Working draft1

November 5, 20132

ver. 2.03

Construction of the CALICE High Granular Scintillator Based4

Electromagnetic Calorimeter Prototype and Its Response to5

Electrons6

CALICE collaboration7

Abstract8

The CALICE collaboration is developing a high granular electromagnetic calorimeter based9

on the technique of scintillator stip for the future linear collider experiments. To confirm its10

feasibility 180mm× 180mm× 21.5X0 prototype has been constructed and tested with electron11

beams at Fermilab May 2009. The prototype consists of 2160 of 10mm× 45mm× 3mm strips12

readout individually. Deviations of the response from linear behavior is less than 2%, and the13

intrinsic-relative energy resolution, σE/E is determined to be {12.9±0.1(stat.)±0.4(syst.)}/√

E(GeV)⊕14

{1.2 ± 0.1(stat.)+0.4−1.2(syst.)}%.15

1

Contents16

1 Introduction 317

2 The ScECAL physics prototype 418

2.1 Construction of ScECAL physics prototype . . . . . . . . . . . . . . . . . . . . . 419

2.2 MPPCs and their saturation collection . . . . . . . . . . . . . . . . . . . . . . . . 720

2.2.1 Characterization of all MPPCs in the physics prototype . . . . . . . . . . 721

2.2.2 The number of effective pixels . . . . . . . . . . . . . . . . . . . . . . . . . 722

2.2.3 Measurement of the number of effective pixels . . . . . . . . . . . . . . . . 823

2.3 Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924

3 Test beam at FNAL 1025

3.1 Beams and setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1026

3.2 Temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027

3.3 Runs for calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1028

4 Analysis: Reconstruction 1229

4.1 Analysis flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1230

4.2 ADC-MIP conversion factor as a function of temperature . . . . . . . . . . . . . 1231

4.3 ADC-photon conversion factor as a function of temperature . . . . . . . . . . . . 1432

4.4 Inter-calibration constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1533

4.5 Electron energy spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1534

4.5.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1535

4.5.2 The energy spectrum after event selections . . . . . . . . . . . . . . . . . 1636

5 Results: Performance of the physics prototype 1737

5.1 Mean and resolution of measured energy of each beam momentum . . . . . . . . 1738

5.2 Systematic uncertainties on the mean and the standard deviation of the energy39

spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1840

5.2.1 Difference of the mean value of deposited energy among runs . . . . . . . 1841

5.2.2 Event selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1842

5.2.3 ADC-MIP conversion factor . . . . . . . . . . . . . . . . . . . . . . . . . . 1943

5.2.4 ADC-photon conversion factor . . . . . . . . . . . . . . . . . . . . . . . . 1944

5.2.5 Inter-calibration constant . . . . . . . . . . . . . . . . . . . . . . . . . . . 1945

5.2.6 The number of effective pixels of the MPPC . . . . . . . . . . . . . . . . . 1946

5.2.7 Beam momentum fluctuation . . . . . . . . . . . . . . . . . . . . . . . . . 2047

5.2.8 Summary of uncertainties on each beam momentum . . . . . . . . . . . . 2048

5.3 Linearity and the energy resolution of the ScECAL physics prototype . . . . . . 2149

6 Comparison with Monte Carlo simulation 2250

6.1 ScECAL physics prototype in the Simulation . . . . . . . . . . . . . . . . . . . . 2251

6.2 Comparison with the ideal detectors . . . . . . . . . . . . . . . . . . . . . . . . . 2352

7 Discussion 2453

8 Summary 2554

9 Acknowledge 2655

2

1 Introduction56

The International Linear Collider (ILC) experiments are designed to perform high precision57

measurements using the clear initial states of the electron-positron collisions and well recon-58

structed final states. To characterize final states dominated by gauge bosons and heavy quarks,59

the reconstruction of jets is a key issue. One of the ways to precisely reconstruct jets is to60

measure individual particles within jets, by combining calorimetry and tracking. This method,61

called particle flow approach (PFA) [1][2] requires highly granular calorimeters; finer than 10mm62

lateral and longitudinal segmentations for the electromagnetic calorimeter (ECAL) 1 [2][3].63

Such a granularity was until recently difficult for the scintillator technique, because a suf-64

ficiently small and sensitive readout technology did not exist. The situation was drastically65

changed when the pixelated photon detector (PPD or SiPM) was developed. Each small seg-66

mented plastic scintillator can be directly read out by a PPD without a large dead volume67

coming from the readout. Taking one of such methods, the scintillator strip based electromag-68

netic calorimeter (ScECAL) is a unique solution, which is being developed by the CALICE69

collaboration. In order to increase the feasibility of such a calorimeter and to prevent dead70

volume from PPDs, it is proposed that each scintillator is shaped as a 45mm long and 5 -71

10 mm width strip, with the scintillator strips in odd layers orthogonal to those in the even72

layers [4][5]. A special algorithm has already been developed to achieve the fine square segmen-73

tation from such rectangular segmentation [4][5]. To achieve the longitudinal granularity, the74

ScECAL takes a sampling calorimeter method with 2 - 4mm thick tungsten plates interleaved75

with 25 - 30 sensor layers.76

The first ScECAL physics prototype had constructed with a transverse area of 90mm× 90 mm77

and 26 sensor layers and tested at DESY [6]. The second physics prototype has been built78

transversally twice as large as the first prototype, 180mm× 180 mm. The number of lay-79

ers has been also increased to 30 in 266 mm, leading to a total radiation length of 21.3 X080

with absorber layers. Consequently, the total number of readout channels becomes 2160. The81

scintillator-PPD unit is designed according to the results from the experiments with the first82

prototype; 45mm× 10mm× 3mm scintillator hermetically enveloped into a reflector foil with83

a wave length shifting (WLS) fiber inserted centrally along the longitudinal direction of each84

strip and read out with a PPD sit into a housing at one of the edge of the scintillator strip. The85

LED gain monitoring system for each channel also has been implemented, while the first physics86

prototype has had only one monitor for each layer. Hereafter the “physics prototype” denotes87

the second physics prototype. The physics prototype has been tested in the combination with88

other CALICE prototype detectors; the analog hadoron calorimeter (AHCAL) [7], and the tail89

catcher muon tracker (TCMT) [8]. These were used to make the purity of the beam quality.90

Details of the design of physics prototype are shouwn in the successive section. The multi-91

pixel photon counter (MPPC) provided from Hamamatsu K.K. [9] is used in the physics proto-92

type as a kind of PPD. The features of MPPC especially the saturation correction of response93

are discussed in section 2. Although this physics prototype has been tested with the various94

types of beams at Fermilab, the response to electron beams are reported in this paper. The95

experimental setup is reported in section 3. The analysis and its results are shown in section 496

and 5, respectively. The results are compared with the Monte Carlo simulation and discussed97

in section 6. Finally, comprehensive discussion and summary are shown in section 7 and 8,98

respectively.99

1Current requirement to the lateral segmentation is 5× 5mm2 [3]. This requirement can be achieved by using5mm wide scintillator strips.

3

2 The ScECAL physics prototype100

2.1 Construction of ScECAL physics prototype101

The physics prototype starts with a 3.5 mm thick tungsten absorber layer alternately followed102

with scintillator layers and absorber layers. The number of pairs of absorber and scintillator103

layers is 30 in 266 mm of the total thickness. Figure 1 shows the physics prototype in front of104

the CALICE analog HCAL.

Figure 1: A flat cable with nine MPPCs. An overview of the physics prototype put in front of AHCAL.105

Figuer 2 shows a scintillator layer consists of four rows of 18 scintillator strips. Figure 3106

shows a plastic scintillator strip picked up from Fig. 2 with a photo of a MPPC. This scintillator107

strip is cut out from a scintillator bar simultaneously together with a hole for WLS fiber made108

with the extrusion method. A housing space of MPPC was mechanically shaped with depth of109

1.40±0.05 mm and width of 4.46±0.03 mm for 1.3 mm× (4.2±0.2)mm× (3.2±0.2)mm MPPC110

package. Four sides of each strip were polished to make fine sizing and good reflection since111

our current technology could not control the fine size enough. From the measuring results of112

mean and the standard deviation of randomly sampled 20 strips, their width are 9.85±0.01 mm,113

length are 44.71±0.04mm, and thickness are 3.02±0.02 mm. The sizes of MPPC package and114

their uncertainties were taken from the catalogue of Hamamatsu. Nine MPPCs soldered on115

a poryimide flat cable shown in Fig. 4 were inserted into the MPPC housings on the strips,116

respectively. A double clad one mm diameter WLS fiber, Y-11, provided by KURARAY Co.,117

Ltd. was inserted in the hole of each strip with the length of 43.6 ± 0.1mm. Each strip was118

hermetically enveloped in a reflector foil of 57µm thick. The reflector foil provided by KIMOTO119

Co., Ltd. has evaporated silver layer and aluminum layer in between polyethylene terephtalate120

layers. The reflection ratio of this foil is 95.2% for 450 nm light referring to KIMOTO’s catalogue121

[10]. Since the number of photons directly coming from scintillator has position dependence, a122

shade made of reflector film was put between MPPC package and scintillator with a hole as a123

window for WLS in order to accept only photons from WLS fiber . Figure 5 is a photo of such a124

shade in the MPPC housing on the strip. With this shade, sensitivity at the other end of strip125

from MPPC is 88.3± 0.4% of that in front of MPPC. The uncertainty is the standard deviation126

of the 2160 channels.127

Each pair of the absorber and the scintillator layer was held in an iron frame. Each frame128

held four 100 mm × 100mm× (3.49±0.01)mm tungsten carbide absorbers aligned to make 200129

mm × 200 mm absorber layer in front of the scintillator layer. The measured density of eight130

absorber plates are 14.25±0.04 g/cm3 and the chemical composition measured by using the X-131

lay diffraction method and the energy-dispersive X-lay spectroscopy is W : C : Co : Cr = 0.816132

: 0.055 : 0.125 : 0.005 as the ratios of weight, where W means tungsten, C means carbon, Co133

4

Figure 2: A layer aligned 72 scintillator strips hermetically enveloped in the reflector foil. Each strip has ahole on the reflector to introduce the LED light for the LED calibration. The unit of numbers is mm.

Figure 3: Top view and side view of a scintillator strip (left), MPPC housing of scintillator strip (middle),and a photo of 1600 pixel MPPC (right). The unit of numbers is mm.

Figure 4: A flat cable with nine MPPCs. MPPCs on this cable are inserted into the MPPC housings onrespective strips shown in Fig. 2. Therefore, eight cables are mounted on a scintillator layer.

means cobalt, and Cr means Crome, and tungsten and carbon are exist as a chemical compound134

of tungsten carbide. These values are used in the simulation study.135

In the right hand coordination where x is horizontal direction, y is vertical direction and z is136

5

Figure 5: A shade to reject photons coming to MPPC directly from scintillator strip.

beam direction which has origin on upstream of the detector and towards the downstream, the137

ScECAL has two types of layers called x (y) layers which have the fine segmented direction in x138

(y), i.e., longitudinal direction of strip along y (x). To avoid MPPCs exist on the same position139

in all x (y) layers, the ScECAL layers are categorized in more two, cold + or - for x (y) layers,140

where MPPCs exist plus (minus) side of y coordination in +x (-x) layers. Figure 6 shows such141

four types of layers, and the layers were aligned as +x, +y, -x, -y, +x, · · ·, in other words, strip142

direction is rotated 90 degrees as layer number increases.143

Figure 6: Four types of ScECAL layers. Particular types of layers have difference positions of flat cables,respectively. This difference indicates difference of positions of MPPC in order to reduce overlapping ofMPPCs (see text). The scintillator/MPPC units and fibers introducing LED light are hermetically coveredwith black sheet. Strips of fiberglass board (G10) are used in order to support MPPC from the backward.

In order to monitor the sensitivity of all MPPCs, the LED gain monitoring system was144

implemented in the physics prototype. For 18 strips in each row, a clear fiber having 18 notches145

lay down along to the holes row (Fig. 2) to deliver the LED light from a LED. Figure 7 shows146

such clear fibers with notches emitting bright LED light. The LED is driven with a special card147

made by the Czech Republic group [11]. The ADC-photon conversion factor of each MPPC is148

6

measured during the test beam experiments by using those LED lights, and the factor is used149

to implement the MPPC saturation correction discussed in the next section.

Figure 7: A bundle of clear fibers. Each fiber has 18 notches to derive the LED light into 18 strips in a rowof scintillators.

150

2.2 MPPCs and their saturation collection151

2.2.1 Characterization of all MPPCs in the physics prototype152

In order to use the MPPCs with similar characters especially with the uniform gain of whole of153

the detector, the characterization of 2300 MPPCs with their gain as a function of bias voltage,154

noise rate, and capacitance were measured before they were loaded into the physics prototype.155

A pixel in a MPPC multiplies the number of electrons originated from a photo-electron. The156

multiplying ratio, gain (G) is proportional to the difference of the bias voltage from the break-157

down voltage where MPPC starts to get the gain. This difference is referred to the over-voltage158

(∆V). Therefore, the gain is expressed in G = C∆V, where C is the capacitance of one pixel159

of the MPPC. Figure 8 left shows the breakdown voltage and right shows C, as the differential160

coefficient (slope) of gain with respect to the bias voltage. The bias voltage on each MPPC at161

the test beam was determined optimizing with those results to have the same over-voltage (∆V162

= - 3.0V) through all channels.

(-V)dumBreakdown Voltage 68 70 72 74 76

MP

PC

s

0

100

200

300

400

produced in 2008

produced in 2007

CALICE ScECAL

(pF)dumydCapacitance 0.018 0.02 0.022 0.024 0.026 0.028

MP

PC

s

0

200

400

600

produced in 2008

produced in 2007

CALICE ScECAL

Figure 8: The breakdown voltages (left) and the capacitances (right) of 2300 MPPCs, respectively. Differenceof features among the production lots are shown in those distributions. Black histograms show the 2000products obtained in 2008 and blue and red histograms show those obtained in 2007. Bias voltages at thetest beam experiment were determined by using those values. Products obtained in 2008 were set in theupstream layers, and 2007’s ones have been set in the downstream layers.

163

2.2.2 The number of effective pixels164

The PPDs including the MPPC are known to be non-linear devices. The output of the MPPCin terms of number of fired pixels (Nfired) can be parametrized as a function of the number of

7

incident photons (Nin) by the response function:

Nfired = N effpix

(1 − exp

(−ϵNin

N effpix

)), (1)

where N effpix is the number of “effective” pixels on the MPPC, ϵ is the photon detection efficiency165

and Nin is the number of photons incident on the sensor. Each MPPC used in the physics166

prototype has 1600 physical pixels. However, as each pixel can recover quickly with a time167

constant of ∼4 ns [12], it can emit another signal if the incident light has a duration longer than168

the pixel recovery time. This leads to an enhancement of the “effective” number of pixels for a169

single shot of light input from a scintillator strip.170

The inverse function of Eq. 1, which has Nfired as an input and gives Nin as an output, is171

used as the “MPPC saturation correction function”. To apply the saturation correction the172

MPPC output (measured in units of ADC counts) must first be translated to Nfired using a173

ADC-photon conversion factor (cp.e.) measured in LED runs during the test beam experiment174

for each channel. The only free parameter to be determined in the inverse function of Eq. 1,175

N effpix, is obtained by fitting Eq. 1 to test bench data as discussed in the following.176

2.2.3 Measurement of the number of effective pixels177

The N effpix is measured with 72 strips in the physics prototype after FNAL test beam experiment178

by using pico-second pulse laser, PiL040X (Head) + EIG2000DX (Controller) provided by Ad-179

vanced Laser Diode System A.L.S. GmbH, at Shinshu University. Figure 9 shows a schematic180

of the setup used to measure the saturation responses.

Figure 9: Setup of measurement the N effpix, a. a target scintillator enveloped in the reflector, kept in a layer

alignment of the physics prototype (left: top view, right: side view), b. WLS fiber, c. irradiation positionwith a small hole on the reflector, d. MPPC, e. half mirror, f. photomultiplier tube, g. lens, h. polaroid(fixed), and i. polaroid (rotatable).

181

Eq. 1 has a limit of fitting range since this equation does not correspond to the timing182

duration of scintillations mentioned in section 2.2.2. Figure 10 left shows a typical MPPC183

response as a function of the ADC counts of the photo multiplier tube (PMT) validated that it184

has linear response in the applied range. Therefore, the fitting range is prevented within a range185

determined with a criterion in the following: since the derivative of Eq. 1 with respect to Nin is186

an exponential function of Nin, the difference of the number of fired pixels with respect to the187

ADC counts of the PMT is also required to be fitted with an exponential function. However, in188

the case of the real data, the plot of the difference shows two separable ranges corresponding to189

two exponential functions as shown in Fig. 10 right. Therefore, only first part in Fig. 10 right is190

taken as the fitting range. The solid curve in left shows the result of the fit of Eq. 1 to the data191

and that in right is the result of one exponential fit to the difference of Nfired with respect to192

the ADC counts of PMT.193

8

(ADC)dumResponse of MPT0 20 40 60 80 100

du

mm

y123

4p.

e.

0

500

1000

1500

2000

2500

3000

13± = 2589 effpixN

CALICE ScECAL

Layer: 30, Channel: 32

(ADC)dumResponse of MPT0 100 200 300 400

(p.e

./AD

C)

duG

radi

ent

10

210CALICE ScECAL

Layer: 30, Channel: 32

Figure 10: left MPPC response to the laser pulse as a function of the response of PMT. right the differenceof Nfired with respect to the ADC counts of PMT, giving a criterion to determine the fit range in it left plot.

Figure 11 shows the distribution of measured N effpix obtained as a fitting parameter of Eq. 1,194

having a mean value of 2428±39 pixels and a standard deviation over 245 pixels. This mean195

value is used to implement the MPPC saturation correction and the standard deviation is used196

to estimate the systematic uncertainty from the uncertainty of N effpix in section 5.2.6.

effpixN

1500 2000 2500 3000 3500

Cha

nnel

s

0

5

10

15

20

Mean = 2428.4

RMS = 245.1

CALICE ScECAL

Figure 11: Distribution of the number of effective pixels, N effpix, measured from 72 strips.

197

2.3 Data acquisition system198

The readout concept of the ScECAL physics prototype is based upon the same architecture199

as that of the CALICE AHCAL [7]. The readout system for the back-end data acquisition,200

the CALICE readout cards (CRC) were provided synchronizing the data taking with AHCAL201

and TCMT. An ASIC developed for PPD was implemented on the front-end electronics for 18202

channels [13]. The ASIC has 18-fold multiplexed chain of pre-amplifier, shaper, and sample-and-203

hold circuit [14]. The signals from twelve ASICs were fed into one of the eight input ports of204

the CRC. The ASIC takes peak hold methods. Therefore, the timing (hold time) was measured205

with real data taking optimizing to have the largest ADC counts.206

The ASIC has two operation mode; the low gain mode and the high gain mode. The low207

gain mode is used for the data taking of beam runs, while the high gain mode is used to take a208

few photon events to make the gain monitoring. The hold times have been determined for both209

9

low gain mode and hight gain mode respectively at the test beam experiment.210

3 Test beam at FNAL211

3.1 Beams and setup212

The physics prototype constructed in section 2.1 has been explored with various type of beams;213

electrons up to 32 GeV to study the response to electromagnetic events, 32 GeV muons for the214

calibration, charged pions up to 32 GeV to study the hadron response in the combination with215

AHCAL and TCMT, and neutral pions to evaluate two cluster separations. Those beams were216

provided at the Meson test beam facility number 6 (MT6) in the Fermi accelerator institute217

(FNAL) in September 2008 and in May 2009. This paper reports the response of the physics218

prototype to the electron beams from 2 GeV to 32 GeV analyzed with data taken in May 2009.219

Data taken in September 2008 has problem on temperature data. Recovery of the temperature220

data in 2008 is ongoing.221

The setup of the beam line is shown in Figure 12. A Cerenkov counter placed upstream222

the experimental area was used for trigger purpose, together with some combinations of plastic223

scintillators of different sizes. A pair of 20 cm × 20 cm trigger counters was used for the muon224

runs whereas the trigger counters are 10 cm ×10 cm for pion and electron runs. The combinations225

of trigger counter and the pressure of the Cerenkov counter for the electron funs and muon runs226

are listed in Table 1.

Figure 12: Configuration of the beam line at the MT6 in FNAL. The right handed coordinate systemis shown. Italic numbers at right bottom of the detectors show the thickness of them. All distances anddimensions are in mm.

227

3.2 Temperature measurement228

Temperature of the physics prototype were measured with two thermo-couplings put on the229

surface of the top of the first layer and of the bottom of the last layer, respectively. Figure 13230

shows the temperature of data acquisitions averaged of the 1 Hz temperature data taking. Tem-231

perature of the physics prototype varied between 19◦C to 27.5◦C due to two days malfunction232

of the air conditioning of the experimental hall. Consequently, the performance of the prototype233

in this severe condition (∆T = 8◦C) is presented in this paper.234

3.3 Runs for calibrations235

The responses of all channels in the physics prototype are normalized with a common physics236

signal of muons as the minimum ionizing particles (MIP). Although a MPPC response depends237

on its temperature and the electron data were acquired in various temperature shown in Fig. 13,238

the dependence on the temperature is removed from the response by applying this calibration239

10

Table 1: A list of trigger systems for different particles. The pressure of the Cerenkov counter usedfor each trigger setup is also indicated.

Particle p(GeV/c) Trigger Cerenkov pressure

muon 32 20 cm×20 cm -electron 1 10 cm×10 cm 345 hPaA (outer)electron 3 10 cm×10 cm 345 hPaA (outer)electron 6 10 cm×10 cm 345 hPaA (outer)electron 12 10 cm×10 cm 138 hPaA (outer)electron 16 10 cm×10 cm 138 hPaA (outer)electron 25 10 cm×10 cm 138 or 103 hPaA (outer)electron 32 10 cm×10 cm 103 hPaA (outer)

Figure 13: Detector temperature of the muon runs and the electron runs in 2009. During the left of theblue vertical line, the air conditioning system of the experimental hall malfunctioned.

with the ADC-MIP conversion factors as a function of temperature. In fact, six muon runs were240

taken in the wide temperature range for this reason (Fig. 13).241

The muon beams were switched by putting iron target into the 32 GeV pion beams on the242

upstream of MT6 by FNAL beam control center. The trigger counter T20 in Fig. 12 was used243

instead of T10 in order to expose the whole of detector to the muon beams.244

The ADC-photon conversion factors are required to convert the ADC counts to the number245

of detected photons for the saturation correction as discussed in section 2.2.2. To determine an246

ADC-photon conversion factor, the spacial data “LED data” were acquired with the LED runs247

which were taken more than one run in a day as a general rule. In an LED run 50000 events data248

were taken with an LED pulse in each event provided through the clear fiber discussed in section249

2.1. The each LED power supply was changed in eleven steps (configurations) in 50000 events250

to take a suitable photon yield for each channel. The selection of the suitable configuration was251

achieved in the off-line analysis. Since an ADC-photon conversion factor also depends on the252

temperature, this factor is also delivered as a function of temperature in use.253

In the determination of an ADC-photon conversion factor, the photo-electron peaks of the254

ADC distribution of a few incidental photon were used. Therefore, the LED runs were taken with255

high gain amplifier (Calibration mode), while the beam runs were taken with low gain amplifier256

11

(Physics mode) in order to have enough dynamic range of the measurement. This means that257

the ADC-photon conversion factors obtained in the calibration mode must be converted into258

the values corresponding to the physics mode. The ASIC discussed in section 2.3 has gain; 92.3259

mV/pC for the calibration mode and 8.18 mV/pC for the physics mode. Since the ratio of the260

amplitude of the physics mode to the calibration mode depends not only on those gains but261

also on the integration condition due to the difference of MPPC signal shape for each channel,262

this ratio of the amplitude “inter-calibration constant” were measured with the special runs,263

“inter-calibration run”. In the inter-calibration runs LED lights were delivered into each channel264

and the ADC counts were measured in both the physics mode and the calibration mode of the265

amplifier with the same strength of LED which can be measured with both modes, consequently266

it was high intensity that the ELD calibration mode. In an inter-calibration run 50000 events267

data were acquired also changing the strength of LED power in eleven steps, and the suitable268

step of photon yields was selected in the offline analysis.269

Those three calibration steps are summarized in the following:270

1. the MIP calibration to determine the ADC-MIP conversion factor (cMIPl,s ),271

2. the LED calibration to determine the ADC-photon conversion factor (cp.e.l,s ),272

3. and the inter-calibration to determine the ration between physics mode and calibration273

mode of the amplifier (cinterl,s ),274

where, l and s denote layer number and strip number respectively. Hereafter we drop those275

suffixes unless it is confused without those.276

4 Analysis: Reconstruction277

4.1 Analysis flow278

As discussed in section 3.3, the calibration procedure is separated in three steps; MIP calibration279

for the comprehensive calibration using MIP signals, the LED calibration for the MPPC gain280

monitoring in order to apply the MPPC saturation correction, and the inter-calibration to281

convert between the high gain mode and the low gain mode. In the successive three subsections,282

the procedures to measure those conversion factors or constants are discussed. The procedure283

to create the electron spectra by using those calibrations is discussed in section 4.5.284

The ADC counts in those discussions are subtracted values with the pedestal ADC counts.285

In the beam runs 500 of random trigger events were acquired between beam spills for the286

measurement of pedestal of each channel, and the mean ADC counts of pedestal was defined287

as the pedestal ADC counts. In the measurement of the ADC-photon conversion factors, the288

pedestal ADC counts are not subtracted from the signal ADC counts, since a distance between289

the pedestal peak and the one photo-electron peak in a spectrum is a ADC-photon conversion290

factor as shown in the Fig. 17.291

4.2 ADC-MIP conversion factor as a function of temperature292

The distribution of the MIP energy deposits measured in the ADC counts on each channel is293

fitted with a landau function convoluted with a gaussian resolution function. The most probable294

value (MPV) obtained as an fitting parameter is directly the ADC-MIP conversion factor (cMIP).295

Figure 14 shows a typical distribution of MIP energy deposit and the fitting result.296

The beams for the cMIP contains almost no electrons or pions because of the iron dumper.297

Therefore, the MIP events are simply required to have the same X (Y) “hit” position of channels298

at least in ten different X (Y) layers, respectively. A “hit” is defined as a signal larger than the299

mean value of pedestal by at least three standard deviations of the pedestal.300

The MPV of each channel is measured for six runs acquired in different temperature con-ditions so that the correlation between MPV and the temperature of detector is obtained inFig. 15. A temperature data in the plot is averaged temperature during the data taking. The

12

Figure 14: A distribution of energy deposit by mip like particles on a channel. Solid line shows the fittingresult of a landau function convoluted with a gaussian function.

cMIP can be approximately expressed as a linear function of temperature. The solid line inFig. 15 shows the result of the linear fit. Consequently, the ADC-MIP conversion factor is afunction of temperature:

cMIP(T ) = cMIP(T0) +dcMIP

dT(T − T0), (2)

where T is the temperature at the measurement and T0 is a nominal temperature. The fitting301

parameters, cMIP(T0) and dcMIP/dT for each channel are stored to use for the analysis of electron302

beam data. The energy deposit by electron beams measured at temperature T ′ calibrated with303

cMIP(T ′) no as the function of the temperature.

Figure 15: A cMIP as a function of detector temperature. Solid line shows the result of linear fit.

304

Figure. 16 left shows the distribution of the ADC-MIP conversion factors estimated at 20◦C305

{cMIP(T = 20◦C)} with 19% of the coefficient of variation in 2160 channels. Figure. 16 right306

shows the distribution of the value dcMIP/dT/cMIP. The mean of gaussian fit is -2.95±0.45%/K,307

where the uncertainty is the standard deviation.308

13

Figure 16: left Distribution of cMIP(20◦C). right Distribution of the slope of cMIP, dcMIP/dT/cMIP. Solidline shows the result of a gaussian fit.

4.3 ADC-photon conversion factor as a function of temperature309

An ADC-photon conversion factor (cp.e.) is determined by using a few-photon spectrum of LED310

light acquired in the LED runs discussed in section 3.3. A mean of ADC counts corresponding311

to one photo-electron is a cp.e. for the corresponding channel. The sensitivity of the MPPC has312

the temperature dependence contributed from the temperature dependence of two sources; the313

gain and the photon detection efficiency. However, the temperature dependence of the cp.e. is314

only affected by temperature dependence of the gain, because the cp.e. is obtained by the ADC315

counts corresponding to the distance of one photo-electron peak. From the fact that the photo-316

electron peaks can be clearly seen in the MPPC spectrum, the absolute value of the ADC counts317

corresponding to the number of photo-electrons are measurable. Figure 17 shows an example of318

spectrum of LED run.

Figure 17: A typical spectrum of LED run of a channel. Solid line shows the result of three-gaussian fit.An arrow shows the cp.e. of this channel.

319

The LED run data of each channel were acquired in nine runs with different temperatureconditions. Therefore, cp.e. also can be converted into a function of temperature as the same asthe cMIPs case:

cp.e.(T ) = cp.e.ls (T0) +

dcp.e.ls

dT(T − T0). (3)

Figure 18 left shows the distribution of cp.e.(T = 20◦C), and right shows the distribution of320

dcp.e./dT/cp.e.(20◦C). Approximately ∼80% of all channels are successfully read out during321

14

LED light spectra recording. When the LEDs are on, some channels exhibit large noise while322

others have excessively high pedestals. Some channels have too small or too large cp.e.(T0)

Figure 18: left Distribution of cp.e.(20◦C). Difference of feature of products between 2007 and 2008appears around 240 ADCs (see also Fig. 8) right Distribution of dcp.e./dT/cp.e.. Solid line shows the resultof a gaussian fit in order to get the mean value and the standard deviation.

323

The fitting parameters cp.e.(T0) and dcp.e./dT are applied to the MPPC saturation correction324

for each channel.325

To apply the MPPC saturation correction, individual cp.e.(T0 = 20◦C) are used where these326

are available (successful channels) to measure cp.e., where it is required to have the cp.e.(T0 =327

20◦C) between 170 and 260 ADCs/photon and its uncertainty is between 0.2 to 50 ADCs/photon.328

For channels where LED data read out was not successful, the average value of the successful329

channels was used. With regard to dcp.e./dT , the mean of the gaussian fit shown in Fig. 18 right330

is used uniformly for all channels.331

4.4 Inter-calibration constant332

The inter-calibration process also uses LED light but needs more photons so that it allows to tomeasure the mean of signals in both the physics mode and the calibration mode. Figure 19 leftand right show typical ADC distributions with the same LED power supply but the differentamplifier modes respectively. An inter-calibration constant, cinter becomes

cinter =⟨ADCs⟩high

⟨ADCs⟩low, (4)

where ⟨ADCs⟩high(low) is the mean of signals in the high gain mode (low gain mode) of a333

corresponding channel.334

Because of the same reason due to the LED noise as the cp.e. case, around 20% of channels335

cannot have measured cinter. For those channels, the average cinter of other 80% of channels336

with succeeded one photo-electron measurement is used for the reconstruction of the electron337

spectra .338

4.5 Electron energy spectra339

4.5.1 Reconstruction340

An energy of an incident electron is reconstructed as the sum of the energy deposits of all hitsin an event (an electron) on the physics prototype:

E =∑l,s

Acorr.MIPsl,s , (5)

15

(adc)dResponse to LED light 0 5000 10000

Eve

nts

0

20

40

60 Layer:1, Strip:1

CALICE ScECAL

(adc)dResponse to LED light 0 1000 2000 3000 4000

Eve

nts

0

50

100

150

200 Layer:1, Strip:1

CALICE ScECAL

Figure 19: Distribution of the energy deposit of a inter-calibration run with the calibration mode (left)and the physics mode (right). The same LED power was supplied on the both case.

where Acorr.MIPsl,s is the energy deposit normalized with cMIP

l,s (T ) and corrected for the MPPCsaturation response with cp.e.

l,s (T ) and cinterl,s :

Acorr.MIPsl,s = F−1

{AADCs

l,s (T )cinterl,s

cp.e.l,s (T )

} cp.e.l,s (T )

cinterl,s

cMIPl,s (T ), (6)

where the function F−1 is a revers function of Eq. 1, AADCsl,s (T ) is the signal from the strip s341

of layer l read in the ADC counts, and T is the temperature of the detector at the measuring342

time. Note that an Acorr.MIPsl,s is no longer a function of temperature after applying cMIP

l,s (T ) and343

cp.e.l,s (T ) to AADCs

l,s (T ).344

4.5.2 The energy spectrum after event selections345

The electron-tuned beams still contain the contamination of pions and muons even with the346

Cerenkov counter. Additionally, the physical volume of 180mm× 180 mm× 21.5X0 makes a347

limit of fiducial volume. Therefore, the event selection criteria are applied to extract the electron348

events as the following:349

1. the shower maximum in the ScECAL must be on the upstream than 20th layer,350

2. the deposit energy on the shower maximum layer in the ScECAL must be greater than;351

10 MIPs for 1 GeV/c,352

15 MIPs for 2 GeV/c,353

27 MIPs for 4 GeV/c,354

54 MIPs for 8 GeV/c,355

80 MIPs for 12 GeV/c,356

95 MIPs for 15 GeV/c,357

125 MIPs for 20 GeV/c,358

200 MIPs for 30 GeV/c,359

and 200 MIPs for 32 GeV/c,360

3. the deposit energy on the shower maximum layer in AHCAL must be less than 20 MIPs,361

4. the deposit energy on the most downstream layer of AHCAL must be less than 0.4 MIPs362

of AHCAL, and363

5. (6). the gravitational center of electromagnetic shower must be in ± 4 cm from center on364

the x, (y) axis.365

Figure 20 left shows an energy spectrum of 32GeV/c electrons in a run with the effects of366

cuts and right shows the shape of spectrum after all cuts. The spectrum is fitted well with a367

16

gaussian function in the range including 90% of entries. The reduced χ2 for all spectra except368

one GeV/c are between 0.9 to 1.2 indicating that the fitting region is reliably clean from the369

contaminations. The mean value and the standard deviation normalized by the mean from370

the result of gaussian fit are defined as the energy response and the energy resolution of the371

physics prototype, respectively. Although one GeV/c electron data have been acquired, the pion372

contamination could not removed enough from them with those selection criteria. Therefore,373

the results of one GeV/c runs are removed from the evaluation of the performance of the physics374

prototype in this paper.

Figure 20: Spectra of 32 GeV/c electrons. Left shows the effects of selection criteria 1-6 (cut 1-6, seesection 4.5.2 for criteria) ; black: before any cut, sky-blue: after cut 1, purple: after cut 2, yellow: after cut3, blue: after cut 4, green: after cut 5, and red after cut 6 (effects of cut 4 - 6 are small to appear). Althougha small amount of double particle events (around 8500 MIPs) and pion’s tail remains, after all cuts (red line,and pion, those events are three digit smaller than the signal events. Therefore, the effect on the mean andthe standard deviation of the spectrum is negligible. Right shows the spectrum after all cuts. Red line is theresults of the gaussian fit in the range 90% entries.

375

5 Results: Performance of the physics prototype376

5.1 Mean and resolution of measured energy of each beam momentum377

Even in the same beam momentum, differences of the mean values of the measured energy de-posit are seen among runs and these are larger than the variation expected from the uncertaintiesof respective runs. One possible source could be difference of beam tuning which can be slightlydifferent among runs even for a same beam energy. To remove the effects of these fluctuationon the result of the energy resolution, each spectrum of run is separately analyzed so that themean and resolution for a beam momentum are defined as the average of them estimated byusing a standard weighted least-squares procedure:

x ± δx =∑

i wixi∑i wi

± (∑

i

wi)−1/2, (7)

where xi is mean value or resolution of run i and wi is 1/(δxi)2. The sizes of discrepancies378

of the energy resolution among runs are consistent with their uncertainty as shown in Fig. 21.379

Therefore, the effect of those discrepancy on the energy resolution is safely removed by this380

way, while the systematic uncertainty on the mean value from these discrepancies must be381

implemented as discussed in section 5.1.382

17

Figure 21: The energy resolutions of 4 GeV electrons depending on the runs.

Table 2 lists such the mean value and the resolution of measured energy deposit for each383

beam momentum with the statistical uncertainty of those values. Systematic uncertainties on384

those values are discussed in section 5.2 and the linearity and the quadratic parameterization385

of energy resolution of the physics prototype are evaluated in section 6.2.386

Table 2: Mean and resolution of measured energy of each beam momentum.

Beam momentum (GeV/c) Mean (MIPs) Resolution† (%)2 281.56±0.08 9.628±0.0344 544.78±0.12 6.852±0.0268 1074.29±0.14 5.042±0.01512 1596.02±0.22 4.419±0.01615 1974.81±0.24 4.253±0.01420 2608.21±0.30 3.840±0.01330 3872.6 ±0.5 3.353±0.01632 4177.4 ±0.7 3.359±0.020

† Intrinsic beam momentum spread has not been subtracted yet.

5.2 Systematic uncertainties on the mean and the standard deviation387

of the energy spectrum388

5.2.1 Difference of the mean value of deposited energy among runs389

Uncertainties from the discrepancies among beam runs discussed in section 5.1 are implemented390

based on the standard deviation from the expected value, and summarized for respective beam391

momenta in Table 3 together with other systematic uncertainties.392

5.2.2 Event selections393

As discussed in section 4.5.2, six event selections have been applied to reduce the effects from out394

of fiducial events. To estimate the systematic uncertainties arising from these selection criteria,395

the impact of cut variations are measured and evaluated.396

The uncertainties of mean value from the variation of the cut ranges, except for the cut of397

the centre of gravity of deposited energy, are less than 0.05%.398

The uncertainties due to the different cut variations on the horizontal (x) and vertical (y)399

position of the centre-of-gravity on ScECAL surface for every energy are listed in Table 3. The400

18

nominal cut position is ± 40mm for both x and y. Although the cut variation of those values401

considered for this study is ± 20mm to ± 80mm, only positive uncertainty (with narrow range)402

is considered because wider windows obviously make energy leakage.403

Contributions from the cut variations for the energy resolution are negligibly small (< factor404

0.005) compared to the factor 0.03–0.09 of the uncertainty coming from the beam momentum405

spread.406

5.2.3 ADC-MIP conversion factor407

The uncertainties coming from the cMIP on the mean and the resolution of measured energy408

deposits are estimated.409

An cMIP(T ) defined in Eq 2 has two parameters: the value of the ADC-MIP conversion factor410

at a certain temperature, cMIP(T0), and the slope of the ADC-MIP conversion factor, dcMIP/dT .411

The propagations of the statistical uncertainties of these parameters are studied using pseudo-412

experiments in which each parameter is randomly fluctuated within its uncertainty as sigma of413

the gaussian random function. Deviations from the nominal measured mean energy and energy414

resolution in 20 trials are taken as the systematic uncertainties from the cMIP. The measured415

deviation from linearity varies in region of 0.09–0.24% and 0.02–0.06% due to the uncertainties416

of cMIP(T0) and dcMIP/dT respectively, as summarized in Table 3.417

The systematic uncertainties coming from cMIP(T0) are 0.08% and 0.07% as the absolute418

deviation values for the stochastic term and the constant term, respectively. It is 0.01% for419

both the stochastic and the constant term from the variation of dcMIP/dT .420

5.2.4 ADC-photon conversion factor421

An ADC-photon conversion factor for each channel, cp.e. is also a linear function of temperature422

of the detector and it is used to convert ADC counts to the number of photons (fired pixels of423

the MPPC). The number of detected photons required for the MPPC saturation correction to424

be applied is discussed in section 2.2.2. Although the propagation of statistical uncertainties425

of these parameters are also studied by using pseudo-experiments as in the study of the ADC-426

MIP conversion factors, systematic uncertainties of mean and energy resolution of the measured427

energy deposit due to the uncertainty of these parameters are confirmed to be negligible.428

5.2.5 Inter-calibration constant429

The systematic uncertainty due to the uncertainty of the inter calibration constants is also430

studied by using a pseudo-experiment method. Although most of the uncertainties of gain inter431

calibration constant for each channel are taken as the sigma of the Gaussian used to make the432

variation, the standard deviation of the measured gain constants is used for the channels which433

are not successful to estimate the inter calibration constant. This is for the same reason as in434

the measurement of the ADC-photon conversion factor. The deviation from linearity as a result435

of fit at each of 20 trials of varies by about 0.02% on value of the deviation and the uncertainty436

of both stochastic and constant terms from the uncertainty of the inter calibration constant437

leads to an absolute deviation of less than 0.01%. Therefore, the systematic uncertainty of the438

mean value of the energy deposit and the energy resolution from the inter calibration constant439

is considered to be enough small.440

5.2.6 The number of effective pixels of the MPPC441

The mean value of the number of effective pixels of the MPPC, Npix measured for 72 strips is442

applied as an input of the MPPC saturation correction as discussed in section 2.2.2. Therefore,443

the standard deviation of the distribution of Npix is taken as the uncertainty of Npix to create444

the pseudo-experiments which are to estimate the contribution from the variation of Npix. The445

deviation from linear fit at each energy is varied by 0.01–0.16%. The uncertainties are 0.07%446

and 0.06% for the stochastic and constant terms, respectively. Therefore, the contribution of447

19

the uncertainty of the number of the effective pixels of the MPPC to the uncertainty of the448

mean values and energy resolution is small.449

5.2.7 Beam momentum fluctuation450

The MTest beam has a momentum spread, ∆p/p = 2% as its design value for 1 – 60 or451

90 GeV/c [15]. A calorimetry test for the Muon g-2 experiment at the MTest estimates 2.7± 0.3%452

of the beam momentum spread for 1–4 GeV/c using a Pb/Glass calorimeter [16]. The other453

experiment for a SiFi calorimeter with tungsten estimates 2.3± 0.3% for 8 GeV/c by using their454

own detector and the results of the previous one [17]. Preceding this study, they have estimated455

2.3% in the range 1.5–3.5 GeV/c [18]. From these measurements we take the MTest beam456

momentum spread in two incidental beam momentum ranges, 2.7± 0.3% for 2–4 GeV/c, and457

2.3± 0.3% for 8–32 GeV/c. To estimate the intrinsic energy resolution of the physics prototype,458

this momentum spread must be quadratically subtracted from the energy resolution estimated459

in section 5.1.460

The systematic uncertainty comes from the uncertainty of the intrinsic beam momentum461

spread, 0.3% is the largest uncertainty on the energy resolution of each spectrum.462

5.2.8 Summary of uncertainties on each beam momentum463

Significant uncertainties of the measured mean value for each beam momentum are listed in464

Table 3.465

Table 3: The uncertainties of mean value of measured energy deposit.

pabeam runsb range-xc range-yd cMIP(20◦C)e dcMIP/dT f Npixg stath totali

2 ±0.31 +0.23 +0.16 ±0.23 ±0.03 ±0.11 ±0.03 +0.49−0.40

4 ±0.23 +0.28 +0.09 ±0.09 ±0.02 ±0.01 ±0.02 +0.39−0.25

8 ±0.27 +0.14 +0.03 ±0.21 ±0.03 ±0.05 ±0.01 +0.38−0.35

12 ±0.81 +0.13 +0.02 ±0.16 ±0.03 ±0.05 ±0.01 +0.84−0.83

15 ±0.45 +0.10 +0.02 ±0.13 ±0.04 ±0.04 ±0.01 +0.48−0.47

20 ±0.66 +0.43 +0.01 ±0.13 ±0.04 ±0.04 ±0.01 +0.80−0.68

30 ±0.10 +0.14 +0.01 ±0.12 ±0.06 ±0.16 ±0.01 +0.27−0.23

32 ±0.10 +0.03 +0.01 ±0.23 ±0.04 ±0.13 ±0.02 +0.29−0.29

a Beam momentum (GeV/c).b Uncertainty comes from difference on run-by-run (%).c Uncertainty comes from variation of range of gravitational center of shower in x (%).d Uncertainty comes from variation of range of gravitational center of shower in y (%).e Uncertainty comes from uncertainty of the offset value of cMIP(%).f Uncertainty comes from uncertainty of the slope of cMIP(%).f Uncertainty comes from uncertainty of N eff

pix (%).g Statistical uncertainty (%).h Total of uncertainties (%).

The expected energy resolution for each beam momentum and its total uncertainty are listed466

in Table 4. The intrinsic beam momentum fluctuation has already been subtracted.467

20

Table 4: The uncertainties of the resolutions of measured energy deposit.

pabeam energy resolution (%)b total of uncertaintiesc

2 9.24 ±0.304 6.30 ±0.308 4.49 ±0.3012 3.77 ±0.3015 3.58 ±0.3020 3.06 ±0.3030 2.44 ±0.3032 2.45 ±0.30

a Beam momentum (GeV/c).b Beam momentum fluctuation is subtruced.c Absolute value: uncertainty of σE/p (%).

5.3 Linearity and the energy resolution of the ScECAL physics pro-468

totype469

Figure 22 left shows the deposited energy as a function of the momentum of the incident beams.470

The solid line is the result of a linear fit with the values in Table 2 and the uncertainties in Table 3.471

The slope, dMIP/dGeV and offset are 130.24±0.24 MIP/GeV and 24.0±1.3 MIP Figure also472

shows the deviation from linearity at each beam momentum. The maximum deviation from473

linearity is 2.0±0.8%. at 12 GeV.474

Figure 22 right shows the energy resolution as a function of the inverse of the square root475

of the incident beam momentum. Each data point and its uncertainty on the σ/E are taken476

from Table 4 so that the intrinsic beam momentum fluctuation has been subtracted. The curve477

shows the result of a fit to the data with a quadratic parametrization of the resolution.

(MIP

)du

mD

epos

it en

ergy

in E

CA

L

0

1000

2000

3000

4000 CALICE ScECAL

(GeV/c)dummBeam momentum

0 10 20 30Dev

iatio

n(%

)

-4-2024

)GeV/c (1/ dumm beam

p1/

0 0.2 0.4 0.6 0.8

(%)

dum

my1

2

E /

Eσ

0

2

4

6

8

10

12CALICE ScECAL

Figure 22: Response of the ScECAL prototype to 2 - 32 GeV electron (left, top), deviation from the resultof linear fit (left, bottom), and the energy resolution as a function of inverse of square root of the beammomentum (right).

478

Propagations of the systematic uncertainties from three calibration factor, cMIP, cp.e., and479

cinter to stochastic term and the constan term were investigated by using pseudo-experiment480

method. Figure 23 shows the the distribution of fluctuation of the stochastic term (left) and481

the constant term from the uncertainty of the cMIP(T0 = 20◦C). The systematic uncertainties482

21

on the stochastic term and the constant term from dcMIP/dT , cp.e.(T0 = 20◦C), dcp.e./dT , and483

cinter are negligibly small.

(%)dummstochastic term12.8 13 13.2 13.4 13.6

dum

Pse

udo

expe

rimen

ts

0

2

4

6

8

Mean = 13.20 0.08 d RMS =

CALICE ScECAL

(%)dummyConstant term2 2.2 2.4 2.6 2.8 3

dum

Pse

udo

expe

rimen

ts

0

2

4

6

8

Mean = 2.51 RMS = 0.08

CALICE ScECAL

Figure 23: Distribution of the stochastic term (left) and the constant term (right) of the energy resolutionin 20 pseudo-expeirment on cMIP(T0 = 20◦C). The standard deviations are 0.08% for both the stochasticterm and the constant term.

484

The uncertainty from the intrinsic beam momentum fluctuation is naturally considered485

in the case that the size of the beam momentum spread is correlated among all beam mo-486

mentum. Therefore, propagation of those uncertainties of the stochastic term and the con-487

stant term are conservatively estimated by examination with highest and lowest cases of beam488

momentum spread within the given uncertainty of 0.3% quoted in section 5.2.7. Observed489

variation among those trial in terms of stochastic and constant term of energy resolution490

are taken as those systematic uncertainties resulting in 12.9±0.1(stat.)±0.4(syst.)%√

GeV and491

1.2±0.1(stat.)+0.4−1.2(syst.)% for the stochastic and constant terms, respectively.492

6 Comparison with Monte Carlo simulation493

6.1 ScECAL physics prototype in the Simulation494

The physics prototype and the test beam setup are constructed in a simulation space with495

Mokka [19], a Geant4 based Monte Carlo program. One unit of layers consist of the absorber496

layer, reflector layer, scintillator layer, second reflector layer, readout layer, and the air gap. A497

readout layer consists of materials of polyimide flat cable, clear fiber, black sheet, an amount of498

glass fiber material and air mixed together uniformly. A scintillator layer has the actual strip499

segmentation in the laterally but has not been implemented boundary reflector and MPPCs. An500

absorber layer is made of mixed elements discussed in section 2.1 with the measured density. The501

beam line setup upstream of the physics prototype also simulated with three trigger counters502

of plastic scintillators, one veto plastic scintillator, and four drift chambers, although those are503

not used with their functions. On the other hand, AHCAL and the TCMT are not simulated,504

because injected beams are contamination free in the simulation. Therefore, two selection criteria505

on AHCAL information are not used, while they were used in the real data analyses.506

Injected beam shape is tuned …YUJI … . The beam positions are adjusted to the real data507

for respective runs. It was confirmed that the beam position did not affect on the mean energy508

deposit and its fluctuation within the given variation of beam position. Dead channels also509

implemented acceding to the real data.510

22

6.2 Comparison with the ideal detectors511

Figure 24 left shows the simulated response of the physics prototype to the electron beams.512

The slope, dMIP/dGeV and offset are 128.18±0.01MIP/GeV and -6.78±0.19 MIP, respectively.513

The slope is consistent with real data’s one. Although the offset size is not so large, it disagrees514

between simulation and data. These values are discussed in the following.515

The yellow solid line and dots in Fig. 24 right shows the energy resolution of the simulation.516

The constant term and stochastic term is 0.66±0.08% and 13.26±0.08%·√

GeV, respectively.517

Both values are consistent with those of real data within the uncertainty. More detail compar-518

isons are discussed in the following/

Figure 24: The response (left) and the energy resolution (right) of the simulated physics prototype to theelectron beams.

519

Effect of the leakage. By comparing this energy resolution with one on the three times520

larger detector in each dimension, the effect of energy leakage from 180mm× 180 mm× 21.5X0521

physics prototype is studied. Figure 25 shows the relative energy leakages into the lateral side522

(lateral leakage) and downstream side (longitudinal leakage) to the total energy. Total leakage is523

kept in 2.3 - 3%, as the results of compensation between the lateral wreckage and the longitudinal524

leakage.

Figure 25: Relative leakage of the electron energy in the lateral side (blue dots) and the longitudinal side(red). Black dots show the total leakage.

23

525

The green solid line and dots in Fig. 24 right shows the energy resolution of large detector.526

Comparison between yellow line and green line indicates that the effect of the leakage on the527

constant term is +0.66%.528

Effect of the non-uniformity of response in each strip and the uncertainty of529

the saturation correction. The non-uniformity of the response in the each strip has been530

measured with muon events by using position information from even (odd) layers for the odd531

(even) layers. The mean ratio of the response at the scintillator edge on the other side of MPPC532

to the response of MPPC side is 88.3% with the distribution of 4.2% of the standard deviation.533

The black line and dots in Fig. 24 right show the energy resolution in the case where this non-534

uniformity of response on each scintillator strip is implemented additional to the fluctuation of535

N eftpix. Clearly, both effects are negligible indicating that the estimation of uncertainty from the536

fluctuation of N eftpix is consistent with this result and that the MPPC/scintillator units have the537

enough uniform response.538

Effect of the Intrinsic beam momentum fluctuation. The purple solid line and539

dots in Fig. 24 right show the simulation results of the energy resolution where the beam has540

been implemented the momentum fluctuation discussed in section 5.2.7. The Open circles and541

dashed line show the measured energy resolution from the real data before the beam momentum542

fluctuation. Data and the simulation result are consistent with each other.543

7 Discussion544

The ScECAL prototype shows enough linearity for the ILC physics such that the maximum545

deviation from linear behavior is less that 2% at least in the range from two to 32 GeV. This546

ability was accomplished with 1600-pixel MPPCs by preventing the saturation behavior with a547

saturation correction method as discussed in section 2.2. Although the maximum electron energy548

might be 250 GeV in the Bhabha scattering events at the 500 GeV ILC, resent progress of the549

MPPC development with greater than ten thousands-pixel MPPCs provides us an expectation550

of the enough linearity for such a large energy measurement.551

Although this experiment was haven in the large temperature variance such that the change552

was between from 19◦C to 27.5◦C, the calibration procedure with the ADC-MIP conversion553

factor and the ADC-photon conversion factor for each channel as functions of temperature554

remove the influence of the temperature variance. This fact gives an evidence that the ScECAL555

can be employed in such a extreme temperature conditions. In order to be clear how this556

procedure works, Fig. 26 shows the deviations of responses from linear behavior of both cases in557

which the calibration was done with ADC-MIP conversion factor fixed at a temperature and in558

which the calibration was done with ADC-MIP conversion factors and ADC-photon conversion559

factors as temperature functions.560

The standard deviation of distribution of the ADC-MIP conversion factors in Fig. 16 is 19.0%561

of its mean. Since the over-voltages of channels are tuned to 3 V, this variance of the ADC-MIP562

conversion factor is apparently larger than the expected value considering of variance of the563

capacitance of MPPCs shown in Fig. 8. Most probable reason of this variance is the mismatch564

of the position of WLS fiber and MPPC. This mismatch comes from the difficulty of the control565

of position and size of the hole for the WLS fiber by the extrusion method. Although the566

performance of the physics prototype is enough good, there exists the potential to have better567

performance by making better quality control of the position of WLS fiber or by the direct568

coupling of MPPC/scintillator. In fact, current effort of the CALICE scintillator group is to569

make the direct coupling between the MPPC and 5 mm width scintillator strip in order to make570

more fine granular ScECAL (5mm× 5mm).571

The mean value of the numbers of photo-electrons at the most probable value of the MIP572

energy deposit of all channels is 14 photo-electrons calculated from the mean value of the ADC-573

24

Beam momentum (GeV/c)0 10 20 30

(%)

dum

Dev

iatio

n

-20

0

20

C.°

:with ADC-MIP. at 20

:with ADC-MIP. as a function of temperature.

CALICE ScECAL

Figure 26: The divination from the result of linear fit: data were calibrated with the ADC-MIP andADC-photon conversion factors at 20◦C (circles: only with statistic errors), and with the ADC-MIP andADC-photon conversion factors as functions of temperature (black dots: with statistic and systematic errors).

MIP conversion factor, ADC-photon conversion factor, and the inter calibration constants. This574

means that the mean of sampling ratio of the MPPC from the scintillator is less than 5% by a575

theoretical expectation. On the other hand, the Monte Carlo simulation directly evaluate the576

energy deposit in the scintillator meaning that this small sampling fraction is not considered.577

In spite of this fact, the energy resolution of the result of simulation agree the result from the578

real data. This means that the small sampling ratio of MPPC/scintillator does not affect on the579

energy resolution and it then gives us an important advantage for the ScECAL development,580

since 14 or less p.e./MIP is suitable in order to have large dynamic range of the ScECAL and581

simultaneously to have enough noise rejection of the one photo-electron dark noises by the582

threshold of 0.5 MIP.583

The mean ratio of the response at the scintillator edge on the other side of MPPC to the584

response of MPPC side is 88.3%. From discussion in 6.2, this 88.3% of uniformity can be585

concluded that the MPPC/scintillator units of this Prototype have the enough uniform response,586

while the scintillators of extrusion method in the previous physics prototype did not have such587

uniformity. This improvement to the previous physics prototype comes from the application of588

the shades in front of MPPC shown in Fig. 5 and the improvement of the scintillator quality.589

The physics prototype has four dead channels in 2160 channels. Although further inves-590

tigation is needed, one of the provable reason is that a short circuit happened between the591

electrodes of MPPC since the reflector has a small conductivity on its cutting cross-section and592

the electrodes touched it. This conductivity also became the reason that the detector total593

thickness, 274 mm, was larger than expected since the press to make it thinner could not be594

arrowed by this conductivity. The modification of thickness is expected that the shower radius595

in ScECAL becomes shorter and the lateral leakage then decreases, which is the largest origin596

of the constant term of the energy resolution except the intrinsic beam momentum fluctuations.597

8 Summary598

The physics prototype of the CALICE ScECAL for the future linear colluder has been con-599

structed and tested at the Fermilab in May 2009. It is also one of the large scale applications600

of the novel PPD (MPPC) sensors. The ScECAL physics prototype is a feasibility study for601

the realization of a highly granular calorimeter using this new type of photodetectors. The602

25

work presented comprises the operation of the prototype during the test beam data taking pe-603

riods, the calibration of all calorimeter channels and the reconstruction of the electron beams.604

The combined setup consisting of the ScECAL, the AHCAL, the TCMT, the trigger system,605

Cerenkov counter and various devices for particle identification and monitoring of the beam606

parameters was installed and commissioned.607

The response of the physics prototype to the electron beams with the energy range of 2 to 32608

GeV is studied. Besides the many advantages of the PPD (MPPC) sensors, their temperature609

dependence and non-linear behavior possess a challenge on the calibration of the ScECAL. A610

mip based calibration is used, which is obtained from 32 GeV muon beam data. The tempera-611

ture dependent response of the physics prototype has been measured and understood by using612

those data to remove the interference to the response from the temperature fluctuations. The613

saturation behavior of the MPPCs are determined by using the pico second laser system. The614

method including those calibrations has been established and provided a set of clean electron615

energy spectra on the ScECAL physics prototype.616

The systematic uncertainties are also studied considering contribution from a variety of617

sources, precision of the measurement of the beam momentum spread, event selection cuts,618

ADC-MIP conversion factor, ADC-photon conversion factor, inter calibration constants; the619

number of effective pixels of the MPPC. The most important uncertainty in the energy resolution620

is due to the uncertainty of the beam momentum spread. The intrinsic energy resolution, after621

subtraction of the beam momentum spread, is determined to be 12.9± 0.1(stat.) ± 0.4(syst.)%622

for the stochastic term and 1.2±0.1(stat.)+0.4−1.2(syst.)% for the stochastic term. The deviations623

of the response from linear behavior is less than 2%.624

9 Acknowledge625

References626

[1] J.-C. Brient and H. Videau, eConf, vol.C010630, p. E3047 (2001), arXiv:hep-ex/0202004.627

[2] M. Thomson, NIM, A611, 25 (2009).628

[3] ILD Concept Group, The international Large Detector Letter of Intent (2009).629

[4] CALICE Collaboration, arXiv:1212.5127 (2012).630

[5] ILD Concept Group, The Detailed Design Report (2013).631

[6] CALICE Collaboration, …ScECAL DESY TB.632

[7] CALICE Collaboration, JINST, 5, P05007 (2010).633

[8] CALICE Collaboration, JINST, 7, P09017 (2012).634

[9] Hamamatsu Photonics KK, http://jp.hamamatsu.com/en/index.html.635

[10] KIMOTO CO., LTD., http://www.kimoto.co.jp/english/company/index.html.636

[11] Ivo Polak, IP ASCR Pargue, ECFA meeting in Valencia (2007).637

http://www-hep2.fzu.cz/calice/files/ECFA Valencia.Ivo CMB Devel nov06.pdf638

[12] .Sudo san’s study.639

[13] http://omega.in2p3.fr.640

[14] Blin, et al., Dedicated very front-end electronics for an ILC prototype hadronic calorimeter with641

SiPM readout. LC-DET-2006-007.642

[15] C. Johnstone, Proc.,EPAC 2006, Edinburgh, Scotland.643

[16] T. Tsai, Special Reports of All Experimenters meetings FNAL, (2012)644

http://www.fnal.gov/directorate/program planning/all experimenters meetings/special reports/645

Tsai T1018 01 30 12.pdf.646

[17] C. Polly, Special Reports of All Experimenters meetings FNAL, (2010),647

http://www.fnal.gov/directorate/program planning/all experimenters meetings/special reports/648

Polly T1005 08 23 10.pdf.649

26

[18] R. McNabb, et al, NIM, A 602, 396-402(2009).650

[19] http://polzope.in2p3.fr:8081/MOKKA/.651

27