# Test of a small prototype of the COMET cylindrical drift chamber

C. Wu1, T.S. Wong  Y. Kuno1, M. Moritsu  Y. Nakazawa2, A. Sato  H. Sakamoto3,
N.H. Tran4, M.L. Wong5, H. Yoshida1, T. Yamane  J. Zhang  Department of
Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan  Department of
Physics, Nanjing University, Nanjing 210093, China  Institute of Particle and
Nuclear Studies, High Energy Accelerator Research Organization, Tsukuba
305-0801, Japan  Experimental Physics Division, Institute of High Energy
Physics, Chinese Academy of Sciences, Beijing 100049, China  State Key
Laboratory of Particle Detection and Electronics, Institute of High Energy
Physics, Chinese Academy of Sciences, Beijing 100049, China  University of
Chinese Academy of Sciences, Beijing 100049, China

###### Abstract

The performance of a small prototype of a cylindrical drift chamber (CDC) used
in the COMET Phase-I experiment was studied by using an electron beam. The
prototype chamber was constructed with alternating all-stereo wire
configuration and operated with the He$-$iC4H10(90/10) gas mixture without a
magnetic field. The drift space-time relation, drift velocity, d$E$/d$x$
resolution, hit efficiency, and spatial resolution as a function of distance
from the wire were investigated. The average spatial resolution of $150\,\mu$m
with the hit efficiency of $99\,\%$ was obtained at applied voltages higher
than 1800 V. We have demonstrated that the design and gas mixture of the
prototype match the operation of the COMET CDC.

###### keywords:

Drift chamber, helium-based gas, spatial resolution, COMET

††journal: Nuclear Instruments and Methods in Physics Research A
fn1fn1footnotetext: Present address: Research Center for Nuclear Physics,
Osaka University, Ibaraki, Osaka 567-0047, Japanfn2fn2footnotetext: Present
address: Institute of Particle and Nuclear Studies, High Energy Accelerator
Research Organization, Tsukuba 305-0801, Japanfn3fn3footnotetext: Present
address: Centre for Computational Science, RIKEN, Kobe,
Japanfn4fn4footnotetext: Present address: Department of Physics, Boston
University, Boston, MA 02215, USAfn5fn5footnotetext: Present address:
Laboratoire de Physique de Clermont, Campus Universitaire des Cézeaux 4 Avenue
Blaise Pascal 63178 Aubière Cedex, France

##  1 Introduction

The COherent Muon to Electron Transition (COMET) experiment at the Japan
Proton Accelerator Research Complex (J-PARC) in Tokai, Japan, is to search for
the neutrinoless coherent transition of a muon to an electron ($\mu$$-$$e$
conversion) in the field of a nucleus, with its single event sensitivity of
$2\times 10^{-17}$, which is more than four orders of magnitude improvement
over the current upper limit of $7\times 10^{-13}$ at 90 % C.L. from the
SINDRUM II experiment [1]. The COMET experiment is organized as a two-stage
project. The first stage, COMET Phase-I, is seeking a sensitivity of $3\times
10^{-15}$ with 3.2-kW proton beam power [2, 3]. It will be carried out at the
Hadron Experimental Facility of J-PARC using a bunched 8-GeV proton beam that
is slowly extracted from the J-PARC Main Ring.

The main detector system for the $\mu$$-$$e$ conversion search in COMET
Phase-I is the Cylindrical Detector (CyDet). It consists of a cylindrical
drift chamber (CDC) and a cylindrical trigger hodoscope. The primary function
of the CDC is to measure the momentum of $\mu$$-$$e$ conversion electrons.
Figure 1 shows a schematic layout of the CyDet. It is located downstream of
the muon transport section, and installed within the warm bore of a large 1-T
superconducting detector solenoid. The CyDet must accurately and efficiently
identify and measure signal electrons of 105 MeV from aluminum target disks
whilst suppressing backgrounds. It is designed to avoid high hit rates from
the beam particles, background electrons from muon decay-in-orbit (DIO), and
low energy protons emitted after the nuclear capture process of negative
muons.

Figure 1: Schematic layout of the cylindrical detector system. A muon beam
comes from left and stops in the target disks located in the center of the
detector solenoid.

The momentum resolution of CDC should be less than 200 keV/$c$ for the
105-MeV/$c$ electrons in order to distinguish the signal electrons from the
DIO electrons. Note that the momentum resolution for the electrons at this
momentum is dominated by the multiple scattering effect. In order to suppress
this effect, He$-$iC4H10(90/10) is selected as a gas mixture for its long
radiation length of 1313 m [4]. He$-$iC4H10 was so far used to achieve high-
momentum resolution in a low-momentum region in only a few experiments, e.g.
KLOE [5] and MEG-II [6] with a ratio of 90/10, and BaBar [7] with 80/20.

A major motivation of this work is to demonstrate that the current design of
the cell and wire structure of the CDC with the He$-$iC4H10(90/10) gas mixture
can work in the COMET Phase-I experiment. We constructed a prototype chamber
of the CDC and performed a beam test. In this paper, an experimental setup and
an analysis method for the CDC prototype test are introduced. Then the drift
space-time relation, drift velocity, spatial resolution, hit efficiency, gas
gain and d$E$/d$x$ resolution are discussed.

##  2 Experiment

###  2.1 A prototype chamber

The prototype chamber was manufactured as a small partial copy of the CDC
structure. It consists of 79 drift cells with 8 sensitive layers and 1 dummy
layer. The purpose of sensitive layers is to detect the ionization electrons,
whereas the dummy layer is used to study the effect of crosstalk from the
electronics, which is not described in this paper. All the wires are strung
with an alternating stereo angle of approximately $\pm 4$ degrees layer by
layer. The cell shape is almost square with dimensions of (16.8$\times$16.0)
mm2. The layout of the cell structure at the centre of the longitudinal
direction is shown in Figure 2, and pictures of the chamber are shown in
Figure 3. The size of the chamber is 600 mm in length, 170 mm in height, 280
mm in width. There are 87 gold-plated tungsten wires with a diameter of 25
$\mu$m as anode wires, and 265 aluminum wires with a diameter of 126 $\mu$m as
cathode wires.

The endplates and walls of the chamber are made of aluminum. An engineering
tolerance for the position of the wire ends with feedthroughs is less than 50
$\mu$m. There are four aluminized Mylar windows with thickness of 200 $\mu$m
in all walls so that the effects of electromagnetic showers by the electron
beam to the chamber can be minimized. A positive high voltage (HV) is supplied
to the anode wires from one side of the endplates. From the other side, two
front-end electronics boards are connected to the anode wires through
decoupling capacitors. The electronics boards are covered with an aluminum box
to suppress electromagnetic noise.

Figure 2: Layout of wire configuration at the centre of the chamber together
with an expanded view of a unit cell. The cell deformation angle, $\beta$,
ranges approximately 60 to 120 degrees depending on the $z$ position of the
chamber. Figure 3: Pictures of the prototype chamber with dimensions of
$(600\times 170\times 280)$ mm3.

The front-end readout electronics were fabricated based on the Readout
Electronics for the Central Drift Chamber of Belle-II Experiment (RECBE) [8,
9] with some modifications. There are two outputs from the frontend amplifier-
shaper-discriminator ASIC of RECBE [10]; one is discriminated inside the ASIC
and converted to timing information with 960-MHz TDC in an FPGA; the other is
used to measure the charge with 10-bit, 30-MHz sampling rate ADC. The SiTCP
protocol [11] is used to transmit the event data to a data-acquisition
computer via Gigabit Ethernet fiber link.

###  2.2 Experimental setup

Figure 4: Schematic layouts of the experimental setup. The upper figure is a
side view and the lower figure is a top view.

The test experiment with an electron beam was performed in the Laser Electron
Photon facility at SPring-8 (LEPS) [12, 13], Japan. A photon beam of backward
Compton scattering from UV laser, of 1.5 to 2.4 GeV was used to generate a
1-GeV electron beam by colliding with a lead converter. The momentum selection
of the electron beam was made with a dipole magnet located downstream of the
lead converter. Two plastic scintillating counters of ($300\times 90\times
10$) mm3 size were installed at both upstream and downstream of the prototype
chamber. Schematic layouts of the experimental setup is shown in Figure 4.
There was no significant magnetic field around the prototype chamber in this
setup. The beam spreads over the whole chamber in the horizontal direction,
whereas the vertical spread of the beam is around 5 to 6 cm.

The timing and charge of wire hits were measured by RECBE and recorded by a
data-acquisition computer using DAQ Middleware [14]. The event trigger was
issued by a coincidence of signals from the two trigger counters. The average
trigger rate was around 4–5 kHz. The high voltage and discrimination threshold
were scanned at every 500 thousands events. A detailed list of the
experimental conditions is shown in Table 1.

The gas flow rate is controlled at 20 cc/min. As the gas gain of the chamber
is sensitive to the environmental condition, the temperature of $26.0\pm 0.5$
∘C, the atmospheric pressure of $979\pm 3$ hPa, and the humidity of $53\pm 5$
% were maintained during the tests.

Table 1: List of the experimental conditions. Here the discrimination threshold is defined as the analogue output of the ASIC after amplification. Gas mixture | High voltage [V] | Threshold [mV]
---|---|---
He$-$iC4H10(90/10) | 1650–1830 | 10–30

##  3 Data Analysis

###  3.1 Track reconstruction

In the beginning of the data analysis, the wire hits were classified by their
ADC sum, i.e. a sum of the ADC values measured by the RECBE subtracting their
pedestal level. A typical ADC sum distribution of a cell is shown in Figure 5.
Since signals and noises were clearly separated, a cut for signal hit
identification was applied based on the ADC sum for each drift cell.

Figure 5: ADC sum distribution measured at a drift cell for He$-$iC4H10(90/10)
at 1800 V with 10-mV threshold. In this case the ADC sum larger than 25 was
selected.

In order to test the performance of a specific cell and layer, the hits in the
dummy layer and a layer to be tested were excluded from the track
reconstruction to avoid bias. Events with the total number of signal hits
larger than 6 were used for track reconstruction. Using a drift space-time
relation, which will be discussed in the following subsection, drift time was
converted into the drift distance, $d$. The residual of a signal hit was
defined as $r=d-d^{\textrm{fit}}$, where $d^{\textrm{fit}}$ is the distance of
the closest approach from the reconstructed track to the anode wire in the hit
cell. Excluding the layer to be tested, the sum of normalized residuals of
signal hits was defined as the $\chi^{2}$ of the reconstructed track:

$\chi^{2}=\sum_{i}\Bigg{(}\frac{d_{i}-d_{i}^{\textrm{fit}}}{\sigma(d_{i})}\Bigg{)}^{2},$
(1)

where $i$ is a hit index, and $\sigma(d)$ denotes spatial resolution as a
function of the distance $d$, the details of which will be discussed in
Section 4.2. A $\chi^{2}$–minimization algorithm was applied to obtain a
realistic reconstructed track. In the following study, the central forth layer
was chosen as the layer to be tested, so as to minimize a tracking error,
unless otherwise noted.

###  3.2 Drift space-time relation

Figure 6: Space-time distribution of the central layer obtained for
He$-$iC4H10(90/10) at 1800 V with 10 mV threshold. Figure 7: Fitted space-time
relation for He$-$iC4H10(90/10) at 1800 V with 10-mV threshold. The open
circles represent the averaged space-time distribution, and the solid line is
the fitted function. Notice that the number of circles shown here is less than
the used intervals for a better visualization.

A drift space-time (hereafter $s$-$t$ ) relation was studied by an iterative
procedure starting from an initial value obtained from Garfield++ [15]. A
typical $s$-$t$ distribution is shown in Figure 6. The $s$-$t$ relation was
calibrated layer by layer. The distribution was averaged over 200-$\mu$m
intervals near the anode wire and over 3-ns intervals near the cell boundary.
To get a parameterized $s$-$t$ relation, the averaged distribution was then
fitted by a piecewise continuous third-order polynomial functions connecting
four different drift time region. An example of the $s$-$t$ relation fitting
is shown in Figure 7. The $s$-$t$ relations for data sets with different high
voltages or thresholds were calibrated separately, and applied for the
following analysis procedures accordingly.

###  3.3 Drift velocity

The drift velocity was calculated by taking derivatives of the $s$-$t$
relation as a function of the distance from the wire. The local electric field
in a drift cell was calculated by using the Garfield++ simulation. Then we
obtained the drift velocity as a function of the local electric field as shown
in Figure 8. The drift velocity in He$-$iC4H10(90/10) gas mixture is
unsaturated near 1000 V/cm/atm. Figure 8 also shows other results of
calculations [16] and experimental measurements [17, 18, 19] together with
Garfield++ simulation. In the Garfield++ simulation, we considered an
experimental uncertainty of gas mixture ratio as ranging from $89.6:10.4$ to
$90.4:9.6$, and an uncertainty of water vapor contamination as ranging from 0
to 0.12% 111The experimental uncertainty of the gas mixture ratio is given by
specifications of mass flow controllers; and the uncertainty of the water
vapor contamination is estimated by some tests under different circumstances
after the beam test.. All data shows good agreement; the minimal deviations
could be justified within small differences in operating conditions, such as
pressure, temperature, gas mixture ratio, and water vapor contamination.

Figure 8: Drift velocity versus the electric field for He$-$iC4H10(90/10) at 1
atm by comparing with Garfield++ simulation, calculations of Sharma-Sauli
[16], and experiments of P. Bernardini [17], C. Grab [18], and a KLOE-CDC
prototype [19]. For the band of Garfield++ simulation, the lower boundary
corresponds to the gas mixture ratio between He and iC4H10 at $90.4:9.6$, and
the upper boundary corresponds to the gas mixture ratio at $89.6:10.4$ with
0.12% water vapor.

##  4 Results and Discussion

###  4.1 Scan of applied high voltage

In order to determine an optimal operation high voltage, the spatial
resolution and cell hit efficiency were studied as a function of applied high
voltage. The intrinsic spatial resolution was extracted from the standard
deviation of residual distributions, $\sigma_{\textrm{total}}$, by subtracting
a tracking error in quadrature. Since the tracking error is caused by
extrapolating or interpolating the reconstructed track, it was estimated from
a simulation with assumed intrinsic spatial resolution. Comparing the
simulation with the experimental data, the tracking error was derived to be 94
$\mu$m for the central layer. The cell hit efficiency was defined as the ratio
of the number of hits with the residual within $\pm
5\,\sigma_{\textrm{total}}$ to the number of tracks passing through the cell.

The results are shown in Figure 9 for high voltages from 1650 to 1830 V. Note
that an optimal threshold value which gave the best spatial resolution was
selected for each high-voltage data set. The plateau-like behavior of
efficiency and spatial resolution are consistent with other literatures [5,
20]. We obtained the best spatial resolution of 150 $\mu$m with 99% hit
efficiency at the voltages higher than 1800 V.

Figure 9: Cell hit efficiency (circles) and intrinsic spatial resolution
(triangles) as a function of the applied voltage for He$-$iC4H10(90/10).

###  4.2 Spatial resolution

The spatial resolution varies depending on the distance from the anode wire.
Detailed contributions to spatial resolution was studied using a similar
method of [19]. The components of spatial resolution can be grouped into
primary ionization statistics ($\sigma_{\textrm{ion}}$), electron longitudinal
diffusion ($\sigma_{\textrm{diff}}$), and electronics time resolution
($\sigma_{\textrm{ele}}$):

$\sigma=\sqrt{\sigma_{\textrm{ion}}^{2}+\sigma_{\textrm{diff}}^{2}+\sigma_{\textrm{ele}}^{2}}.$
(2)

The contribution of primary ionization statistics was estimated from a Monte
Carlo simulation. Primary ions were generated according to
$\exp(-n_{\textrm{p}}y)$, where $n_{\textrm{p}}$ is the number of primary ions
per unit length, and $y$ is the track path length in a drift cell.
$\sigma_{\textrm{ion}}$ was estimated from the standard deviation of the
difference between the distance from anode wire to the track and to the
closest ionization point. Therefore, $\sigma_{\textrm{ion}}$ was obtained as a
function of the distance to wire and $n_{\textrm{p}}$.

The function of $\sigma_{\textrm{diff}}$ follows an approximation of a
classical diffusion theory based on the Boltzmann statistics:
$\sigma_{\textrm{diff}}(x)=\sqrt{(2Dx/v)}$, where $D$, $x$, and $v$ are the
diffusion coefficient, drift distance, and average drift velocity,
respectively. For $\sigma_{\textrm{ele}}$, the main contributions come from
the time resolution of the readout electronics and time walk effect of
signals. The time resolution was determined from specification of the
electronics to be $1.04/\sqrt{12}$ ns, which corresponds to 10 $\mu$m, whereas
the time walk effect was found to be negligible by choosing a low threshold
level of electronics.

Figure 10: Spatial resolution as a function of distance to the anode wire for
He$-$iC4H10(90/10) at 1800 V with 10-mV threshold. The open circles represent
the experimental data. The solid line indicates the fitting results. The dot-
dashed line, dashed line and dotted line shows the contribution of the primary
ionization, longitudinal diffusion, and electronics time resolution,
respectively.

Figure 10 shows the spatial resolution as a function of distance to the anode
wire together with the fitting result by Eq.2. The fitting result shows that
the number of primary ionization $n_{\textrm{p}}=14.2\pm 0.2$ cm-1. For
comparison with other results, the $n_{\textrm{p}}$ value was scaled from the
1-GeV electron in our experiment to minimum ionizing particles taking the
energy loss difference into account. Using the photo-absorption ionization
model [21], we obtained $n_{\textrm{p}}=9.9\pm 0.1$ cm-1 for minimum ionizing
particles. Note that the uncertainty is only statistical, and systematic
uncertainties are not taken into account. The result is slightly smaller but
in a decent agreement with 12.7 cm-1 computed by Sharma and Sauli [16] and
$12.3\pm 0.2$ cm-1 reported in [19].

The fitting result also gives $D/v=(1.05\pm 0.04)\times 10^{-4}$ cm for the
ratio of the diffusion coefficient to the drift velocity. The value
corresponds to 112 $\mu$m for 0.6 cm of drift. It was found that the
deterioration of the spatial resolution near the anode wire is due to the
statistical fluctuation of primary ionization, whereas the longitudinal
diffusion dominates in the long drift distance.

###  4.3 Gas gain

Figure 11: Relation between gas gain and high voltage for He$-$iC4H10(90/10)
with 10-mV threshold.

Once the track was reconstructed, the measured charge at each drift cell was
then divided by the path length of the track in the drift cell (hereafter
$Q$). The gas gain $G$ is computed as $Q/(n_{\textrm{t}}e)$, where
$n_{\textrm{t}}$ is the total number of electron-ion pairs per unit length,
and $e$ denotes the elementary charge. To avoid the non-linear effect in the
Landau tail of the distribution of $Q$ and $n_{\textrm{t}}$ contributed by the
electronics and the space charge effect, we took the most probable values
(MPV) for each distribution in one drift cell. The
$n_{\textrm{t}}^{\textrm{MPV}}$ was computed as
$(dE/dx)^{\textrm{MPV}}/W_{\textrm{I}}$, where $(dE/dx)^{\textrm{MPV}}$ is the
most probable energy deposition per unit length in one drift cell, and
$W_{\textrm{I}}$ is the average ionization energy per ion pair. Ignoring the
Penning effect, $W_{\textrm{I}}$ in He$-$iC4H10(90/10) was computed as 29.3 eV
based on the He and iC4H10 properties given in [22]. According to the photon
absorption ionization model [21], $(dE/dx)^{\textrm{MPV}}$ for an 1-GeV
electron in this gas mixture is computed to be 0.70 keV/cm, therefore
$n_{\textrm{t}}^{\textrm{MPV}}$ = 23.9 cm-1. The gas gain was then calculated
for data sets at different high voltages using the measured
$Q^{\textrm{MPV}}$. Figure 11 shows the relationship between the gas gain and
the applied high voltage. A linear relation in a logarithmic scale can be
observed as expected.

###  4.4 d$E$/d$x$ resolution

Figure 12: d$E$/d$x$ distribution measured for tracks with 10 samples using
data taken from He$-$iC4H10(90/10) at 1800 V with 10-mV threshold. The solid
and dashed lines denote histograms with 80$\,\%$ truncated mean and without
truncation, respectively.

For the measurement of the d$E$/d$x$ resolution, tracks with arbitrary lengths
by combining hits in reconstructed events were simulated. To avoid Landau tail
of collected charge distribution worsening the d$E$/d$x$ resolution, the
truncated mean technique was applied [23]. A comparison of the d$E$/d$x$
distribution with and without truncation is shown in Figure 12. We found that
the best d$E$/d$x$ resolution can be achieved by accepting 80$\,\%$ of hits in
a track, as shown in Figure 13.

Figure 13: d$E$/d$x$ resolution for tracks with 50 and 100 samples using data
taken from He$-$iC4H10(90/10) at 1800 V with 10-mV threshold as a function of
the truncation ratio. Figure 14: d$E$/d$x$ resolution of tracks with different
number of samples taken from He$-$iC4H10(90/10) at 1800 V with 10 mV
threshold. The solid line denotes the fitting result with Eq. 3; here
$\sigma_{0}x^{b}$ is absorbed into $\sigma_{1}$ with $x=1.6$ cm.

The d$E$/d$x$ resolution can be parameterized as [24]

$\sigma_{\textrm{d}E/\textrm{d}x}=\sigma_{0}N^{a}x^{b},$ (3)

where $N$ is the number of samples and $x$ is the track length. By varying the
number of samples included in the combined tracks, a relationship between
d$E$/d$x$ resolution and $N$ was obtained as shown in Figure 14. Since a
typical number of hits in the CDC for a $\mu$$-$$e$ conversion signal track is
around 50, the predicted d$E$/d$x$ resolution in COMET Phase-I was found to be
$4.7\,\%$ for 1-GeV electrons with an assumption of track length per cell
$x=1.6$ cm.

##  5 Conclusions

We have constructed a prototype chamber for the CDC used in the COMET Phase-I
experiment. The cell and wire structure of the protoytpe is identical with the
CDC. A test experiment was carried out using a 1-GeV electron beam at
SPring-8. Experimental data were obtained with a gas mixture of
He$-$iC4H10(90/10) for a couple of high voltages and discrimination thresholds
of electronics without a magnetic field. We confirmed a similar drift velocity
with other literatures. The spatial resolution of 150 $\mu$m with the hit
efficiency of $99\,\%$ was obtained at applied voltages higher than 1800 V.
The behavior of spatial resolution with respect to the distance from the anode
wire was able to understood adequately. The gas gain behavior with respect to
the high voltages was also observed as expected. The d$E$/d$x$ resolution was
estimated to be 4.7% assuming a typical $\mu$$-$$e$ conversion signal in COMET
Phase-I. We have demonstrated that the CDC design with the He$-$iC4H10(90/10)
gas mixture provides sufficient performance in the COMET Phase-I experiment.

## Acknowledgements

The experiment was performed at the BL33LEP of SPring-8 with the approval of
the Japan Synchrotron Radiation Research Institute (JASRI) as a contract
beamline (Proposal No. BL33LEP/6001-Q038). We are very thankful for staffs and
students in the LEPS facility for their support during the beam time. This
work of the Osaka University group was supported in part by the Japan Society
of the Promotion of Science (JSPS) KAKENHI Grant No. 25000004 and 18H05231;
and the Chinese Academy of Sciences (CAS) President’s International Fellowship
Initiative under Contract No. 2018PM0004. The work of the Institute of High
Energy Physics (IHEP) was support in part by the National Natural Science
Foundation of China (NSFC) under Contracts No. 11335009 and 11475208; Research
Program of IHEP under Contract No. Y3545111U2; and the State Key Laboratory of
Particle Detection and Electronics of IHEP, China, under Contract No.
H929420BTD.

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