Construction of the CALICE High Granular Scintillator Based Electromagnetic Calorimeter Prototype and Its Response to Electrons

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1 1 2 3 Working draft November 5, 2013 ver Construction of the CALICE High Granular Scintillator Based Electromagnetic Calorimeter Prototype and Its Response to Electrons 7 CALICE collaboration 8 Abstract The CALICE collaboration is developing a high granular electromagnetic calorimeter based on the technique of scintillator stip for the future linear collider experiments. To confirm its feasibility 180 mm 180 mm 21.5 X 0 prototype has been constructed and tested with electron beams at Fermilab May The prototype consists of 2160 of 10 mm 45 mm 3 mm strips readout individually. Deviations of the response from linear behavior is less than 2%, and the intrinsic-relative energy resolution, σ E /E is determined to be {12.9±0.1(stat.)±0.4(syst.)}/ E(GeV) {1.2 ± 0.1(stat.) (syst.)}%. 1

2 Contents 1 Introduction 3 2 The ScECAL physics prototype Construction of ScECAL physics prototype MPPCs and their saturation collection Characterization of all MPPCs in the physics prototype The number of effective pixels Measurement of the number of effective pixels Data acquisition system Test beam at FNAL Beams and setup Temperature measurement Runs for calibrations Analysis: Reconstruction Analysis flow ADC-MIP conversion factor as a function of temperature ADC-photon conversion factor as a function of temperature Inter-calibration constant Electron energy spectra Reconstruction The energy spectrum after event selections Results: Performance of the physics prototype Mean and resolution of measured energy of each beam momentum Systematic uncertainties on the mean and the standard deviation of the energy spectrum Difference of the mean value of deposited energy among runs Event selections ADC-MIP conversion factor ADC-photon conversion factor Inter-calibration constant The number of effective pixels of the MPPC Beam momentum fluctuation Summary of uncertainties on each beam momentum Linearity and the energy resolution of the ScECAL physics prototype Comparison with Monte Carlo simulation ScECAL physics prototype in the Simulation Comparison with the ideal detectors Discussion 24 8 Summary 25 9 Acknowledge 26 2

3 Introduction The International Linear Collider (ILC) experiments are designed to perform high precision measurements using the clear initial states of the electron-positron collisions and well reconstructed final states. To characterize final states dominated by gauge bosons and heavy quarks, the reconstruction of jets is a key issue. One of the ways to precisely reconstruct jets is to measure individual particles within jets, by combining calorimetry and tracking. This method, called particle flow approach (PFA) [1][2] requires highly granular calorimeters; finer than 10 mm lateral and longitudinal segmentations for the electromagnetic calorimeter (ECAL) 1 [2][3]. Such a granularity was until recently difficult for the scintillator technique, because a sufficiently small and sensitive readout technology did not exist. The situation was drastically changed when the pixelated photon detector (PPD or SiPM) was developed. Each small segmented plastic scintillator can be directly read out by a PPD without a large dead volume coming from the readout. Taking one of such methods, the scintillator strip based electromagnetic calorimeter (ScECAL) is a unique solution, which is being developed by the CALICE collaboration. In order to increase the feasibility of such a calorimeter and to prevent dead volume from PPDs, it is proposed that each scintillator is shaped as a 45 mm long and 5-10 mm width strip, with the scintillator strips in odd layers orthogonal to those in the even layers [4][5]. A special algorithm has already been developed to achieve the fine square segmentation from such rectangular segmentation [4][5]. To achieve the longitudinal granularity, the ScECAL takes a sampling calorimeter method with 2-4 mm thick tungsten plates interleaved with sensor layers. The first ScECAL physics prototype had constructed with a transverse area of 90 mm 90 mm and 26 sensor layers and tested at DESY [6]. The second physics prototype has been built transversally twice as large as the first prototype, 180 mm 180 mm. The number of layers has been also increased to 30 in 266 mm, leading to a total radiation length of 21.3 X 0 with absorber layers. Consequently, the total number of readout channels becomes The scintillator-ppd unit is designed according to the results from the experiments with the first prototype; 45 mm 10 mm 3 mm scintillator hermetically enveloped into a reflector foil with a wave length shifting (WLS) fiber inserted centrally along the longitudinal direction of each strip and read out with a PPD sit into a housing at one of the edge of the scintillator strip. The LED gain monitoring system for each channel also has been implemented, while the first physics prototype has had only one monitor for each layer. Hereafter the physics prototype denotes the second physics prototype. The physics prototype has been tested in the combination with other CALICE prototype detectors; the analog hadoron calorimeter (AHCAL) [7], and the tail catcher muon tracker (TCMT) [8]. These were used to make the purity of the beam quality. Details of the design of physics prototype are shouwn in the successive section. The multipixel photon counter (MPPC) provided from Hamamatsu K.K. [9] is used in the physics prototype as a kind of PPD. The features of MPPC especially the saturation correction of response are discussed in section 2. Although this physics prototype has been tested with the various types of beams at Fermilab, the response to electron beams are reported in this paper. The experimental setup is reported in section 3. The analysis and its results are shown in section 4 and 5, respectively. The results are compared with the Monte Carlo simulation and discussed in section 6. Finally, comprehensive discussion and summary are shown in section 7 and 8, respectively. 1 Current requirement to the lateral segmentation is 5 5 mm 2 [3]. This requirement can be achieved by using 5 mm wide scintillator strips. 3

4 The ScECAL physics prototype 2.1 Construction of ScECAL physics prototype The physics prototype starts with a 3.5 mm thick tungsten absorber layer alternately followed with scintillator layers and absorber layers. The number of pairs of absorber and scintillator layers is 30 in 266 mm of the total thickness. Figure 1 shows the physics prototype in front of the CALICE analog HCAL. Figure 1: A flat cable with nine MPPCs. An overview of the physics prototype put in front of AHCAL Figuer 2 shows a scintillator layer consists of four rows of 18 scintillator strips. Figure 3 shows a plastic scintillator strip picked up from Fig. 2 with a photo of a MPPC. This scintillator strip is cut out from a scintillator bar simultaneously together with a hole for WLS fiber made with the extrusion method. A housing space of MPPC was mechanically shaped with depth of 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 MPPC package. Four sides of each strip were polished to make fine sizing and good reflection since our current technology could not control the fine size enough. From the measuring results of mean and the standard deviation of randomly sampled 20 strips, their width are 9.85±0.01 mm, length are 44.71±0.04 mm, and thickness are 3.02±0.02 mm. The sizes of MPPC package and their uncertainties were taken from the catalogue of Hamamatsu. Nine MPPCs soldered on a poryimide flat cable shown in Fig. 4 were inserted into the MPPC housings on the strips, respectively. A double clad one mm diameter WLS fiber, Y-11, provided by KURARAY Co., Ltd. was inserted in the hole of each strip with the length of 43.6 ± 0.1 mm. Each strip was hermetically enveloped in a reflector foil of 57 µm thick. The reflector foil provided by KIMOTO Co., Ltd. has evaporated silver layer and aluminum layer in between polyethylene terephtalate layers. The reflection ratio of this foil is 95.2% for 450 nm light referring to KIMOTO s catalogue [10]. Since the number of photons directly coming from scintillator has position dependence, a shade made of reflector film was put between MPPC package and scintillator with a hole as a window for WLS in order to accept only photons from WLS fiber. Figure 5 is a photo of such a shade in the MPPC housing on the strip. With this shade, sensitivity at the other end of strip from MPPC is 88.3 ± 0.4% of that in front of MPPC. The uncertainty is the standard deviation of the 2160 channels. Each pair of the absorber and the scintillator layer was held in an iron frame. Each frame held four 100 mm 100 mm (3.49±0.01) mm tungsten carbide absorbers aligned to make 200 mm 200 mm absorber layer in front of the scintillator layer. The measured density of eight absorber plates are 14.25±0.04 g/cm 3 and the chemical composition measured by using the X- lay diffraction method and the energy-dispersive X-lay spectroscopy is W : C : Co : Cr = : : : as the ratios of weight, where W means tungsten, C means carbon, Co 4

5 Figure 2: A layer aligned 72 scintillator strips hermetically enveloped in the reflector foil. Each strip has a hole 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 on respective 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 compound of tungsten carbide. These values are used in the simulation study. In the right hand coordination where x is horizontal direction, y is vertical direction and z is 5

6 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, the ScECAL has two types of layers called x (y) layers which have the fine segmented direction in x (y), i.e., longitudinal direction of strip along y (x). To avoid MPPCs exist on the same position in all x (y) layers, the ScECAL layers are categorized in more two, cold + or - for x (y) layers, where MPPCs exist plus (minus) side of y coordination in +x (-x) layers. Figure 6 shows such four types of layers, and the layers were aligned as +x, +y, -x, -y, +x,, in other words, strip direction is rotated 90 degrees as layer number increases. 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 of MPPCs (see text). The scintillator/mppc units and fibers introducing LED light are hermetically covered with 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 was implemented in the physics prototype. For 18 strips in each row, a clear fiber having 18 notches lay down along to the holes row (Fig. 2) to deliver the LED light from a LED. Figure 7 shows such clear fibers with notches emitting bright LED light. The LED is driven with a special card made by the Czech Republic group [11]. The ADC-photon conversion factor of each MPPC is 6

7 149 measured during the test beam experiments by using those LED lights, and the factor is used 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 row of scintillators MPPCs and their saturation collection Characterization of all MPPCs in the physics prototype In order to use the MPPCs with similar characters especially with the uniform gain of whole of the detector, the characterization of 2300 MPPCs with their gain as a function of bias voltage, noise rate, and capacitance were measured before they were loaded into the physics prototype. A pixel in a MPPC multiplies the number of electrons originated from a photo-electron. The multiplying ratio, gain (G) is proportional to the difference of the bias voltage from the breakdown voltage where MPPC starts to get the gain. This difference is referred to the over-voltage ( V). Therefore, the gain is expressed in G = C V, where C is the capacitance of one pixel of the MPPC. Figure 8 left shows the breakdown voltage and right shows C, as the differential coefficient (slope) of gain with respect to the bias voltage. The bias voltage on each MPPC at the test beam was determined optimizing with those results to have the same over-voltage ( V = V) through all channels CALICE ScECAL CALICE ScECAL produced in 2008 produced in produced in 2007 MPPCs MPPCs produced in Breakdown Voltage dum (-V) Capacitance dumyd (pf) Figure 8: The breakdown voltages (left) and the capacitances (right) of 2300 MPPCs, respectively. Difference of features among the production lots are shown in those distributions. Black histograms show the 2000 products obtained in 2008 and blue and red histograms show those obtained in Bias voltages at the test beam experiment were determined by using those values. Products obtained in 2008 were set in the upstream layers, and 2007 s ones have been set in the downstream layers The number of effective pixels The PPDs including the MPPC are known to be non-linear devices. The output of the MPPC in terms of number of fired pixels (Nfired ) can be parametrized as a function of the number of 7

8 incident photons (N in ) by the response function: ( N fired = Npix eff 1 exp ( ϵnin )), (1) 165 where Npix eff is the number of effective pixels on the MPPC, ϵ is the photon detection efficiency 166 and N in is the number of photons incident on the sensor. Each MPPC used in the physics 167 prototype has 1600 physical pixels. However, as each pixel can recover quickly with a time 168 constant of 4 ns [12], it can emit another signal if the incident light has a duration longer than 169 the pixel recovery time. This leads to an enhancement of the effective number of pixels for a 170 single shot of light input from a scintillator strip. 171 The inverse function of Eq. 1, which has N fired as an input and gives N in as an output, is 172 used as the MPPC saturation correction function. To apply the saturation correction the 173 MPPC output (measured in units of ADC counts) must first be translated to N fired using a 174 ADC-photon conversion factor (c p.e. ) measured in LED runs during the test beam experiment 175 for each channel. The only free parameter to be determined in the inverse function of Eq. 1, 176, is obtained by fitting Eq. 1 to test bench data as discussed in the following. 177 N eff pix N eff pix Measurement of the number of effective pixels 178 The Npix eff is measured with 72 strips in the physics prototype after FNAL test beam experiment 179 by using pico-second pulse laser, PiL040X (Head) + EIG2000DX (Controller) provided by Ad- 180 vanced Laser Diode System A.L.S. GmbH, at Shinshu University. Figure 9 shows a schematic of the setup used to measure the saturation responses. Figure 9: Setup of measurement the Npix eff, 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 position with a small hole on the reflector, d. MPPC, e. half mirror, f. photomultiplier tube, g. lens, h. polaroid (fixed), and i. polaroid (rotatable) Eq. 1 has a limit of fitting range since this equation does not correspond to the timing duration of scintillations mentioned in section Figure 10 left shows a typical MPPC response as a function of the ADC counts of the photo multiplier tube (PMT) validated that it has linear response in the applied range. Therefore, the fitting range is prevented within a range determined with a criterion in the following: since the derivative of Eq. 1 with respect to N in is an exponential function of N in, the difference of the number of fired pixels with respect to the ADC counts of the PMT is also required to be fitted with an exponential function. However, in the case of the real data, the plot of the difference shows two separable ranges corresponding to two exponential functions as shown in Fig. 10 right. Therefore, only first part in Fig. 10 right is taken as the fitting range. The solid curve in left shows the result of the fit of Eq. 1 to the data and that in right is the result of one exponential fit to the difference of N fired with respect to the ADC counts of PMT. 8

9 p.e.dummy CALICE ScECAL Layer: 30, Channel: 32 eff N pix = 2589 ± 13 Gradientdu(p.e./ADC) CALICE ScECAL Layer: 30, Channel: Response of MPTdum(ADC) Response of MPTdum(ADC) Figure 10: left MPPC response to the laser pulse as a function of the response of PMT. right the difference of N fired with respect to the ADC counts of PMT, giving a criterion to determine the fit range in it left plot. 194 Figure 11 shows the distribution of measured Npix eff obtained as a fitting parameter of Eq. 1, 195 having a mean value of 2428±39 pixels and a standard deviation over 245 pixels. This mean 196 value is used to implement the MPPC saturation correction and the standard deviation is used to estimate the systematic uncertainty from the uncertainty of Npix eff in section CALICE ScECAL Channels Mean = RMS = eff N pix Figure 11: Distribution of the number of effective pixels, Npix eff, measured from 72 strips Data acquisition system The readout concept of the ScECAL physics prototype is based upon the same architecture as that of the CALICE AHCAL [7]. The readout system for the back-end data acquisition, the CALICE readout cards (CRC) were provided synchronizing the data taking with AHCAL and TCMT. An ASIC developed for PPD was implemented on the front-end electronics for 18 channels [13]. The ASIC has 18-fold multiplexed chain of pre-amplifier, shaper, and sample-andhold circuit [14]. The signals from twelve ASICs were fed into one of the eight input ports of the CRC. The ASIC takes peak hold methods. Therefore, the timing (hold time) was measured with real data taking optimizing to have the largest ADC counts. The ASIC has two operation mode; the low gain mode and the high gain mode. The low gain mode is used for the data taking of beam runs, while the high gain mode is used to take a few photon events to make the gain monitoring. The hold times have been determined for both 9

10 low gain mode and hight gain mode respectively at the test beam experiment. 3 Test beam at FNAL Beams and setup The physics prototype constructed in section 2.1 has been explored with various type of beams; electrons up to 32 GeV to study the response to electromagnetic events, 32 GeV muons for the calibration, charged pions up to 32 GeV to study the hadron response in the combination with AHCAL and TCMT, and neutral pions to evaluate two cluster separations. Those beams were provided at the Meson test beam facility number 6 (MT6) in the Fermi accelerator institute (FNAL) in September 2008 and in May This paper reports the response of the physics prototype to the electron beams from 2 GeV to 32 GeV analyzed with data taken in May Data taken in September 2008 has problem on temperature data. Recovery of the temperature data in 2008 is ongoing. 222 The setup of the beam line is shown in Figure 12. A Ĉerenkov counter placed upstream 223 the experimental area was used for trigger purpose, together with some combinations of plastic 224 scintillators of different sizes. A pair of 20 cm 20 cm trigger counters was used for the muon 225 runs whereas the trigger counters are 10 cm 10 cm for pion and electron runs. The combinations 226 of trigger counter and the pressure of the Ĉerenkov counter for the electron funs and muon runs are listed in Table 1. Figure 12: Configuration of the beam line at the MT6 in FNAL. The right handed coordinate system is shown. Italic numbers at right bottom of the detectors show the thickness of them. All distances and dimensions are in mm Temperature measurement Temperature of the physics prototype were measured with two thermo-couplings put on the surface of the top of the first layer and of the bottom of the last layer, respectively. Figure 13 shows the temperature of data acquisitions averaged of the 1 Hz temperature data taking. Temperature of the physics prototype varied between 19 C to 27.5 C due to two days malfunction of the air conditioning of the experimental hall. Consequently, the performance of the prototype in this severe condition ( T = 8 C) is presented in this paper. 3.3 Runs for calibrations The responses of all channels in the physics prototype are normalized with a common physics signal of muons as the minimum ionizing particles (MIP). Although a MPPC response depends on its temperature and the electron data were acquired in various temperature shown in Fig. 13, the dependence on the temperature is removed from the response by applying this calibration 10

11 Table 1: A list of trigger systems for different particles. The pressure of the Ĉerenkov counter used for each trigger setup is also indicated. Particle p(gev/c) Trigger Ĉerenkov pressure muon 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 cm 10 cm 138 hpaa (outer) electron cm 10 cm 138 hpaa (outer) electron cm 10 cm 138 or 103 hpaa (outer) electron cm 10 cm 103 hpaa (outer) Figure 13: Detector temperature of the muon runs and the electron runs in During the left of the blue 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 were taken in the wide temperature range for this reason (Fig. 13). The muon beams were switched by putting iron target into the 32 GeV pion beams on the upstream of MT6 by FNAL beam control center. The trigger counter T20 in Fig. 12 was used instead of T10 in order to expose the whole of detector to the muon beams. The ADC-photon conversion factors are required to convert the ADC counts to the number of detected photons for the saturation correction as discussed in section To determine an ADC-photon conversion factor, the spacial data LED data were acquired with the LED runs which were taken more than one run in a day as a general rule. In an LED run events data were taken with an LED pulse in each event provided through the clear fiber discussed in section 2.1. The each LED power supply was changed in eleven steps (configurations) in events to take a suitable photon yield for each channel. The selection of the suitable configuration was achieved in the off-line analysis. Since an ADC-photon conversion factor also depends on the temperature, this factor is also delivered as a function of temperature in use. In the determination of an ADC-photon conversion factor, the photo-electron peaks of the ADC distribution of a few incidental photon were used. Therefore, the LED runs were taken with high gain amplifier (Calibration mode), while the beam runs were taken with low gain amplifier 11

12 (Physics mode) in order to have enough dynamic range of the measurement. This means that the ADC-photon conversion factors obtained in the calibration mode must be converted into the values corresponding to the physics mode. The ASIC discussed in section 2.3 has gain; 92.3 mv/pc for the calibration mode and 8.18 mv/pc for the physics mode. Since the ratio of the amplitude of the physics mode to the calibration mode depends not only on those gains but also on the integration condition due to the difference of MPPC signal shape for each channel, this ratio of the amplitude inter-calibration constant were measured with the special runs, inter-calibration run. In the inter-calibration runs LED lights were delivered into each channel and the ADC counts were measured in both the physics mode and the calibration mode of the amplifier with the same strength of LED which can be measured with both modes, consequently it was high intensity that the ELD calibration mode. In an inter-calibration run events data were acquired also changing the strength of LED power in eleven steps, and the suitable step of photon yields was selected in the offline analysis. Those three calibration steps are summarized in the following: the MIP calibration to determine the ADC-MIP conversion factor (c MIP l,s ), the LED calibration to determine the ADC-photon conversion factor (c p.e. l,s ), and the inter-calibration to determine the ration between physics mode and calibration 274 mode of the amplifier (c inter l,s ), where, l and s denote layer number and strip number respectively. Hereafter we drop those suffixes unless it is confused without those Analysis: Reconstruction 4.1 Analysis flow As discussed in section 3.3, the calibration procedure is separated in three steps; MIP calibration for the comprehensive calibration using MIP signals, the LED calibration for the MPPC gain monitoring in order to apply the MPPC saturation correction, and the inter-calibration to convert between the high gain mode and the low gain mode. In the successive three subsections, the procedures to measure those conversion factors or constants are discussed. The procedure to create the electron spectra by using those calibrations is discussed in section 4.5. The ADC counts in those discussions are subtracted values with the pedestal ADC counts. In the beam runs 500 of random trigger events were acquired between beam spills for the measurement of pedestal of each channel, and the mean ADC counts of pedestal was defined as the pedestal ADC counts. In the measurement of the ADC-photon conversion factors, the pedestal ADC counts are not subtracted from the signal ADC counts, since a distance between the pedestal peak and the one photo-electron peak in a spectrum is a ADC-photon conversion factor as shown in the Fig ADC-MIP conversion factor as a function of temperature The distribution of the MIP energy deposits measured in the ADC counts on each channel is fitted with a landau function convoluted with a gaussian resolution function. The most probable value (MPV) obtained as an fitting parameter is directly the ADC-MIP conversion factor (c MIP ). Figure 14 shows a typical distribution of MIP energy deposit and the fitting result. The beams for the c MIP contains almost no electrons or pions because of the iron dumper. Therefore, the MIP events are simply required to have the same X (Y) hit position of channels at least in ten different X (Y) layers, respectively. A hit is defined as a signal larger than the mean value of pedestal by at least three standard deviations of the pedestal. The MPV of each channel is measured for six runs acquired in different temperature conditions so that the correlation between MPV and the temperature of detector is obtained in Fig. 15. A temperature data in the plot is averaged temperature during the data taking. The 12

13 Figure 14: A distribution of energy deposit by mip like particles on a channel. Solid line shows the fitting result of a landau function convoluted with a gaussian function. c MIP can be approximately expressed as a linear function of temperature. The solid line in Fig. 15 shows the result of the linear fit. Consequently, the ADC-MIP conversion factor is a function of temperature: c MIP (T ) = c MIP (T 0 ) + dcmip dt (T T 0), (2) where T is the temperature at the measurement and T 0 is a nominal temperature. The fitting parameters, c MIP (T 0 ) and dc MIP /dt for each channel are stored to use for the analysis of electron beam data. The energy deposit by electron beams measured at temperature T calibrated with c MIP (T ) no as the function of the temperature. Figure 15: A c MIP as a function of detector temperature. Solid line shows the result of linear fit Figure. 16 left shows the distribution of the ADC-MIP conversion factors estimated at 20 C {c MIP (T = 20 C)} with 19% of the coefficient of variation in 2160 channels. Figure. 16 right shows the distribution of the value dc MIP /dt /c MIP. The mean of gaussian fit is -2.95±0.45%/K, where the uncertainty is the standard deviation. 13

14 Figure 16: left Distribution of c MIP (20 C). right Distribution of the slope of c MIP, dc MIP /dt /c MIP. Solid line shows the result of a gaussian fit ADC-photon conversion factor as a function of temperature An ADC-photon conversion factor (c p.e. ) is determined by using a few-photon spectrum of LED light acquired in the LED runs discussed in section 3.3. A mean of ADC counts corresponding to one photo-electron is a c p.e. for the corresponding channel. The sensitivity of the MPPC has the temperature dependence contributed from the temperature dependence of two sources; the gain and the photon detection efficiency. However, the temperature dependence of the c p.e. is only affected by temperature dependence of the gain, because the c p.e. is obtained by the ADC counts corresponding to the distance of one photo-electron peak. From the fact that the photoelectron peaks can be clearly seen in the MPPC spectrum, the absolute value of the ADC counts corresponding to the number of photo-electrons are measurable. Figure 17 shows an example of 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 c p.e. of this channel The LED run data of each channel were acquired in nine runs with different temperature conditions. Therefore, c p.e. also can be converted into a function of temperature as the same as the c MIP s case: c p.e. (T ) = c p.e. ls (T 0) + dcp.e. ls dt (T T 0). (3) Figure 18 left shows the distribution of c p.e. (T = 20 C), and right shows the distribution of dc p.e. /dt /c p.e. (20 C). Approximately 80% of all channels are successfully read out during 14

15 322 LED light spectra recording. When the LEDs are on, some channels exhibit large noise while others have excessively high pedestals. Some channels have too small or too large c p.e. (T 0 ) Figure 18: left Distribution of c p.e. (20 C). Difference of feature of products between 2007 and 2008 appears around 240 ADCs (see also Fig. 8) right Distribution of dc p.e. /dt /c p.e.. Solid line shows the result of a gaussian fit in order to get the mean value and the standard deviation The fitting parameters c p.e. (T 0 ) and dc p.e. /dt are applied to the MPPC saturation correction for each channel. To apply the MPPC saturation correction, individual c p.e. (T 0 = 20 C) are used where these are available (successful channels) to measure c p.e., where it is required to have the c p.e. (T 0 = 20 C) between 170 and 260 ADCs/photon and its uncertainty is between 0.2 to 50 ADCs/photon. For channels where LED data read out was not successful, the average value of the successful channels was used. With regard to dc p.e. /dt, the mean of the gaussian fit shown in Fig. 18 right is used uniformly for all channels Inter-calibration constant The inter-calibration process also uses LED light but needs more photons so that it allows to to measure the mean of signals in both the physics mode and the calibration mode. Figure 19 left and right show typical ADC distributions with the same LED power supply but the different amplifier modes respectively. An inter-calibration constant, c inter becomes c inter = ADCs high, (4) low ADCs where ADCs high(low) is the mean of signals in the high gain mode (low gain mode) of a corresponding channel. Because of the same reason due to the LED noise as the c p.e. case, around 20% of channels cannot have measured c inter. For those channels, the average c inter of other 80% of channels with succeeded one photo-electron measurement is used for the reconstruction of the electron spectra. 4.5 Electron energy spectra Reconstruction An energy of an incident electron is reconstructed as the sum of the energy deposits of all hits in an event (an electron) on the physics prototype: E = l,s A corr.mips l,s, (5) 15

16 60 CALICE ScECAL Layer:1, Strip:1 200 CALICE ScECAL Layer:1, Strip:1 Events 40 Events Response to LED light d (adc) Response to LED light d (adc) 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 c p.e. l,s where A corr.mips l,s saturation response with c p.e. l,s is the energy deposit normalized with c MIP l,s (T ) and corrected for the MPPC (T ) and cinter l,s : A corr.mips l,s = F 1{ A ADCs l,s (T ) c inter } l,s c p.e. l,s (T ) c p.e. l,s (T ) c inter l,s c MIP l,s (T ), (6) where the function F 1 is a revers function of Eq. 1, A ADCs l,s (T ) is the signal from the strip s of layer l read in the ADC counts, and T is the temperature of the detector at the measuring time. Note that an A corr.mips l,s is no longer a function of temperature after applying c MIP l,s (T ) and (T ) to AADCs l,s (T ) The energy spectrum after event selections The electron-tuned beams still contain the contamination of pions and muons even with the Ĉerenkov counter. Additionally, the physical volume of 180 mm 180 mm 21.5 X 0 makes a limit of fiducial volume. Therefore, the event selection criteria are applied to extract the electron events as the following: 1. the shower maximum in the ScECAL must be on the upstream than 20th layer, 2. the deposit energy on the shower maximum layer in the ScECAL must be greater than; 10 MIPs for 1 GeV/c, 15 MIPs for 2 GeV/c, 27 MIPs for 4 GeV/c, 54 MIPs for 8 GeV/c, 80 MIPs for 12 GeV/c, 95 MIPs for 15 GeV/c, 125 MIPs for 20 GeV/c, 200 MIPs for 30 GeV/c, and 200 MIPs for 32 GeV/c, 3. the deposit energy on the shower maximum layer in AHCAL must be less than 20 MIPs, 4. the deposit energy on the most downstream layer of AHCAL must be less than 0.4 MIPs of AHCAL, and 5. (6). the gravitational center of electromagnetic shower must be in ± 4 cm from center on the x, (y) axis. Figure 20 left shows an energy spectrum of 32 GeV/c electrons in a run with the effects of cuts and right shows the shape of spectrum after all cuts. The spectrum is fitted well with a 16

17 gaussian function in the range including 90% of entries. The reduced χ 2 for all spectra except one GeV/c are between 0.9 to 1.2 indicating that the fitting region is reliably clean from the contaminations. The mean value and the standard deviation normalized by the mean from the result of gaussian fit are defined as the energy response and the energy resolution of the physics prototype, respectively. Although one GeV/c electron data have been acquired, the pion contamination could not removed enough from them with those selection criteria. Therefore, the results of one GeV/c runs are removed from the evaluation of the performance of the physics prototype in this paper. Figure 20: Spectra of 32 GeV/c electrons. Left shows the effects of selection criteria 1-6 (cut 1-6, see section for criteria) ; black: before any cut, sky-blue: after cut 1, purple: after cut 2, yellow: after cut 3, blue: after cut 4, green: after cut 5, and red after cut 6 (effects of cut 4-6 are small to appear). Although a 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 and the standard deviation of the spectrum is negligible. Right shows the spectrum after all cuts. Red line is the results of the gaussian fit in the range 90% entries Results: Performance of the physics prototype 5.1 Mean and resolution of measured energy of each beam momentum Even in the same beam momentum, differences of the mean values of the measured energy deposit are seen among runs and these are larger than the variation expected from the uncertainties of respective runs. One possible source could be difference of beam tuning which can be slightly different among runs even for a same beam energy. To remove the effects of these fluctuation on the result of the energy resolution, each spectrum of run is separately analyzed so that the mean and resolution for a beam momentum are defined as the average of them estimated by using a standard weighted least-squares procedure: x ± δx = i w ix i i w ± ( w i ) 1/2, (7) i i where x i is mean value or resolution of run i and w i is 1/(δx i ) 2. The sizes of discrepancies of the energy resolution among runs are consistent with their uncertainty as shown in Fig. 21. Therefore, the effect of those discrepancy on the energy resolution is safely removed by this way, while the systematic uncertainty on the mean value from these discrepancies must be implemented as discussed in section

18 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 each beam momentum with the statistical uncertainty of those values. Systematic uncertainties on those values are discussed in section 5.2 and the linearity and the quadratic parameterization of energy resolution of the physics prototype are evaluated in section 6.2. Table 2: Mean and resolution of measured energy of each beam momentum. Beam momentum (GeV/c) Mean (MIPs) Resolution (%) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±0.020 Intrinsic beam momentum spread has not been subtracted yet Systematic uncertainties on the mean and the standard deviation of the energy spectrum Difference of the mean value of deposited energy among runs Uncertainties from the discrepancies among beam runs discussed in section 5.1 are implemented based on the standard deviation from the expected value, and summarized for respective beam momenta in Table 3 together with other systematic uncertainties Event selections As discussed in section 4.5.2, six event selections have been applied to reduce the effects from out of fiducial events. To estimate the systematic uncertainties arising from these selection criteria, the impact of cut variations are measured and evaluated. The uncertainties of mean value from the variation of the cut ranges, except for the cut of the centre of gravity of deposited energy, are less than 0.05%. The uncertainties due to the different cut variations on the horizontal (x) and vertical (y) position of the centre-of-gravity on ScECAL surface for every energy are listed in Table 3. The 18

19 nominal cut position is ± 40 mm for both x and y. Although the cut variation of those values considered for this study is ± 20 mm to ± 80 mm, only positive uncertainty (with narrow range) is considered because wider windows obviously make energy leakage. Contributions from the cut variations for the energy resolution are negligibly small (< factor 0.005) compared to the factor of the uncertainty coming from the beam momentum spread ADC-MIP conversion factor The uncertainties coming from the c MIP on the mean and the resolution of measured energy deposits are estimated. An c MIP (T ) defined in Eq 2 has two parameters: the value of the ADC-MIP conversion factor at a certain temperature, c MIP (T 0 ), and the slope of the ADC-MIP conversion factor, dc MIP /dt. The propagations of the statistical uncertainties of these parameters are studied using pseudoexperiments in which each parameter is randomly fluctuated within its uncertainty as sigma of the gaussian random function. Deviations from the nominal measured mean energy and energy resolution in 20 trials are taken as the systematic uncertainties from the c MIP. The measured deviation from linearity varies in region of % and % due to the uncertainties of c MIP (T 0 ) and dc MIP /dt respectively, as summarized in Table 3. The systematic uncertainties coming from c MIP (T 0 ) are 0.08% and 0.07% as the absolute deviation values for the stochastic term and the constant term, respectively. It is 0.01% for both the stochastic and the constant term from the variation of dc MIP /dt ADC-photon conversion factor An ADC-photon conversion factor for each channel, c p.e. is also a linear function of temperature of the detector and it is used to convert ADC counts to the number of photons (fired pixels of the MPPC). The number of detected photons required for the MPPC saturation correction to be applied is discussed in section Although the propagation of statistical uncertainties of these parameters are also studied by using pseudo-experiments as in the study of the ADC- MIP conversion factors, systematic uncertainties of mean and energy resolution of the measured energy deposit due to the uncertainty of these parameters are confirmed to be negligible Inter-calibration constant The systematic uncertainty due to the uncertainty of the inter calibration constants is also studied by using a pseudo-experiment method. Although most of the uncertainties of gain inter calibration constant for each channel are taken as the sigma of the Gaussian used to make the variation, the standard deviation of the measured gain constants is used for the channels which are not successful to estimate the inter calibration constant. This is for the same reason as in the measurement of the ADC-photon conversion factor. The deviation from linearity as a result of fit at each of 20 trials of varies by about 0.02% on value of the deviation and the uncertainty of both stochastic and constant terms from the uncertainty of the inter calibration constant leads to an absolute deviation of less than 0.01%. Therefore, the systematic uncertainty of the mean value of the energy deposit and the energy resolution from the inter calibration constant is considered to be enough small The number of effective pixels of the MPPC The mean value of the number of effective pixels of the MPPC, N pix measured for 72 strips is applied as an input of the MPPC saturation correction as discussed in section Therefore, the standard deviation of the distribution of N pix is taken as the uncertainty of N pix to create the pseudo-experiments which are to estimate the contribution from the variation of N pix. The deviation from linear fit at each energy is varied by %. The uncertainties are 0.07% and 0.06% for the stochastic and constant terms, respectively. Therefore, the contribution of 19

20 the uncertainty of the number of the effective pixels of the MPPC to the uncertainty of the mean values and energy resolution is small Beam momentum fluctuation The MTest beam has a momentum spread, p/p = 2% as its design value for 1 60 or 90 GeV/c [15]. A calorimetry test for the Muon g-2 experiment at the MTest estimates 2.7 ± 0.3% of the beam momentum spread for 1 4 GeV/c using a Pb/Glass calorimeter [16]. The other experiment for a SiFi calorimeter with tungsten estimates 2.3 ± 0.3% for 8 GeV/c by using their own detector and the results of the previous one [17]. Preceding this study, they have estimated 2.3% in the range GeV/c [18]. From these measurements we take the MTest beam momentum spread in two incidental beam momentum ranges, 2.7 ± 0.3% for 2 4 GeV/c, and 2.3 ± 0.3% for 8 32 GeV/c. To estimate the intrinsic energy resolution of the physics prototype, this momentum spread must be quadratically subtracted from the energy resolution estimated in section 5.1. The systematic uncertainty comes from the uncertainty of the intrinsic beam momentum spread, 0.3% is the largest uncertainty on the energy resolution of each spectrum Summary of uncertainties on each beam momentum Significant uncertainties of the measured mean value for each beam momentum are listed in Table 3. Table 3: The uncertainties of mean value of measured energy deposit. p a beam runsb range-x c range-y d c MIP (20 C) e dc MIP /dt f Npix g stat h total i 2 ± ±0.23 ±0.03 ±0.11 ± ± ±0.09 ±0.02 ±0.01 ± ± ±0.21 ±0.03 ±0.05 ± ± ±0.16 ±0.03 ±0.05 ± ± ±0.13 ±0.04 ±0.04 ± ± ±0.13 ±0.04 ±0.04 ± ± ±0.12 ±0.06 ±0.16 ± ± ±0.23 ±0.04 ±0.13 ±0.02 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 c MIP (%). f Uncertainty comes from uncertainty of the slope of c MIP (%). f Uncertainty comes from uncertainty of Npix eff (%). g Statistical uncertainty (%). h Total of uncertainties (%) The expected energy resolution for each beam momentum and its total uncertainty are listed in Table 4. The intrinsic beam momentum fluctuation has already been subtracted. 20

21 Table 4: The uncertainties of the resolutions of measured energy deposit. p a beam energy resolution (%)b total of uncertainties c ± ± ± ± ± ± ± ±0.30 a Beam momentum (GeV/c). b Beam momentum fluctuation is subtruced. c Absolute value: uncertainty of σ E /p (%) Linearity and the energy resolution of the ScECAL physics prototype Figure 22 left shows the deposited energy as a function of the momentum of the incident beams. The solid line is the result of a linear fit with the values in Table 2 and the uncertainties in Table 3. The slope, dmip/dgev and offset are ±0.24 MIP/GeV and 24.0±1.3 MIP Figure also shows the deviation from linearity at each beam momentum. The maximum deviation from linearity is 2.0±0.8%. at 12 GeV. Figure 22 right shows the energy resolution as a function of the inverse of the square root of the incident beam momentum. Each data point and its uncertainty on the σ/e are taken from Table 4 so that the intrinsic beam momentum fluctuation has been subtracted. The curve shows the result of a fit to the data with a quadratic parametrization of the resolution. Deposit energy in ECALdum(MIP) 4000 CALICE ScECAL / E dummy12(%) σ E CALICE ScECAL Deviation(%) Beam momentumdumm(gev/c) / p dumm (1/ beam GeV/c) Figure 22: Response of the ScECAL prototype to 2-32 GeV electron (left, top), deviation from the result of linear fit (left, bottom), and the energy resolution as a function of inverse of square root of the beam momentum (right) Propagations of the systematic uncertainties from three calibration factor, c MIP, c p.e., and c inter to stochastic term and the constan term were investigated by using pseudo-experiment method. Figure 23 shows the the distribution of fluctuation of the stochastic term (left) and the constant term from the uncertainty of the c MIP (T 0 = 20 C). The systematic uncertainties 21

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