Update of the Analysis of the Test Beam Experiment of the1

ScECAL Physics Prototype2

The CALICE-ScECAL group3

October 12, 20124

Abstract5

The analysis of the test beam at Fermilab of the ScECAL physics prototype (2009) is updated6

on two issues: 1) Temperature correction via the ADC-photon conversion factor is applied for7

each channel of each event. 2) Systematic uncertainties are estimated and evaluated. The8

response of the ScECAL for the electron beams increases by 3% with this temperature correction.9

The intrinsic energy resolution of the ScECAL is determined to be 12.9±0.1(stat)±0.4(sys)%10

and 1.2±0.1(stat)+0.4/-1.2(sys)% for the stochastic term and constant term, respectively.11

1 Intruduction12

This note updates with continuation of analysis documented on CALICE Note 16 and 16a.13

The ScECAL measures the energy deposited of a particle by using scintillator strips where14

each strip is read out with a pixelated photon detector (PPD). A PPD has saturation behav-15

ior due to its fundamental principle, and the saturation effect is corrected by using measured16

properties of the magnitude of the PPD output toward the incident photons: the number of17

detected photons as a function of the number of incident photons to the PPD. Therefore, the18

ADC-photon conversion factor is required for each channel to convert the ADC output into the19

number of detected photons. The sensitivity of a PPD depends on the temperature. Most of20

the temperature dependence of the PPD is comprehensively corrected by using the ADC-MIP21

conversion factor depending on the temperature in the previous CALICE note [?]. As an ad-22

ditional temperature correction via the ADC-photon conversion factor is applied and evaluated23

in this update.24

Systematic uncertainties including also the uncertainty from the ADC-photon conversion25

factor are estimated and evaluated in this update.26

2 Temperature correction on the ADC-photon conversion27

factor28

2.1 PPD saturation correction29

The property of the PPD saturation is expressed in Eq. ??, considering the incident photonsarrived simultaneously at the same pixel. This function is the number of detected photons (firedpixels) as a function of the number of incident photons in the PPD:

Nfired = Npix

(1 − exp

(−ϵNin

Npix

)), (1)

1

where Nfired is the number of photons detected by the PPD, Npix is the number of pixels on the30

PPD, ϵ is the photon detection efficiency and Nin is the number of photons incident into the31

PPD sensor. The inverse function of Eq. ?? is used to apply the PPD saturation correction by32

inputting the number of detected photons so that the output is the number of incident photons33

into the PPD sensor. The number of detected photons is determined from ADC counts of each34

hit by using an ADC-photon conversion factor for each channel. The ADC-photon conversion35

factor for each channel is determined in the following section.36

The only parameter of the inverse function of Eq. ??, Npix is determined by fitting Eq. ?? to37

test bench data in the previous note [?]. One of the update issues is that Npix is determined by38

measuring 72 channels of the ScECAL prototype in this note [?]. Therefore, the fluctuation of39

Npix can be evaluated to estimate the uncertainty from the PPD saturation correction. Figure ??40

shows the distribution of measured Npix having the mean value of 2428.39±28.88 pixels and the41

standard deviation of 245.07 pixels.

Figure 1: Distribution of the number of pixels, Npix, measured with 72 strips.42

2.2 ADC-photon conversion factor43

An ADC-photon conversion factor is determined by using few-photon spectra of LED light takenoften between beam data taking [?]. The ADC counts corresponding to one photon is an ADC-photon conversion factor for the channel (l, s). The ADC conversion factor can be expressed witha linear function of temperature as in 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) +( ∆d

∆T

)l,s

· (T − T0), (2)

where l and s is the layer number and strip number of this channel, respectively, T is the44

temperature of the detector measured by using two thermo couplings on the surface of the45

detector during the data taking and T0 is a certain temperature to give the offset of the function.46

Figure ??, left shows the distribution of d(T0 = 20◦C; l, s) and right shows the distribution of47

(∆d/∆T )l,s/d(T0 = 20◦C; l, s). The number of entries is ∼70% due to some problems to take48

LED light spectra1. To apply the temperature correction, individual d(T0 = 20◦C; l, s) are used49

for the succeeded channels to measure d where it is required to have the d(T0 = 20◦C; l, s)50

between 170 and 260 ADC/photon and its uncertainty between 0.2 to 50 ADCs/photon, while51

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

2

the average value of these succeeded channels are used for the failed channels. With regard to52

(∆d/∆T )l,s, mean of gaussian fit in Fig. ?? right is used uniformly for all channels.

Figure 2: Distribution of d(T0 = 20◦C; l, s) (left) and (∆d/∆T )l,s/d(T0 = 20◦C; l, s) (right) with the fittingresult of a gaussian function. The small peak of d(T0 = 20◦C; l, s) near 235 ADCs/photon is well understooddue to the difference of the product lot of PPD. The mean value of the gaussian fit (-1.520± 0.012) isconsistent with the mean of all entries within its uncertainty.

53

2.3 Results of the temperature correction on the ADC-photon con-54

version factor55

Figure ??, left shows the linear behavior of the energy deposit and deviations from the result56

of a linear fit and right shows the energy resolution analyzed with d(T ; l, s) as a function of57

the temperature measured by two thermocouples put on the detector surface during the data58

taking. Although the effect of this temperature correction is not large as compared with the case59

of ADC-MIP conversion factor, the linear relation between the detector response measured in60

the number of MIPs and incident beam momentum, the slope of the response linearity increases61

from 127.6 MIPs/(GeV/c) [?] to 131.3 MIPs/(GeV/c) and the linearity is a little improved from62

the result in [?] except for the 30 GeV/c beam.63

The energy resolutions with higher beam momentum except 30 GeV/c show a little degra-64

dation from the case in [?]. This phenomenon can be explained as the following: All LED data65

were taken in ∼ 20◦C in 2009, and some beam data takings are at higher temperature. There-66

fore, the detected number of photons with PPD are corrected to more than the case without67

this temperature correction, since the value of (∆d/∆T )l,s is negative. In such case with the68

fact that the PPD response as the function of the number of incident photons decreases as the69

number of incident photons increase, the energy resolution looks better in the case without this70

temperature correction.71

The fact that the LED data have been taken at lower temperature than average of the beam72

data taking also explains the increasing the slope of the response linearity by this temperature73

correction.74

3 Systematic uncertainties75

After the temperature correction of the ADC-photon conversion factor is implemented, the76

systematic uncertainties of not only from ADC-photon conversion factor but also from other77

sources of systematic uncertainties are studied and evaluated in this section.78

3

Figure 3: Response linearity (left) and energy resolution (right) after the temperature correction of theADC-photon conversion factor has been applied. The uncertainties are only the statistic uncertainties.Figure ?? shows the results with also systematic uncertainties..

3.1 Beam momentum fluctuation79

The MTest beam has a momentum spread, ∆p/p = 2% as the designed value for 1 - 60 or80

90GeV/c [?]. A calorimetry test for the Muon g-2 experiment at the MTest estimates 2.7± 0.3%81

of the beam momentum spread for 1 - 4 GeV/c using a Pb/Glass calorimeter [?]. The other82

experiment for a SiFi calorimeter with tungsten estimates 2.3± 0.3% for 8 GeV/c by using their83

own detector and the results of the previous one [?]. Preceding this study, they have estimated84

2.3% in the range 1.5 - 3.5 GeV/c [?]. From these measurements we estimate the MTest beam85

momentum spread in two incidental beam momentum ranges, 2.7± 0.3% for 2 - 4 GeV/c, and86

2.3± 0.3% for 8 - 32 GeV/c. To estimate the intrinsic energy resolution of the ScECAL, this87

momentum spread should be quadratically subtracted from the energy resolution estimated in88

section ??.89

The result of the intrinsic energy resolution evaluated with other systematic uncertainties90

will be shown in section ?? as the summary of this section.91

3.2 Event selection92

As discussed in [?], six event selections have been implemented to reduce out of fiducial events.93

To estimate the systematic uncertainties from these selection cuts, the cut variations are mea-94

sured and evaluated.95

The mean value uncertainties from the variation of the cut ranges except for the cut of the96

center of gravity of energy are less than 0.05%. Uncertainties due to the different cut variations97

on the x and y position of the center of gravity of energy are listed in Table ??.98

Contributions from the cut variations for the energy resolution are negligibly small (< 0.5%)99

compared to the 3% of the uncertainty coming from the beam momentum spread.100

3.3 ADC-MIP conversion factor101

The individual strip response is calibrated using MIP signals as discussed in [?]. The uncer-102

tainties on the mean of the measured energy deposit and energy resolution coming from the103

uncertainty of the ADC-MIP conversion factor are estimated.104

An ADC-MIP conversion factor is a linear function of the temperature of the detector.105

Therefore, it is expressed with two parameters; the value of the ADC-MIP conversion factor at106

a certain temperature (c(T0; l, s)), and the slope of the ADC-MIP conversion factor [(∆c/∆T )l,s].107

4

Table 1: Uncertainty of the measured energy deposit from the event selections (%).

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

The propagation of the statistical uncertainties of these parameters is studied by using pseudo-108

experiments in which each parameter is randomly fluctuated by a gaussian function within109

its uncertainty. Deviations of the recreated mean and resolution of the energy deposit from110

the nominal value in 20 trials are taken as the systematic uncertainties from the ADC-MIP111

conversion factor. The mean value of each energy is varied by 0.09 - 0.24% and 0.02 - 0.06% of112

the value due to the uncertainties of c(T0; l, s) and (∆c/∆T )l,s, respectively, as listed in Table ??.113

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

Deviation (%) from;Beam momentum (GeV/c) c(20◦C; l, s) (∆c/∆T )l,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 ?? shows the distributions of the stochastic term and the constant term of the energy114

resolution varying c(T0; l, s). The systematic uncertainties coming from c(T0; l, s) are 0.08%115

and 0.07% for the stochastic term and the constant term, respectively. It is 0.01% for both the116

stochastic and the constant term from the variation of (∆d/∆T )l,s.117

3.4 ADC-photon conversion factor118

An ADC-photon conversion factor for each channel is also a linear function of temperature of119

the detector and it is used to convert ADC counts to the number of photons (fired pixels of the120

PPD). The number of detected photons are required to apply the PPD saturation correction as121

discussed in section ??. Therefore, the propagation of uncertainties of these parameters is also122

studied by using pseudo-experiments as well as the ADC-MIP conversion factors.123

Systematic uncertainties of mean and energy resolution of the measured energy deposit due124

to the uncertainty of these parameters are negligible.125

5

Figure 4: Distribution of the stochastic term (left) and the constant term (right) of the energy resolutionin twenty times of pseudo-experiments on c(T0; l, s).

3.5 Inter calibration constant126

The systematic uncertainty due to the uncertainty of the inter calibration constants is also127

studied by using a pseudo-experiment method. Although most of the uncertainties of gain128

inter calibration constant for each channel are taken as the sigma of the gaussian used to make129

the variation, the standard deviation of the measured gain constants is used for the channels130

which are not succeeded to estimate the inter calibration constant due to the same reason for the131

measurement of the ADC-photon conversion factor. The mean value of each energy is fluctuated132

less than 0.02% and the uncertainty of both stochastic and constant term from the uncertainty133

of the inter calibration constant is less than 0.01%.134

3.6 The number of effective pixels of the PPD135

The mean value of the number of effective pixels of the PPD, Npix measured for 72 strips is136

used as an input of the PPD saturation correction as discussed in section ??. Therefore, the137

standard deviation of the distribution of Npix is taken as the uncertainty of Npix to create the138

pseudo-experiments to estimate the contribution from the variation of Npix. The mean value of139

each energy is varied by 0.01 - 0.16%. The uncertainties are 0.07% and 0.06% for the stochastic140

term and the constant term, respectively.141

3.7 Difference of the mean value of deposited energy among runs142

After temperature correction and saturation correction, there are larger variations of mean values143

of the measured energy deposit among runs than the variation expected from the uncertainties144

of respective runs. Therefore, uncertainties from these discrepancies are implemented from the145

standard deviation of the expected value, and listed for respective beam momenta in Table ??.146

3.8 Summary of uncertainties147

The total systematic uncertainties estimated in this section and the statistic uncertainties for148

each beam momentum are listed in Table ??. Figure ??, left shows the deposited energy with149

the result of a linear fit with those uncertainties, and the deviation of each data point from the150

fitting.151

The intrinsic energy resolution with systematic uncertainties discussed in this section is152

shown in Fig. ??, right as a function of the inverse of the square root of the incident beam153

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 deposited 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 the intrinsic energy resolution (right) of the ScECAL with thestatistic uncertainty and the systematic uncertainties. The energy resolution is subtracted the contributionof the beam momentum spread.

momentum. The curve shows the result of a fit to the data after subtracting the beam mo-154

mentum spread contribution with a quadratical parametrization of the resolution, resulting in155

7

12.9±0.1(stat)±0.4(sys)% and 1.2±0.1(stat)+0.4/-1.2(sys)% for the stochastic term and con-156

stant term, respectively. The systematic uncertainties are estimated considering the case that157

the beam momentum spread is varied coherently for all beam momenta.158

4 Discussions159

The temperature correction for the ADC-photon conversion factor is applied in section ??. With160

this correction, the deviation from the result of a linear fit is less than 2%2. Therefore, we can161

conclude that this temperature correction does not affect the linearity. However, the 3% increase162

of the slope of the response linearity shows that this correction is also necessary.163

Comprehensive studies of the systematic uncertainties are also discussed in section ??. To164

explain the 1.2±0.1(stat)±+0.4/-1.2(sys)% of the constant term of the energy resolution, the165

Monte Carlo simulation study is ongoing.166

References167

[1] CALICE collaboration, CALICE note 16a.168

[2] CALICE collaboration, CALICE note 16.169

[3] W. Choi, Shinshu University Diploma thesis, 2010 (in japanese).170

[4] C. Johnstone, Proc.,EPAC 2006, Edinburgh, Scotland.171

[5] T. Tsai, Special Reports of All Experimenters meetings FNAL, (2012)172

http://www.fnal.gov/directorate/program planning/all experimenters meetings/special reports/173

Tsai T1018 01 30 12.pdf.174

[6] C. Polly, Special Reports of All Experimenters meetings FNAL, (2010),175

http://www.fnal.gov/directorate/program planning/all experimenters meetings/special reports/176

Polly T1005 08 23 10.pdf.177

[7] R. McNabb, et al, NIM, A 601, 396-402(2009).178

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

8