the CFT to obtain the incident proton energy at
the BGO surface. Figure 29 shows the correlation between the scattering angle
$\theta$ and the BGO pulse height for protons. The two loci corresponding to
the $pp$ and $p$C elastic scatterings are confirmed in this figure. These
angular dependences of the pulse height were compared with the simulated
relation between the angle $\theta$ and the energy deposit in the BGO
calorimeter, as shown in Figure 30 and 31 for the $p$C and $pp$ scattering
events, respectively.

Figure 29:  Correlation between the scattering angle $\theta$ and the BGO
pulse height for protons.

Figure 30:  Angular dependences of the pulse height in the data (top) and the
simulated energy deposit (bottom) in the BGO calorimeter for the $p$C
scattering events. By selecting a large pulse height region of the BGO
calorimeter, $p$C scattering events were selected.

Figure 31:  Angular dependences of the pulse height in the data (top) and the
simulated energy deposit (bottom) in the BGO calorimeter for the $pp$
scattering events. In the data analysis shown in the top figure, the back-to-
back hit correlation in the $\phi$1 layer was required to select the $pp$
scattering event.

The $p$C elastic scattering events were selected in a large pulse height
region of the BGO calorimeter, as shown in the top figure of Figure 30. The
$pp$ scattering events can be selected more accurately by requiring the back-
to-back hit correlation in the $\phi$1 layer corresponding to the two protons
in the $pp$ scattering event. After this selection, the top figure of Figure
31 shows the correlation between the scattering angle and the BGO pulse height
for the $pp$ scattering event. To avoid the misidentification resulting from
the overlap between the $pp$ and $p$C scattering events, the angular regions
of 20 $\leq\theta$ (degree) $\leq$ 45 and the 20 $\leq\theta$ (degree) $\leq$
30 were selected for the $pp$ and $p$C scattering events, respectively. By
comparing the measured pulse height of the BGO calorimeter to the simulated
energy (bottom figures of Figures 30 and 31) for the same scattering angle
$\theta$, the relation between the BGO pulse height and the energy deposit was
obtained as shown in Figure 32. Light yield saturation with a large energy
deposit per unit length in the inorganic scintillator could account for the
correction. A phenomenological model describes this correlation by the
following equation [21]:

$PH=a\times E-b\times\ln\left(\frac{E+b}{b}\right),$ (2)

where $PH$ and $E$ correspond to the pulse height and the energy deposit in
the BGO calorimeter, respectively. The parameters $a$ and $b$ were obtained by
fitting the data points in Figure 32 with this function. The BGO energy
calibration was performed for all BGO segments using the method presented
above.

Figure 32:  Correlation between the measured BGO pulse height and the
simulated energy deposit for the $pp$ and $p$C scatterings. The red line shows
the energy calibration function of Equation (2).

####  5.4.1 The BGO energy resolution

In this section, the energy resolution of the BGO calorimeter is discussed. It
is difficult to evaluate the intrinsic energy resolution of the BGO
calorimeter from this experiment. This is because the energy spread in the BGO
calorimeter is affected by the energy struggling in the CFT. Here, we
approximately evaluate the energy resolution by comparing the data and the
simulation considering the energy resolution of the BGO calorimeter, and we
determine whether the assumed resolution is obtained. Figure 33 shows the BGO
energy distribution for the scattering angle of 25 $\leq$ $\theta$ (degree)
$\leq$ 30\. The peaks at 63 MeV and 48 MeV correspond to the $p$C and $pp$
scatterings, respectively. Because there are contributions of the $p$C
inelastic scattering, there exists a tail toward the low-energy side of the
$p$C elastic scattering peak. Therefore, the width of the $p$C elastic
scattering peak was estimated by fitting the energy spectrum of the asymmetric
region to exclude the contribution of the inelastic scattering. The energy
dependence of the BGO energy width ($\sigma$) was estimated from the $pp$ and
$p$C scattering events with different angular regions, as shown in Figure 34.
In this energy spread, the contributions from the energy resolution of the BGO
and the energy struggling in the CFT are included. This width was compared to
the simulation involving the same experimental setup, including the CFT, by
replacing the intrinsic energy resolution of the BGO with an assumption of
energy dependence of $\frac{\sigma_{E_{BGO}}}{E}\propto\frac{1}{\sqrt{E}}$ for
the BGO energy resolution. The experimental width could be approximately
reproduced through the simulation, where the BGO energy resolution was 1.5%
for 80 MeV protons. Therefore, the energy resolution with such levels might be
obtained, and it is concluded that the energy resolution is better than the
required value of 3% for 80 MeV protons.

Figure 33:  Energy distribution measured using the BGO calorimeter for the
scattering angle of 25 $\leq$ $\theta$ (degree) $\leq$ 30\.  Figure 34:
Energy dependence of the BGO energy width estimated from the $pp$ and $p$C
scattering events with different angular regions.

###  5.5 Energy calibration of the CFT

The energy calibration of the CFT was performed by comparing a measured ADC
value to a simulated energy deposit for each scattering angle $\theta$, as
mentioned in the calibration of the BGO calorimeter. The energy deposits for
protons with similar scattering angles are different in the $\phi$ and $uv$
layers owing to the layer structure. They are explained separately in the
following section.

####  5.5.1 Normalization of ADC data of the CFT

To ensure that the operating condition was uniform among all the MPPCs, the
amplification factor of each MPPC was set to be as uniform as possible by
adjusting the operation voltage one after the other through the VME-EASIROC
board. In the ideal case, the energy calibrations of the CFT should be
performed sequentially for each fiber to manage the possible gain difference.
However, this approach is not realistic owing to the huge numbers of segments
and insufficient statistics of the calibration data for each fiber. Therefore,
we normalized the ADC values for all fibers in each layer, and the calibration
was performed for the normalized ADC for each layer. The mean value of the ADC
distribution for the $pp$ elastic scattering of 20 $\leq$ $\theta$ (degree)
$\leq$ 30 was normalized to be five for all fibers. This normalized ADC was
calibrated to the energy of each layer.

####  5.5.2 Energy calibration for the $\phi$ layers

Because the $\phi$ layer’s fiber is placed parallel to the direction of the
beam, the path length inside the fiber depends on the scattering angle
$\theta$ of the proton, as shown in Figure 35. Specifically, for the proton
from the $p$C scattering experiment, the energy deposit in the fiber mainly
depends on the path length because the energy of the proton does not
significantly depend on the scattering angle. The top and bottom figures of
Figure 36 show the correlations between the scattering angle and the
normalized ADC (energy deposit for the simulation) of the $p$C scattering for
data and the simulation, respectively. The normalized ADC and the energy
deposit vary depending on the scattering angle. Similar to the energy
calibration of the BGO calorimeter, the normalized ADC of the CFT was compared
to the simulated energy deposit for each scattering angle, as shown in Figure
37. As shown in the figure, it is clear that the normalized ADC becomes
saturated for the large energy deposit owing to the saturation effect of the
MPPC. The output of the MPPC is proportional to the number of activated APD
pixels in the MPPC by incident photons. As the number of incident photons
increases, multiple photons are incident on the same APD pixel, thereby
resulting in the non-linearity of the output signals. The relationship between
the number of the activated APD pixels and the energy deposit, which is
assumed to be proportional to the number of the incident photons for
simplicity, is expressed as follows:

$N_{detected}=N_{pixel}\left\\{1-\exp\left(\frac{-b\times
dE}{N_{pixel}}\right)\right\\},$ (3)

where $N_{detected}$ and $N_{pixel}$ represent the numbers of activated APD
pixels and the effective pixels covering the fiber edge, respectively, and
$b\times dE$ corresponds to the incident photon number expressed from a
parameter $b$, i.e., a coefficient from the energy deposit ($dE$) to the
photon number. By fitting the correlation presented in Figure 37 to this
function, the energy calibration function is obtained. As a result, the
effective pixel number $N_{pixel}$ was 200, which was almost consistent with
the pixel number of 180 covered geometrically by a fiber of 0.75 mm in
diameter. Similar calibration functions were obtained for all $\phi$ layers,
and this was reasonable because the operational condition was almost common
for all MPPCs.

Figure 35:  Schematic illustration of the relationship between a path length
in a fiber and a scattering angle $\theta$ for the $\phi$ layer.

Figure 36:  (Top) Scatter plot between $\theta$ and the normalized ADC for the
$\phi$ layer. (Bottom) Simulated angular dependence of the energy deposit in
the CFT $\phi$ layer for $p$C scattering.  Figure 37:  Correlation between the
normalized ADC and the simulated energy deposit for the $\phi$ layer in the
CFT. The red line shows the calibration function obtained by fitting the data
points to the function defined in Equation (3).

####  5.5.3 Energy calibration for the $uv$ layers

Contrary to the $\phi$ layers, the energy deposit in the $uv$ layers does not
depend on the scattering angle because the cross section of the $uv$ layer
becomes elliptical, as shown in Figure 38. Therefore, it was difficult to make
the correlation between the simulated energy deposit and the normalized ADC,
as shown in Figure 37 for the $\phi$ layers. From the study of the $\phi$
layers, the effective pixel number is almost similar because it is determined
from the geometrical point of view between the MPPC and the fiber size.
Therefore, we also used $N_{eff}$=200 (the typical value for the $\phi$
layers) for the $uv$ layers. The parameter $b$ was then obtained, so that the
energy deposit for $\theta$=25o corresponded to the estimated value from the
simulation. Here, the ambiguity of the energy deposit in one fiber depends
strongly on the energy of the incident proton. To minimize the uncertainty of
the incident proton’s energy, the higher energy proton emitted to the forward
angular region of $\theta$=25o was used in this calibration.

Figure 38:  Cross sectional shape of the CFT $uv$ fiber for the scattering
plane of the scattered proton. The cross section of the $uv$ layer becomes
elliptical, and the angular dependence of the path length in the $uv$ fiber is
much smaller compared to that of the $\phi$ fiber.

####  5.5.4 Energy resolution of the CFT

The energy deposit in the CFT can be measured by summing up the energy
deposits in all the CFT layers. The energy resolution for the total energy
loss in the CFT was estimated from the width in the total $dE$ spectrum for
the $pp$ and $p$C scattering experiments. The energy dependence of the
resolution can be roughly estimated by changing the scattering angle of the
proton, as shown in Figure 39. There were only small energy dependences in the
energy resolution, and typically 20% was obtained for 10 MeV energy deposits
in the CFT. This energy resolution is sufficient to separate the proton from
$\pi$ using the $\Delta E$-$E$ method from the partial energy deposit in the
CFT and the total energy deposit in the BGO calorimeter. This is because the
energy deposit for $\pi$ is estimated to be approximately 1.5 MeV [15].

Figure 39:  Energy dependence of the energy resolution ($\sigma/E$) of the CFT
obtained from the $pp$ and $p$C scattering experiments.

###  5.6 Kinematic identification of scattering events

Because the energy calibrations of the CFT and the BGO calorimeter were
performed, the kinetic energy of the scattered proton was reconstructed by
adding the energy deposits in two detectors. Figure 40 shows the scatter plot
between the scattering angle $\theta$ measured using the CFT and the kinetic
energy of the proton measured using the CFT and the BGO calorimeter. The loci
corresponding to the $pp$ and $p$C scattering experiments are identified. The
kinematic lines of the $pp$ and $p$C elastic scatterings are also overlaid in
Figure 40. Although the CFT and BGO were calibrated separately, the
reconstructed correlations are well consistent with these kinematic lines. To
identify the elastic scattering, we introduce the index $\Delta E_{kin}$
defined in Equation (1), which represents the consistency between the measured
energy and the calculated energy from the scattering angle for each scattering
kinematic. This $\Delta E_{kin}$ corresponds to the difference between the
measured energy and the kinematic lines presented in Figure 40. The top figure
of Figure 41 shows the scatter plots between the $\Delta E_{kin}$ and $\theta$
values for the $pp$ elastic scattering. The bottom figure of Figure 41 shows
the $\Delta E_{kin}$ distribution for the $pp$ elastic scattering, and the
width ($\sigma$) was 2.8 MeV for the entire $\theta$ region. This performance
satisfies the requirement of 7 MeV for the identification of $\Sigma p$
scattering [15]. The $pp$ scattering event was identified by selecting the
$\Delta E_{kin}$ peak in the $\pm 3\sigma$ region.

Figure 40:  Scatter plot between the scattering angle $\theta$ measured using
the CFT and the kinetic energy of the proton measured using the CFT and the
BGO calorimeter. The solid lines show the kinematic relationship between the
$pp$ and $p$C elastic scatterings.

Figure 41:  (Top) Correlations between the $\Delta E_{kin}$ and the scattering
angle $\theta$ for the $pp$ scatterings. (Bottom) $\Delta E_{kin}$
distribution for the $pp$ scatterings for the entire $\theta$ region.

###  5.7 CFT tracking efficiency

The CFT tracking efficiency depends on both the kinetic energy and the
scattering angle of the proton. However, because there is a one-to-one
correlation between the kinetic energy and the scattering angle of the $pp$
elastic scattering, we estimate the CFT efficiency as a function of the
scattering angle for the $pp$ elastic scattering. This efficiency is necessary
for the derivation of the differential cross section, as described in the next
section. To select the $pp$ scattering events without the kinematic
identification, we required two fiber hits with a back-to-back correlation in
the $\phi 1$ layer corresponding to the two protons from the $pp$ scattering
experiment. In this analysis, the scattering angles were estimated from the
BGO energy because there is a one-to-one correlation between them in the $pp$
scattering experiment, as shown in Figure 31. The tracking efficiency for a
scattering angle $\theta$ was estimated as follows:

$\epsilon_{CFT}(\theta)=\frac{N_{CFT}(E_{BGO})}{N_{BGO}(E_{BGO})},$ (4)

where $N_{BGO}(E_{BGO})$ and $N_{CFT}(E_{BGO})$ represent the number of
protons detected using the BGO calorimeter and the number of tracked events
using the CFT, respectively, for each BGO energy region ($E_{BGO}$)
corresponding to the scattering angle $\theta$ based on the $pp$ scattering
kinematics. The bottom figure of Figure 42 shows the angular dependence of the
tracking efficiency of the CFT. To estimate $N_{BGO}(E_{BGO})$ in Equation
(4), protons have to arrive at the BGO calorimeter with a reasonable kinetic
energy. Therefore, the estimation of the CFT tracking efficiency is restricted
to the angular region less than 45∘. As shown in the top figure of Figure 42,
the forward angular acceptance is determined by the CFT’s acceptance. The
efficiency suddenly drops at the edge region around 20∘. On the other hand,
the efficiency gradually decreases as the scattering angle moves toward 45∘.
This is caused by the geometrical effect in the $uv$ layers. As shown in
Figure 43, there are ineffective regions for the tracks with scattering angles
at approximately 45∘ owing to the zigzag structure of the $uv$ layers. It is
difficult to detect protons passing near the boundary region of the
neighboring fibers, such as ”track 2” shown by the dotted line in Figure 43.
This geometrical effect reaches the maximum at 45∘. Therefore, the efficiency
gradually drops as the scattering angle approaches 45∘.

Figure 42:  (Top) Schematic drawing of the detector geometry with tracks of
scattering angles of 20∘ and 45∘. The forward angular coverage of 20∘ is
determined by the CFT’s acceptance. (Bottom) $\theta$ dependence of the CFT
tracking efficiency in which $\theta$ is estimated through the energy of
protons measured using the BGO calorimeter.  Figure 43:  Cross section of a
CFT $uv$ layer and the position dependence of the pass length in the layer.
The cross section becomes an ellipse with respect to a plane including the
beam axis owing to the tilt angle in the layer. There are ineffective regions
for the tracks with scattering angles at approximately 45∘ owing to the zigzag
structure of the $uv$ layers. The ”track 2” shown by the dotted line is a
typical example of such undetectable tracks.

###  5.8 Relative differential cross sections of the $pp$ elastic scattering
experiments

To evaluate the performance for deriving the differential cross sections using
CATCH, we finally derived the differential cross section of the $pp$
scattering experiment. The differential cross section was derived as follows:

$\frac{d\sigma}{d\Omega}=\frac{N_{scat}(\theta_{CM})}{N_{beam}\cdot
N_{target}\cdot\epsilon_{CFT}\cdot\epsilon_{acc}\cdot d\Omega},$ (5)

where $N_{beam}$, $N_{target}$, and $d\Omega$ represent the number of proton
beams, the number of the target protons per unit square, and the solid angles,
respectively. $\epsilon_{CFT}$ and $\epsilon_{acc}$ represent the tracking
efficiency of the CFT and the detector acceptance representing the probability
of arriving at the BGO calorimeter, respectively. The acceptance
$\epsilon_{acc}$ was obtained based on the Monte Carlo simulation.
$N_{scat}(\theta_{CM})$ represents the number of the protons scattered to the
scattering angle $\theta_{CM}$ in the c.m. frame. This $N_{scat}(\theta_{CM})$
is obtained from the $\Delta E_{kin}$ spectrum for each scattering angle. In
this experiment, the $N_{beam}$ could not be measured accurately because the
intensity of the beam was low. Therefore, it is difficult to derive the
absolute value of the differential cross section. Here, we discuss the
relative differential cross section by normalizing the differential cross
section at $\theta_{CM}$=70o to one. Figure 44 shows the obtained relative
differential cross section for the angular region of 40 $\leq$ $\theta_{CM}$
(degree) $\leq$ 90\. The differential cross section was derived for the three
different target positions to determine the $z$ dependence of the detector
performance, and the obtained values were almost consistent with each other.
The obtained relative differential cross section was almost flat in this
angular region. A result obtained from a partial-wave analysis [22] based on
the rich experimental data of nucleon-nucleon scattering experiments is also
referred to as the cyan circle, as shown in Figure 44. We concluded that the
obtained relative differential cross section was reasonably consistent with
the reliable calculation. However, there are significant errors, especially
regarding both edges of the angular acceptance. This error in such angular
regions results from the rapid drop in the total efficiency
($\epsilon_{CFT}\cdot\epsilon_{acc}$). Even with discrepancies in the cross-
sections for the different target positions, the systematic errors are below
10%. The systematic error mainly results from the uncertainty in the
efficiency estimation of the CFT, especially at the edge of the angular
acceptance. This estimation can be improved using a higher-energy proton beam
because two proton tracks can be reconstructed using CATCH, whereas two-track
reconstruction is difficult in this experiment owing to the low energy.
Detecting a proton from the $pp$ scattering, one can reconstruct the other in
the $pp\to pX$ reaction’s missing momentum. The tracking efficiency is defined
as the number of detected tracks divided by the number of predicted ones. In
our future studies, we shall improve efficiency estimation using this method.
The current systematic error also satisfies the requirements because the
statistical uncertainty in $\Sigma p$ scattering experiments is expected to be
at 10%. Therefore we concluded that CATCH meets the required performance for
deriving the differential cross section.

Figure 44:  Relative differential cross sections, which are normalized to one
at $\theta_{CM}$=70o, for the $pp$ elastic scatterings obtained in this
experiment for three different target positions. The results obtained from a
partial-wave analysis based on rich experimental data of nucleon-nucleon
scattering experiments [22] is also shown as a reference.

##  6 Summary

In summary, we completed the development of a recoil proton detector called
CATCH for the $\Sigma p$ scattering experiment at J-PARC. CATCH is a
cylindrical detector system covering an inner target to measure the trajectory
and energy of an emitted proton from the target for the kinematic
identification of the $\Sigma p$ scattering event. CATCH comprises a
cylindrical fiber tracker (CFT), a BGO calorimeter, and a plastic scintillator
hodoscope (PiID), which are coaxially arranged from the inner to the outer
sides. The CFT is the tracking detector comprising eight cylindrical layers of
scintillation fibers arranged in parallel and spiral configurations based on
the direction of the beam to obtain a three-dimensional trajectory. Each CFT
fiber is read out one after the other using an MPPC, and approximately 5,000
MPPCs are controlled using the VME-EASIROC boards, which are readout boards
using the EASIROC chips designed for multi-PPD readout. As for the BGO
calorimeter, $24$ BGO crystals are placed around the CFT. To operate the BGO
calorimeter under the high singles rate condition, the readout PMT is operated
at a lower voltage, and the waveform of the shaping amplifier signal is read
out using a flash ADC. Because the fiber positions were slightly deviated from
the desired positions, the fiber positions were corrected in the offline
analysis using cosmic ray data. As a result of the fiber position correction,
the angular resolution of the CFT was 1.30∘ in $\sigma$ for the cosmic ray.

To evaluate the performance of CATCH for the protons, the $pp$ and $p$C
scattering experiments were performed at the cyclotron facility in Tohoku
University (CYRIC) in January 2017. An 80 MeV proton beam was irradiated on a
thin polyethylene (CH2) target installed inside CATCH. The scattered protons
were detected using CATCH. The angular resolution and the time resolution of
the CFT for protons were 1.27∘ and 1.8 ns in $\sigma$, respectively. The
energy calibrations for the BGO calorimeter and the CFT were performed by
comparing them to the simulated energy deposits for each scattering angle.
Although the CFT and the BGO calorimeter were calibrated separately, the
reconstructed correlation between the scattering angle and the kinetic energy
of the scattered protons was well consistent with the kinematic line. To
identify the $pp$ scattering events, the index $\Delta E_{kin}$ corresponding
to the kinematic consistency between the measured energy and the angle was
introduced. The $\Delta E_{kin}$ resolution was 2.8 MeV in $\sigma$ for the
$pp$ scattering of the entire $\theta$ region, and the $pp$ scattering event
was identified by selecting the peak region in the $\Delta E_{kin}$
distribution. The obtained relative differential cross sections for the $pp$
elastic scatterings were consistent with the reliable partial wave analysis
for three target positions. The systematic error was maintained at under 10%,
which is the required performance level for CATCH. From these performance
evaluations, we confirmed that CATCH demonstrates sufficient performance for
the $\Sigma p$ scattering experiment at J-PARC.

## CRediT authorship contribution statement

Y. Akazawa: Supervision, Software, Formal analysis, Investigation, Writing -
Original Draft, Visualization, N. Chiga: Methodology, N. Fujioka: Methodology,
Investigation, S.H. Hayakawa: Software, Investigation, Writing - Review &
Editing, R. Honda: Methodology, Software, Investigation, Writing - Review &
Editing, M. Ikeda: Methodology, Software, Investigation, K. Matsuda:
Investigation, K. Miwa: Project administration, Conceptualization, Software,
Formal analysis, Investigation, Writing - Original Draft, Funding acquisition,
Y. Nakada: Methodology, Software, Investigation, T. Nanamura: Investigation,
S. Ozawa: Methodology, Software, Investigation, T. Shiozaki: Methodology,
Software, Investigation, H. Tamura: Funding acquisition, H. Umetsu:
Methodology.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

## Acknowledgements

We thank the staff of CYRIC for their support in providing the beam used for
the experiment. We are grateful to S. Callier and the OMEGA group for
arranging for the EASIROC chip. We also thank the KEK electronics group for
developing the VME-EASIROC board. This study was supported by JSPS KAKENHI
Grant Numbers
23684011, 15H05442, 15H02079, and 18H03693. It was also supported by Grants-
in-Aid Numbers 24105003 and 18H05403 for Scientific Research from the Ministry
of Education, Culture, Science, and Technology (MEXT), Japan.

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