Update of Analysis of the Test Beam Experiment of ScECAL1

Physics Prototype2

The CALICE-ScECAL group3

October 7, 20124

Abstract5

Analysis of the test beam at Fermilab of ScECAL physics prototype (2009) is updated on two6

issues: 1) Temperature correction via the ADC-photon conversion factor is applied for each chan-7

nel of each event. 2) Systematic uncertainties are estimated and evaluated. The response of ScE-8

CAL for the electron beams increase 3% with this temperature correction. The intrinsic energy9

resolution of the ScECAL is determined as 12.9±0.1(stat)±0.4(sys)% and 1.2±0.1(stat)±+0.4/-10

1.2(sys)% for the stochastic term and constant term, respectively.11

1 Intruduction12

The ScECAL measures energy deposit of a particle by using scintillator strips where each strip13

is read out with a pixelated photon detector (PPD). A PPD has saturation behavior due to14

its mechanism, and the saturation is corrected using measured properties of PPD toward the15

incident photons; the number of detected photons as a function of the number of incident photons16

to the PPD. Therefore, the ADC-photon conversion factor is required for each channel to convert17

the ADC output into the number of detected photons. The sensitivity of a PPD depends on18

temperature. Most of temperature dependence of PPD is comprehensively corrected by using19

the ADC-MIP conversion factor depending on temperature in the previous CALICE note [1].20

Although the effect of temperature correction on ADC-photon conversion factor is expected not21

to be large as comparing with the effect of ADC-MIP conversion factor, it is required to be22

measured and evaluated as a second order correction.23

Systematic uncertainties including also the uncertainty from the ADC-photon conversion24

factor are estimated and evaluated in this update.25

2 Temperature correction on the ADC-photon conversion26

factor27

2.1 PPD saturation correction28

The property of PPD saturation is seen with the number of detected photons (fired pixels) as afunction of the number of incident photons in PPD:

Nfired = Npix

(1 − exp

(−ϵNin

Npix

)), (1)

1

where Nfired is the number of photons detected by PPD, Npix is the number of pixels on the29

PPD, ϵ is the photon detection efficiency and Nin is the number of photons incident into the30

PPD sensor. The revers function of Eq. 1 is used to apply the PPD saturation correction by31

inputting the number of detected photons so that the output is the number of incident photons32

into the PPD sensor. The number of detected photons is determined from ADC counts of each33

hit by using ADC-photon conversion factor for each channel. The ADC-photon conversion factor34

for each channel is determined in the following section.35

The only parameter of the revers function of Eq. 1, Npix is determined by fitting Eq. 1 to a36

bench test data in the previous note [2]. One of the update issues is that Npix is determined37

by measuring 72 channels of ScECAL prototype in this note. Therefore, the fluctuation of Npix38

can be evaluated to estimate the uncertainty from the PPD saturation correction. Figure 139

shows the distribution of measured Npix having the mean value of 2428.39±28.88 pixels and the40

standard deviation of 245.07 pixels.

Figure 1: Distribution of the number of pixels, Npix, measured with 72 strips.41

2.2 ADC-photon conversion factor42

An ADC-photon conversion factor is determined by using few-photon spectra of LED righttaken often between beam data taking [2]. The ADC counts corresponding to one photon isan ADC-photon conversion factor for the channel (l, s). The ADC conversion factor is a linearfunction of temperature as the same as the case of the ADC-MIP conversion factor. Therefore,the ADC-photon conversion factor, d(T ; l, s) is expressed as the following:

d(T ; l, s) = d(T0; l, s) + sdl,s · (T − T0), (2)

where l and s is layer number and strip number of this channel, respectively, T0 is a certain43

temperature to give the offset of the function, and sdl,s is slope of this function for the channel44

l, s. Figure 2, left shows the distribution of d(T0 = 20◦C; l, s) and right shows the distribution45

of sdl,s/d(T0 = 20◦C; l, s). The number of entries are ∼70% due to some problems to take LED46

right spectra1. To apply temperature correction, individual d(T0 = 20◦C; l, s) are used for the47

succeeded channels to measure d where it is required to have the d(T0 = 20◦C; l, s) between 17048

and 260 ADC/photon and the uncertainty between 0.2 to 50 ADCs/photon, while the average49

value of these succeeded channels are used for the failed channels. With regard to sdl,s, mean50

of gaussian fit in Fig. 2 right is used for all channels.51

1Some part of channels have large noise when LED right on, and some part of channels have two top pedestalduring LED data taking.

2

Figure 2: Distribution of d(T0 = 20◦C; l, s) (left) and sdl,s/d(T0 = 20◦C; l, s) (right) with the fitting resultof gaussian function. The small peak of d(T0 = 20◦C; l, s) near 235 ADCs/photon is well understood due tothe difference of the product lot of PPD. The mean value by gaussian fit (-1.520± 0.012) is consistent withthe mean of all data within its uncertainty.

2.3 Results of the temperature correction on the ADC-photon con-52

version factor53

Figure 3, left shows the linear behavior of the energy deposit and deviations from the result54

of linear fit and right shows the energy resolution analyzed with d(T ; l, s) as a function of55

temperature measured by two thermocouples put on the detector surface at the data taking.56

Although effect of this temperature correction is not large as comparing with the case of ADC-57

MIP conversion factor, the linear relation between the detector response measured in the number58

of MIPs and incident beam momentum, MIP/GeV/c increase from 127.6 MIPs/GeV/c [1] to59

131.3 MIPs/GeV/c and the linearity is a little improved from the result in [1] except 30 GeV/c60

beam.61

The energy resolutions with higher energy except 30 GeV/c show a little degradation from62

the case in [1]. This phenomenon can be explained as the following: All LED data were taken in63

∼ 20◦C in 2009, and some beam data takings are in higher temperature. Therefore, the detected64

number of photons with PPD are corrected to more than the case without this temperature65

correction, since the value of sdl,s is negative. In such case with the fact that the PPD response66

as the function of the number of incident photons decrease as the number of incident photons67

increase, the energy resolution looks better in the case without this temperature correction.68

Fact that the LED data have been taken in lower temperature than average of the beam69

data taking also explains the increasing the MIP/GeV/c (3%) by this temperature correction .70

3 Systematic uncertainties71

After temperature correction of on ADC-photon conversion factor is implemented, the system-72

atic uncertainties of not only from ADC-photon conversion factor but also from other source of73

the systematic uncertainties are studied and evaluated in this section.74

3.1 Beam momentum fluctuation75

The MTest beam has momentum spread, ∆p/p = 2% as the designed value for 1 - 60 or76

90GeV/c [3]. A calorimetry test for Muon g-2 experiment at the MTest estimates 2.7± 0.3%77

of the beam momentum spread for 1 - 4 GeV/c using Pb/Glass calorimeter [4]. The other78

3

Figure 3: Distribution of d(T0 = 20◦C; l, s) (left) and sdl,s/d(T0 = 20◦C; l, s) (right) with the fitting resultof gaussian. The small peak of d(T0 = 20◦C; l, s) near 235 ADCs/photon is well understood due to thedifference of the product lot. The mean value by gaussian fit (-1.520± 0.012) is consistent with the mean ofall data within its uncertainty.

experiment for a SiFi Calorimeter with tungsten estimates 2.3± 0.3% for 8 GeV/c by using their79

own detector and the results of the previous one [5]. Preceding this study, they has estimated80

2.3% in the range 1.5 - 3.5 GeV/c [6]. From these measurements we estimate the MTest beam81

momentum spread in two incidental beam momentum ranges, 2.7± 0.3% for 2 - 4 GeV/c, and82

2.3± 0.3% for 8 - 32 GeV/c. To estimate the intrinsic energy resolution of ScECAL, these83

momentum spread should be quadratically subtracted from the energy resolution estimated in84

2.3.85

The result of the intrinsic energy resolution evaluated with other systematic uncertainties86

will be shown in 3.8 as the summary of this section.87

3.2 Event selection88

As discussed in [2], six event selections has bean implemented to reduce out of fiducial events. To89

estimate the systematic uncertainties from these selection cuts, the cut variations are measured90

and evaluated.91

The mean value uncertainties from the variation of the cut ranges except for the cut of92

the gravitational center of energy are less than 0.05%. Uncertainties due to the different cut93

variations on the x and y position of gravitational center of energy are listed in Table 1.94

Contributions from the cut variations for the energy resolution are negligibly small (< 0.5%)95

compare to the 3% of the uncertainty comes from the beam momentum spread.96

3.3 ADC-MIP conversion factor97

Individual strip response is calibrated using MIP signals as discussed in [1]. The uncertainties98

on the mean of the measured energy deposit and energy resolution come from the uncertainty99

of the ADC-MIP conversion factor are estimated.100

An ADC-MIP conversion factor is a linear function of temperature of detector. Therefore,101

it is expressed with two parameters; the value of ADC-MIP conversion factor at a certain102

temperature (c(T0; l, s)), and the slope of ADC-MIP conversion factor (scl,s). Propagation of103

the statistical uncertainties of these parameters are studied by using pseudo-experiments in104

which each parameter is randomly fluctuated by a gaussian function within its uncertainty.105

Deviations of recreated mean and resolution of the energy deposit from the nominal value in106

4

Table 1: Uncertainty from the event selection (%).

Energy center cut in;Beam momentum (GeV/c) x y

2 +0.23 +0.164 +0.28 +0.098 +0.14 +0.0312 +0.13 +0.0215 +0.10 +0.0220 +0.43 +0.0130 +0.14 +0.0132 +0.03 +0.01

20 trials are taken as the systematic uncertainties from the ADC-MIP conversion factor. Mean107

value of each energy is fluctuated in 0.09 - 0.24% and 0.02 - 0.06% of the value due to the108

uncertainties of c(T0; l, s) and scl,s, respectively, as listed in Table 2.109

Table 2: Fluctuation of mean of measured energy deposit created with twenty times pseudo-experiments.

Deviation (%) from;Beam momentum (GeV/c) c(20◦C; l, s) scl,s

2 0.23 0.034 0.09 0.028 0.21 0.0312 0.16 0.0315 0.13 0.0420 0.13 0.0430 0.12 0.0632 0.23 0.04

Figure 4 shows the distributions of stochastic term and the constant term of energy resolution110

varying c(T0; l, s). The systematic uncertainties come from c(T0; l, s) are 0.08% and 0.07% for111

stochastic term and the constant term, respectively. It is 0.01% for both stochastic and the112

constant term from the variation of scl,s.113

3.4 ADC-photon conversion factor114

An ADC-photon conversion factor for each channel is also a linear function of temperature of115

the detector and it is used to convert ADC counts to the number of photons (fired pixels of116

PPD). The number of detected photons are required to apply the PPD saturation correction as117

discussed in 2. Therefore, the propagation of uncertainties of these parameters are also studied118

by using pseudo-experiments as well as the ADC-MIP conversion factors.119

Systematic uncertainties of mean and energy resolution of the measured energy deposit due120

to the uncertainty of these parameters are negligible.121

5

Figure 4: Distribution of the stochastic term (left) and the constant term (right) of the energy resolutionin 20 pseudo-experiments.

3.5 Inter calibration constant122

Systematic uncertainty due to the uncertainty of inter calibration constant is also studied by123

using pseudo-experiment method. Although most of uncertainties of gain inter calibration con-124

stant for each channel are taken as the sigma of gaussian used to make the variation, the125

standard deviation of the measured gain constants is used for the channels which are not suc-126

ceeded to estimate the inter calibration constant due to the same reason for the measurement of127

the ADC-photon conversion factor. Mean value of each energy is fluctuated less than 0.02% and128

the uncertainty of both stochastic and constant term from the uncertainty of inter calibration129

constant is less than 0.01%.130

3.6 The number of effective pixels of PPD131

The mean value of the number of effective pixels of PPD, Npix measured for 72 strips is used132

as an input of the PPD saturation correction as discussed in section 2. Therefore, the standard133

deviation of distribution of Npix is taken as the uncertainty of Npix to create the pseudo-134

experiments to estimate the contribution from the variation of Npix. Mean value of each energy135

is fluctuated in 0.01 - 0.16%. The uncertainties are 0.07% and 0.06% for the stochastic term136

and the constant term, respectively.137

3.7 Difference of mean value of deposit energy among runs138

After temperature correction and saturation correction, there are larger variations of mean values139

of measured energy deposit among runs than the variation expected from the uncertainties of140

respective runs. Therefore, uncertainties from these discrepancies are implemented from the141

standard deviation of the expected value, and listed them for respective beam momenta in142

Table 3.143

3.8 Summary of uncertainties144

Total of systematic uncertainties estimated in this section and the statistic uncertainties for145

each beam momentum are listed in Table 4. Figure 5, left shows the deposit energy with the146

result of linear fitting with those uncertainties, and and deviation of each data from the fitting.147

The intrinsic energy resolution with systematic uncertainties discussed in this section is148

shown in Fig. 5, right as a function of the reverse of the square root of incident beam momentum.149

6

Table 3: Uncertainty estimated from the deviations of the expected values of measured energy depositamong runs.

Beam momentum (GeV/c) Deviation (%)2 0.314 0.238 0.2712 0.8115 0.4520 0.6630 0.1032 0.10

Table 4: Total of systematic and statistical uncertainties of measured deposit energy.

Uncertainty (%)Beam momentum (GeV/c) statistical systematic

2 0.030 0.494 0.022 0.388 0.013 0.3812 0.014 0.8415 0.012 0.4820 0.012 0.8030 0.014 0.2732 0.018 0.29

Figure 5: Response linearity (left) and intrinsic energy resolution (right) of ScECAL.

The curve shows the result of fit to the data after subtracting beam momentum spread contri-150

bution with a quadratical parametrization of the resolution, resulting 12.9±0.1(stat)±0.4(sys)%151

and 1.2±0.1(stat)±+0.4/-1.2(sys)% for the stochastic term and constant term, respectively. The152

systematic uncertainties are estimated considering the case that the beam momentum spread is153

7

varied coherently for all beam momenta.154

4 Discussions155

The temperature correction for the ADC-photon conversion factor is applied in 2. With this156

correction, the deviation from the result of linear fit is less than 2%2. Therefore, we can conclude157

that this temperature correction does not affect on the linearity. However, the 3% of increase158

of the MIP/GeV/c shows that this correction is also necessary.159

Comprehensive study of the systematic uncertainties are also discussed in 3. To explain the160

1.2±0.1(stat)±+0.4/-1.2(sys)% of the constant term of the energy resolution, the Monte Carlo161

simulation study is ongoing.162

References163

[1] CALICE collaboration, CALICE note 16a.164

[2] CALICE collaboration, CALICE note 16.165

[3] C. Johnstone, Proc.,EPAC 2006, Edinburgh, Scotland.166

[4] T. Tsai, Special Reports of All Experimenters meetings FNAL, (2012)167

http://www.fnal.gov/directorate/program planning/all experimenters meetings/special reports/168

Tsai T1018 01 30 12.pdf.169

[5] C. Polly, Special Reports of All Experimenters meetings FNAL, (2010),170

http://www.fnal.gov/directorate/program planning/all experimenters meetings/special reports/171

Polly T1005 08 23 10.pdf.172

[6] R. McNabb, et al, NIM, A 601, 396-402(2009).173

2Some of 8 GeV/c runs have been found to have DAQ problem after [1]. By removing these runs from the analysis,maximum amplitude of the deviation is changed from 1.5% to 2.0%.

8