Shower development of particles with momenta from 1 to 10 GeV in the CALICE Scintillator-Tungsten HCAL
C. Adloff, J.-J. Blaising, M. Chefdeville, C. Drancourt, R. Gaglione, N. Geffroy, Y. Karyotakis, I. Koletsou, J. Prast, G. Vouters, J. Repond, J. Schlereth, J. Smith, L. Xia, E. Baldolemar, J. Li, S. T. Park, M. Sosebee, A. P. White, J. Yu, G. Eigen, M. A. Thomson, D. R.Ward, D. Benchekroun, A. Hoummada, Y. Khoulaki, J. Apostolakis, D. Dannheim, A. Dotti, K. Elsener, G. Folger, C. Grefe, V. Ivantchenko, M. Killenberg, W. Klempt, E. van der Kraaij, C. B. Lam, L. Linssen, A.-I. Lucaci-Timoce, A. Muennich, S. Poss, A. Ribon, A. Sailer, D. Schlatter, J. Strube, V. Uzhinskiy, C. Carloganu, P. Gay, S. Manen, L. Royer, M. Tytgat, N. Zaganidis, G. C. Blazey, A. Dyshkant, J. G. R. Lima, V. Zutshi, J.-Y. Hostachy, L. Morin, U. Cornett, D. David, A. Ebrahimi, G. Falley, N. Feege, K. Gadow, P. Goettlicher, C. Guenter, O. Hartbrich, B. Hermberg, S. Karstensen, F. Krivan, K. Krueger, S. Lu, B. Lutz, S. Morozov, V. Morgunov, C. Neubueser, M. Reinecke, F. Sefkow, P. Smirnov, M. Terwort, E. Garutti, S. Laurien, I. Marchesini, M. Matysek, M. Ramilli, K. Briggl, P. Eckert, T. Harion, H.-Ch. Schultz-Coulon, W. Shen, R. Stamen, B. Bilki, E. Norbeck, D. Northacker, Y. Onel, G. W. Wilson, K. Kawagoe, Y. Sudo, T. Yoshioka, P. D. Dauncey, et al. (119 additional authors not shown)
PPreprint typeset in JINST style - HYPER VERSION
Shower development of particles with momentafrom 1 to 10 GeV in the CALICEScintillator-Tungsten HCAL
The CALICE Collaboration
C. Adloff, J.-J. Blaising, M. Chefdeville, C. Drancourt, R. Gaglione, N. Geffroy,Y. Karyotakis, I. Koletsou, J. Prast, G. Vouters
Laboratoire d’Annecy-le-Vieux de Physique des Particules, Université de Savoie, CNRS/IN2P3, 9Chemin de Bellevue BP110, F-74941 Annecy-le-Vieux CEDEX, France
J. Repond, J. Schlereth, J. Smith a , L. Xia Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439-4815, USA
E. Baldolemar, J. Li b , S. T. Park, M. Sosebee, A. P. White, J. Yu Department of Physics, SH108, University of Texas, Arlington, TX 76019, USA
G. Eigen
University of Bergen, Inst. of Physics, Allegaten 55, N-5007 Bergen, Norway
M. A. Thomson, D. R. Ward
University of Cambridge, Cavendish Laboratory, J J Thomson Avenue, CB3 0HE, UK
D. Benchekroun, A. Hoummada, Y. Khoulaki
Université Hassan II Aïn Chock, Faculté des sciences, B.P. 5366 Maarif, Casablanca, Morocco
J. Apostolakis, D. Dannheim, A. Dotti, K. Elsener, G. Folger, C. Grefe, V. Ivantchenko,M. Killenberg c , W. Klempt, E. van der Kraaij d , C.B. Lam, L. Linssen,A. -I. Lucaci-Timoce e , A. Münnich c , S. Poss, A. Ribon, A. Sailer, D. Schlatter,J. Strube, V. Uzhinskiy CERN, 1211 Genève 23, Switzerland
C. Cârloganu, P. Gay, S. Manen, L. Royer
Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, BP 10448, F-63000Clermont-Ferrand, France
M. Tytgat, N. Zaganidis
Ghent University, Department of Physics and Astronomy, Proeftuinstraat 86, B-9000 Gent,Belgium
G. C. Blazey, A. Dyshkant, J. G. R. Lima, V. Zutshi
NICADD, Northern Illinois University, Department of Physics, DeKalb, IL 60115, USA – 1 – a r X i v : . [ phy s i c s . i n s - d e t ] J a n . -Y. Hostachy, L. Morin Laboratoire de Physique Subatomique et de Cosmologie - Université Joseph Fourier Grenoble 1 -CNRS/IN2P3 - Institut Polytechnique de Grenoble, 53, rue des Martyrs, 38026 Grenoble CEDEX,France
U. Cornett, D. David, A. Ebrahimi, G. Falley, N. Feege f , K. Gadow, P. Göttlicher,C. Günter, O. Hartbrich, B. Hermberg, S. Karstensen, F. Krivan, K. Krüger, S. Lu g ,B. Lutz, S. Morozov, V. Morgunov h , C. Neubüser, M. Reinecke, F. Sefkow, P. Smirnov,M. Terwort DESY, Notkestrasse 85, D-22603 Hamburg, Germany
E. Garutti, S. Laurien, I. Marchesini i , M. Matysek, M. Ramilli Univ. Hamburg, Physics Department, Institut für Experimentalphysik, Luruper Chaussee 149,D-22761 Hamburg, Germany
K. Briggl, P. Eckert, T. Harion, H. -Ch. Schultz-Coulon, W. Shen, R. Stamen
University of Heidelberg, Fakultät für Physik und Astronomie, Albert Überle Str. 3-5, 2.OG Ost,D-69120 Heidelberg, Germany
B. Bilki j , E. Norbeck b , D. Northacker, Y. Onel University of Iowa, Dept. of Physics and Astronomy, 203 Van Allen Hall, Iowa City, IA52242-1479, USA
G. W. Wilson
University of Kansas, Department of Physics and Astronomy, Malott Hall, 1251 Wescoe HallDrive, Lawrence, KS 66045-7582, USA
K. Kawagoe, Y. Sudo, T. Yoshioka
Department of Physics, Kyushu University, Fukuoka 812-8581, Japan
P. D. Dauncey
Imperial College London, Blackett Laboratory, Department of Physics, Prince Consort Road,London SW7 2AZ, UK
M. Wing
Department of Physics and Astronomy, University College London, Gower Street, London WC1E6BT, UK
F. Salvatore k Royal Holloway University of London, Department of Physics, Egham, Surrey TW20 0EX, UK
E. Cortina Gil, S. Mannai
Center for Cosmology, Particle Physics and Cosmology (CP3) Université catholique de Louvain,Chemin du cyclotron 2, 1320 Louvain-la-Neuve, Belgium
G. Baulieu, P. Calabria, L. Caponetto, C. Combaret, R. Della Negra, G. Grenier,R. Han, J-C. Ianigro, R. Kieffer, I. Laktineh, N. Lumb, H. Mathez, L. Mirabito,A. Petrukhin, A. Steen, W. Tromeur, M. Vander Donckt, Y. Zoccarato
Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPNL 4, rue E. Fermi, 69622 VilleurbanneCEDEX, France – 2 – . Calvo Alamillo, M.-C. Fouz, J. Puerta-Pelayo
CIEMAT, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas, Madrid,Spain
F. Corriveau
Institute of Particle Physics of Canada and Department of Physics Montréal, Quebec, CanadaH3A 2T8
B. Bobchenko, M. Chadeeva, M. Danilov l , A. Epifantsev, O. Markin, R. Mizuk l ,E. Novikov, V. Popov, V. Rusinov, E. Tarkovsky Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya ul. 25, RU-117218Moscow, Russia
N. Kirikova, V. Kozlov, P. Smirnov, Y. Soloviev
P. N. Lebedev Physical Institute, Russian Academy of Sciences, 117924 GSP-1 Moscow, B-333,Russia
D. Besson, P. Buzhan, A. Ilyin, V. Kantserov, V. Kaplin, A. Karakash, E. Popova,V. Tikhomirov
Moscow Physical Engineering Inst., MEPhI, Dept. of Physics, 31, Kashirskoye shosse, 115409Moscow, Russia
C. Kiesling, K. Seidel, F. Simon, C. Soldner, M. Szalay, M. Tesar, L. Weuste
Max Planck Inst. für Physik, Föhringer Ring 6, D-80805 Munich, Germany
M. S. Amjad, J. Bonis, S. Callier, S. Conforti di Lorenzo, P. Cornebise, Ph. Doublet,F. Dulucq, J. Fleury, T. Frisson, N. van der Kolk, H. Li m , G. Martin-Chassard,F. Richard, Ch. de la Taille, R. Pöschl, L. Raux, J. Rouëné, N. Seguin-Moreau Laboratoire de l’Accélérateur Linéaire, Centre Scientifique d’Orsay, Université de Paris-Sud XI,CNRS/IN2P3, BP 34, Bâtiment 200, F-91898 Orsay CEDEX, France
M. Anduze, V. Balagura, V. Boudry, J-C. Brient, R. Cornat, M. Frotin, F. Gastaldi,E. Guliyev n , Y. Haddad, F. Magniette, G. Musat, M. Ruan o , T.H. Tran, H. Videau Laboratoire Leprince-Ringuet (LLR) – École Polytechnique, CNRS/IN2P3, F-91128 Palaiseau,France
B. Bulanek, J. Zacek
Charles University, Institute of Particle & Nuclear Physics, V Holesovickach 2, CZ-18000 Prague8, Czech Republic
J. Cvach, P. Gallus, M. Havranek, M. Janata, J. Kvasnicka, D. Lednicky,M. Marcisovsky, I. Polak, J. Popule, L. Tomasek, M. Tomasek, P. Ruzicka, P. Sicho,J. Smolik, V. Vrba, J. Zalesak
Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221Prague 8, Czech Republic
B. Belhorma, H. Ghazlane
Centre National de l’Energie, des Sciences et des Techniques Nucléaires, B.P. 1382, R.P. 10001,Rabat, Morocco
K. Kotera, T. Takeshita, S. Uozumi
Shinshu Univ. , Dept. of Physics, 3-1-1 Asaki, Matsumoto-shi, Nagano 390-861, Japan – 3 – . Chang, A. Khan, D. H. Kim, D. J. Kong, Y. D. Oh
Department of Physics, Kyungpook National University, Daegu, 702-701, Republic of Korea
M. Götze, J. Sauer, S. Weber, C. Zeitnitz
Bergische Universität Wuppertal, Fachbereich C Physik, Gaussstrasse 20, D-42097 Wuppertal,Germany ♠ Corresponding authorE-mail: [email protected] a Also at University of Texas, Arlington b Deceased c Now at DESY Hamburg, Germany d Now at University of Bergen, Norway e Now at Max Planck Inst. für Physik, Munich, Germany f Now at Stony Brook University (SUNY), Dept. of Physics and Astronomy, Stony Brook, NY, USA g Now at Hamburg University, Germany h On leave from ITEP i Also at DESY Hamburg, Germany j Also at Argonne National Laboratory k Now at University of Sussex, Physics and Astronomy Department, Brighton, Sussex, BN1 9QH,UK l Also at MEPhI and at Moscow Institute of Physics and Technology m Now at LPSC Grenoble n TRIUMF, Vancouver, BC, Canada o Now at IHEP, Beijing, China A BSTRACT : Lepton colliders are considered as options to complement and to extend the physicsprogramme at the Large Hadron Collider. The Compact Linear Collider (CLIC) is an e + e − colliderunder development aiming at centre-of-mass energies of up to 3 TeV. For experiments at CLIC,a hadron sampling calorimeter with tungsten absorber is proposed. Such a calorimeter providessufficient depth to contain high-energy showers, while allowing a compact size for the surroundingsolenoid.A fine-grained calorimeter prototype with tungsten absorber plates and scintillator tiles read out bysilicon photomultipliers was built and exposed to particle beams at CERN. Results obtained withelectrons, pions and protons of momenta up to 10 GeV are presented in terms of energy resolutionand shower shape studies. The results are compared with several GEANT4 simulation models inorder to assess the reliability of the Monte Carlo predictions relevant for a future experiment atCLIC.K EYWORDS : Calorimeter methods; Detector modelling and simulations I; Particle identificationmethods. ontents
1. Introduction 12. Experimental setup 23. Calibration and temperature correction 34. Monte Carlo simulation 4
5. Systematic uncertainties 7
6. Analysis of electron data 8
7. Analysis of hadron data 11
8. Comparison of the calorimeter response for different particle types 209. Summary 22
1. Introduction
The Compact Linear Collider (CLIC) is a possible future e + e − collider [1] that would allow theexploration of a new energy region in the multi-TeV range, beyond the capabilities of today’sparticle accelerators. The main driver for the design of the CLIC detector concept is the requirementfor a jet energy resolution close to 30% / (cid:112) E [ GeV ] . This can be achieved by using fine-grainedcalorimeters and particle-flow analysis techniques [2]. Simulation studies showed that a densematerial has to be used as absorber in the calorimeter, in order to contain the high-energy showers,while limiting the diameter of the surrounding solenoid. The detector concepts being developedfor CLIC feature a barrel calorimeter with tungsten absorber plates.In order to test such a detector, the CALICE collaboration [3] constructed a tungsten ab-sorber structure, to be combined with existing readout layers of the Analog Hadron Calorimeter– 1 – =0 WCh1−18 mm−33 mm Sc1−142 mm WCh2−411 mm−426 mm −659 mm−674 mmWCh3 −722 mmSc2308 mm z −3500 mm−7000 mmChAChB W−AHCAL
Figure 1: Sketch of the experimental setup at the T9 beam line of the CERN PS (not to scale). Sc stands for scintillator , WCh for wire chamber , and Ch for Cherenkov . The beam enters from theright.(AHCAL) [4]. Data were recorded with the CALICE tungsten AHCAL (W-AHCAL) prototypeat the CERN PS in September-October 2010 with mixed beams containing muons, electrons, pi-ons and protons in the momentum range of 1 to 10 GeV/c. This paper presents energy resolutionmeasurements and studies of the longitudinal and radial shower development.In section 2 we briefly describe the experimental setup. The procedure to calibrate the calorime-ter and the temperature corrections are presented in section 3. Section 4 introduces details aboutthe Monte Carlo simulation. The systematic uncertainties are discussed in section 5. In sections 6,7 and 8 the analyses of the electron, pion and proton data and comparisons to the Monte Carlosimulations are presented. A summary of the results is given in section 9.
2. Experimental setup
The W-AHCAL consists of a 30-layer sandwich structure of absorber plates interleaved with 0.5 cmthick scintillator tiles, read out by wavelength shifting fibres coupled to silicon photo-multipliers(SiPMs). The calorimeter has a total of 6480 channels. One absorber plate is 1 cm thick and is madeof a tungsten alloy consisting of 92.99% tungsten, 5.25% nickel and 1.76% copper, with a densityof 17.8 g/cm . The nuclear interaction length of this alloy is λ I = .
80 cm and the radiation lengthis X = .
39 cm. The scintillator tiles are placed into a steel cassette, with 0.2 cm thick walls. Thusone calorimeter layer corresponds to 0.13 λ I and to 2.8 X . The overall dimensions of the prototypeare 0 . × . × .
75 m , amounting to 3.9 λ I and to 85 X . The high granularity of the detector isensured by the 3 × tiles placed in the centre of each active plane, surrounded by 6 × and 12 ×
12 cm tiles at the edges. Since the SiPM response varies with the temperature, the latteris monitored in each layer by 5 sensors [4].The data were recorded in the secondary T9 beam line [5] of the CERN PS East Area [6].The 24 GeV/c primary proton beam hits a target 57 m upstream of the W-AHCAL prototype. Amomentum-selection and focusing system is used to deliver a mixed beam of electrons, muons,pions and protons with momenta between 1 and 10 GeV/c. The momentum spread ∆ p / p is of theorder of 1% for all momenta. The beam size is chosen such that the resulting Gaussian spread onthe W-AHCAL surface is approximately 3 × for 10 GeV/c pions.A sketch of the CERN PS test beam setup is presented in figure 1. The secondary beam passestwo Cherenkov threshold counters (A and B), two trigger scintillators and a tracking system ofthree wire chambers. The Cherenkov counters are filled with CO gas with pressures adjustable up– 2 – [GeV] beam p + p + e e v en t s · CALICE W-AHCAL
Figure 2: Number of events after the selection of a given particle type from the positive-polaritydata.to 3.5 bar. The Cherenkov information is read out through photo-multiplier tubes and subsequentdiscriminators with a fixed threshold. The Cherenkov signals are used offline for particle identifi-cation. The beam trigger is defined by the coincidence of two 10 × × scintillator counters.The information from three 11 ×
11 cm wire chambers [7] is used offline to reconstruct the trackof the incident particle and predict its position on the calorimeter surface.The data recorded by the CALICE W-AHCAL in 2010 contained a mixed beam of particles.The negative-polarity beam contains e − , π − and µ − particles. The anti-proton content was con-sidered to be negligible. The positive-polarity beam contains e + , π + , µ + and protons. The kaoncontent was negligible for both polarities. The distribution of the number of events after the selec-tion of a given particle type from the positive-polarity data is given in figure 2. The numbers forthe negative-polarity beams are similar.
3. Calibration and temperature correction
The responses of all calorimeter cells are calibrated to a common physics signal based on minimumionising particles (MIP) which were obtained in dedicated muon runs. Several steps are necessaryto translate the signals measured with the SiPM readout (in ADC counts) to information about thedeposited energy (in MIP).The calibration of a single cell i is done according to the formula: E i [ MIP ] = A i [ ADC ] A MIP i [ ADC ] · f resp ( A i [ pixels ]) , (3.1)where: • A i [ ADC ] is the pedestal-subtracted amplitude registered in cell i , in units of ADC counts; • A MIP i [ ADC ] is the pedestal-subtracted MIP amplitude in cell i , measured in ADC counts. Itis taken as the most probable value of the energy response for muons; • f resp ( A i [ pixels ]) is the SiPM saturation correction function which corrects for the non-linearityof the SiPM response. This function assumes an effective number of total pixels of about 925.– 3 –he amplitude in units of pixels is obtained by dividing the amplitude of a cell by the corre-sponding SiPM gain factor G i [ ADC ] : A i [ pixels ] = A i [ ADC ] G i [ ADC ] . (3.2)The gain values are obtained from fits of photo-electron spectra taken with low intensity LED lightprovided by a calibration and monitoring LED system. Detailed information about the calibrationand the saturation correction procedures can be found in [8]. After calibration, only cells with anenergy above 0.5 MIP are considered, in order to reduce the noise contribution.During data taking, the SiPM noise spectra were monitored to identify channels which give nosignal, or which give too high a signal. These types of channels are identified based on the RMSvalue of the energy distributions from dedicated random trigger runs: • Dead channels: RMS < 20.5 ADC counts. • Noisy channels: RMS > 140 ADC counts.On average, during the CERN 2010 data taking period less than 3% of the total number of calorime-ter channels were identified as noisy or dead, and discarded from the analysis.As the SiPM response depends on temperature, only muon runs within a narrow temperaturerange ( T = . ± . ◦ C) were used for measuring the A MIP i [ ADC ] calibration constants. From thetotal of 6480 channels, 92% had sufficient statistics and the corresponding A MIP i [ ADC ] calibrationfactors were determined. The other channels were discarded from the analysis.The temperature inside the calorimeter is measured by 5 sensors for each calorimeter layer.The sensors are horizontally centred within the layer and equally spaced vertically. The verticaltemperature spread was found to be of the order of 0 . ◦ C per plane. The average calorimetertemperature for the analysed runs varied from 20 to 25 ◦ C.The MIP calibration factors show an inverse linear dependence on temperature. Therefore, inorder to take into account the possible temperature differences between the muon calibration runsand the analysed data runs, the MIP calibration factors are corrected for the temperature differ-ences. To measure the temperature dependence, muon tracks are identified using a track finder.Then the position of the most probable value was found using the energy distribution of all muontrack hits in a given layer. The dependence of the peak position on the temperature is fitted witha linear function for each calorimeter layer, as illustrated in figure 3. The linear dependence, ex-pressed in percent per Kelvin, is measured relative to the calorimeter response E ref obtained at thetemperature ( T = . ± . ◦ C) quoted above, at which the muon calibration runs were taken. Thedistributions of the MIP temperature slopes per W-AHCAL layer, before and after temperature cor-rection, are shown in figure 4. After correction, the average slope is at the level of − .
4. Monte Carlo simulation
A simulation of the experimental setup is implemented in a GEANT4 [9] based application [10].The simulated geometry includes the full setup starting from 60 m upstream of the calorimeter– 4 –
Layer 6 emperature [deg. C]
20 22 24 26 ) / E r e f r e f ( E − E ± offset = 0.76 0.001 ± slope = −0.030 2/ndf = 1.02 χ CALICE W−AHCAL
Figure 3: Example of the measurementof the MIP temperature dependence for theW-AHCAL layer 6. Each data point corre-sponds to the most probable value of the energyresponse in a given run of all calorimeter cellsin this layer that belonged to a muon track.
Layer number M I P t e m p . g r ad i en t s [ / K ] -0.06-0.04-0.0200.020.04 Before T correctionAfter T correction
CALICE W-AHCAL
Figure 4: Distribution of the linear MIP tem-perature gradients per W-AHCAL layer, beforeand after temperature correction. The averagegradient is − . − . The physics models in the GEANT4 simulation are combined into so-called physics lists, providinga balance between the level of physics precision and CPU performance. Within a list, the modelsare valid in different energy ranges and for different particles.Several GEANT4 (version 9.6.p02) physics lists were selected in order to compare them withthe hadron data: • QGSP_BERT_HP : Employs the Bertini (BERT) cascade model which handles incident nu-cleons, pions and kaons with kinetic energy up to 9.9 GeV. From 9.5 to 25 GeV it uses the lowenergy parametrised (LEP) model. For energies above 12 GeV it employs the quark-gluonstring precompound (QGSP) model. • QGSP_BIC_HP : Uses the binary cascade (BIC) model for incident protons and neutronswith a kinetic energy E kin <
10 GeV and pions with E kin < . • FTFP_BERT_HP : Uses the Bertini cascade model up to 5 GeV, then the Fritiof precom-pound (FTFP) model.A more detailed description can be found for example in [11]. The combinations of the simulationsmodels for selected physics lists are presented in figure 5.– 5 – (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
BERT (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
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BERT 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QGSP_BIC_HPFTFP_BERT_HPQGSP_BERT_HP LEP QGSP (cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)
Binary Cascade4 5 9.5 9.9 12 E kinetic [GeV] Figure 5: Schematic representation of selected GEANT4 physics lists with the energy ranges ofthe different models. In the overlap regions between the models, a random choice between thecorresponding models is performed, based on the kinetic energy of the incident particle in eachinteraction.As the W-AHCAL uses tungsten as absorber material, slow neutrons are expected to play animportant role in hadron interactions in this calorimeter. Therefore the above-mentioned physicslists are combined with the data-driven Neutron High Precision (HP) Models and Cross Sections,which treat the detailed simulation of the interaction, transportation, elastic scattering and captureof neutrons with energies below 20 MeV. Since the electromagnetic model is the same for allGEANT4 physics lists, the e ± data are compared with the QGSP_BERT_HP physics list only. Events are generated for each of the selected physics lists described in section 4.1. To comparesimulation with data, one needs to consider realistic detector effects which occur in addition to theparticle interaction and energy deposition. This is done both at the generation and digitisation level.At the generation step, the following aspects are taken into account: • Signal shaping time of the readout electronics : To emulate the signal shaping time, onlyhits within a time window of 150 ns (corrected for the time of flight) are accepted. The startof the time window is defined from the moment when the particle reaches the W-AHCALfront face. • Non-linearity of the light output : In the case of plastic scintillator, the light output per unitlength has a non-linear dependence on the energy loss per unit length of the particle’s track.This behaviour is described by the so-called
Birks’ law [12]: dLdx ∝ dE / dx + k Birks · dE / dx , (4.1)where dL / dx represents the light output per unit length, dE / dx is the energy lost by theparticle per unit length of its path (in units of MeV/mm), and k Birks is a material-dependentfactor (Birks constant). The Birks’ law is applied to the W-AHCAL hits, using a factor of k Birks = .
5. Systematic uncertainties
The main contributions to the systematic uncertainties that affect the measurement of the totalcalorimeter response were found to be: • ±
2% uncertainty due to the MIP calibration factors. These factors are obtained by fitting themuon hit energy distributions for a given cell. The fit results depend on the fitting function,on the binning of the histograms, and on the muon track selection, resulting into an overalluncertainty of ±
2% on the MIP calibration factors. • ± .
5% due to the run-wise variation of the calorimeter response. This value is given by theRMS of the mean energy sum in the analysed runs (without subtracting the contribution dueto the statistical error on each mean).In addition, the electromagnetic showers are affected by the uncertainties in the measurementof the saturation scaling factor. This was studied by randomly varying the saturation scaling fac-tors according to a Gaussian distribution with a mean of 0.8, and a sigma of 0.09, as obtained indedicated measurements [8]. The data were calibrated successively 100 times using the smearedscaling factors. With this method, variations of the average total energy deposited in the calorimeterranging from 0.1% for 1 GeV positrons, to 0.4% for 6 GeV positrons, were obtained. This effect isgreatly reduced for hadron-induced showers which typically have a larger number of active cells.The uncertainty on the measurement of the energy per calorimeter layer due to the channel-wise variation of the MIP calibration factors affects the longitudinal profiles, because a signal in anindividual layer can be dominated by a few cells, as in the case of electromagnetic showers. Thisuncertainty was determined from the width of the distribution of the difference between the MIPcalibration factors measured in two independent running periods, resulting in a variation of ± . Due to the imperfect reflective coating of the scintillator tiles, light might leak between neighbour-ing calorimeter cells. This is taken into consideration in the simulation via the so-called cross-talkfactor, which is the fraction of energy leaking into neighbouring cells. Measurements of the cross-talk yielded values of 2.5% [8] per tile edge. Recent measurements in a different sample resulted inestimates between 3.3% and 4.6%. To account for the imperfect knowledge of the cross-talk, andhence of the energy scale, an uncertainty of +
3% is assumed conservatively for the total energysum in the simulation.The impact of the integration time window of 150 ns, which is due to the signal shaping timeof the readout electronics, on the simulated calorimeter response was also studied. Variation of ±
30 ns around the time cut of 150 ns resulted in a negligible impact on the measured energies.– 7 – . Analysis of electron data
As the underlying physics of electromagnetic showers is well understood, the analysis of the e ± data is used to validate the implementation of the detector material and response in the simulation,as well as the calibration chain. The electromagnetic analysis is also important for the study of thedegree of (non)compensation of the hadron calorimeter, which is expressed in the e / π ratio, i.e. theratio of the detector response for electrons to that for hadrons. Only e ± runs up to 6 GeV were considered; for higher energies, the e ± content in the beam wastoo low. The first level of selection is based on Cherenkov threshold counters [14]. Additional cutswere applied in order to reject the small fraction (of the order of a few percent) of hadron and muonevents in the data sample.While hadrons are expected to penetrate deep into the calorimeter, electrons start to showeralready in the first calorimeter layer, and most of the shower is contained within the first five layers.To identify the electromagnetic shower clusters a nearest-neighbour algorithm [15] is used. Furthera cut is applied on the cluster centre-of-gravity in the z -direction, z clustercog , defined as: z clustercog = ∑ i E i · z i ∑ i E i , (6.1)where z i is the z -position of the cluster hits, and E i is their energy. Only events are selected whichcontain only one cluster that has the centre-of-gravity along the beam axis in the first part of thecalorimeter, i.e. with z clustercog <
400 mm, which corresponds to approximately 3 calorimeter layers .To reduce the influence of noise in the e ± events, only calorimeter cells within the first20 calorimeter layers and within the central 10 ×
10 tiles of 3 × are considered. This issafe because in all the runs the beam profile is centred on the calorimeter centre, and the width ofthe beam profile is not more than 3 tiles.The e ± energy sum spectra have a non-Gaussian shape, with tails at high energies, as can beseen for example for 2 GeV positrons in figure 6. These high energy tails originate from the limitednumber of active cells in an electromagnetic shower, due to the 1 cm thick tungsten absorber perlayer, which corresponds to 2.6 radiation lengths X . On average, about 17 cells are active inan electromagnetic shower induced by a 1 GeV particle, and about 38 cells in the 6 GeV case.The energy spectra of individual cells, after pedestal subtraction, are exponentially falling. Withincreasing number of active cells, the total energy distribution becomes more and more Gaussian .The high energy tails are also present in the simulation, at generator level, i.e. before including anydetector effects.The e ± energy spectra are fitted with the Novosibirsk fit function, which accounts for the highenergy tails. This function is defined as [16]: f ( x ) = A · exp (cid:20) − . · (cid:18) ln [ + Λ · τ · ( x − µ )] τ + τ (cid:19)(cid:21) (6.2) The variable z clustercog is calculated in the coordinates of the laboratory frame, with the centre attached to the backplane of the first wire chamber, 308 mm away from the W-AHCAL front face, as indicated in figure 1. The central limit theorem states that the distribution of an average tends to be Gaussian for a large number ofsamples, even when the distribution from which the average is computed is decidedly non-Gaussian. – 8 – nergy sum [MIP] E n t r i e s / . M I P + – = 51.84 m – = 0.052 t – = 11.20 s /ndf = 1.5 c DataSimulation
CALICE W-AHCAL
Figure 6: The distribution of the energy sum deposited by 2 GeV e + in the CALICE W-AHCAL.Data, shown by the black filled circles, are compared to the simulation (filled area). The red line isthe result of a fit of the data using the Novosibirsk function defined in equation 6.2. The fit resultsare also given.where Λ ≡ sinh ( τ · √ ln 4 ) σ · τ · √ ln 4 , (6.3)with µ the peak position, σ the width, and τ the tail parameter. With τ → σ . An example fit for 2 GeV positrons, togetherwith the fit results, is given in figure 6. The fit range is ± σ around the peak of an initial fit with thesame function. The µ parameter gives the mean energy sum in the W-AHCAL, further denoted by (cid:104) E vis (cid:105) , i.e. visible energy. It was checked that the µ parameter from the Novosibirsk fit is the sameas the statistical mean of the distribution within uncertainties. The σ parameter gives the width ofthe distribution, and it is further used to measure the e + energy resolution. The calorimeter response for electromagnetic showers is expected to be linear with the beam mo-mentum. This dependence is shown in figure 7 for the e + data. Similar results (within the errors)are obtained for the e − data. The lines indicate a fit with the function (cid:104) E vis (cid:105) = u + v · p beam , where u is the offset, and v the slope. The ratio between the simulation and the data is shown in the bottompart of the figure. The error bars indicate the overall uncertainties, i.e. the statistical and systematicuncertainties added in quadrature. The data agree with the Monte Carlo simulations within uncer-tainties, the deviations being less than 2%. The results of the linear fit are given in Table 1. Theoffsets, which are consistent with zero, are the combined result of the 0.5 MIP threshold (loss ofenergy) and the detector noise (addition of energy).The e + energy resolution is presented in figure 8. The fit function is: σ E E ≡ σ Novosibirsk µ Novosibirsk = a (cid:112) E [ GeV ] ⊕ b ⊕ cE [ GeV ] , (6.4)where: – 9 – [GeV] beam p [ M I P ] æ v i s E Æ CALICE W-AHCAL + e DataSimulation [GeV] beam p S i m u l a t i on / D a t a Figure 7: Dependence of the mean visi-ble positron energy on the beam momenta.The data are compared with the simulation.The line indicates a fit with the function (cid:104) E vis (cid:105) = u + v · p beam . In the bottom part, theratio between the simulation and the data isshown. The grey band shows the overall un-certainty for both data and simulation. Table 1: Fit parameters of the dependence ofthe mean positron visible energy on the beammomentum: comparison of data with simula-tion.Parameter Data Simulation u [MIP] − . ± . − . ± . v [MIP/GeV] 28 . ± .
49 28 . ± . χ /ndf 1.3/4 0.2/4 • a is the stochastic term , which takes into account the statistical fluctuations in the showerdetection. • b is the constant term , which is dominated by the stability of the calibration, but includesalso detector instabilities (i.e. non-uniformity of signal generation and collection, as well asloss of energy in dead materials); • c is the noise term , the equivalent of the electronic noise in the detector, which includesnoise from all the cells (with and without physical energy deposits). This term depends onthe fiducial volume considered in the analysis.The noise term c is fixed to the spread (RMS) of the energy sum distribution of randomlytriggered noise events inside the beam spill, considering only the central 3 × tiles, con-tained in the first 20 layers, as done for the selection of the electromagnetic data (section 6.1).The measured noise RMS for the e + data is ( . ± . ) MIP. This value is converted into GeVusing the v parameters of the fit given in Table 1, resulting in 0.036 GeV. The results of the fitsto the e + energy spectra are shown in table 2 for both data and simulation. The results agreewithin the experimental uncertainties. A stochastic term of ( . ± . ) % / (cid:112) E [ GeV ] is obtainedfor the CALICE W-AHCAL, which is significantly higher than the stochastic term obtained for– 10 – [GeV] beam p / E E s + e DataSimulation CALICE W-AHCAL [GeV] beam p S i m u l a t i on / D a t a Figure 8: Energy resolution for e + events: com-parison of data with simulation. The error barsshow the overall uncertainties. In the bottompart, the ratio between the simulation and thedata is shown. The grey band shows the overalluncertainty. Table 2: Parameters of the positron energy reso-lution fits for data and the simulation. The noiseterm is fixed to 1 .
06 MIP.Parameter Data Simulation a [%] 29 . ± . . ± . b [%] 0 . ± . . ± . c [GeV] 0 .
036 0 . χ /ndf 5.3/4 10.1/4the CALICE Fe-AHCAL of ( . ± . ) % / (cid:112) E [ GeV ] [8]. This degradation of the resolution isdue to the coarser sampling of the W-AHCAL with 2.8 X per layer compared to 1.2 X for theFe-AHCAL.The longitudinal profile, i.e. the energy sum per layer as a function of the calorimeter layernumber, is shown in figure 9 for 2 GeV e + . Due to the dense absorber material, most of the energyof the electromagnetic shower is deposited in the first 5 calorimeter layers. The data and the MonteCarlo simulation agree within the uncertainties, the deviations being smaller than 10% up to about20 X .
7. Analysis of hadron data
The selection of low energy hadrons is complicated by the presence of muons from decays in flight,which are not sufficiently suppressed using Cherenkov threshold counters. In addition, the energysum distributions for muons and pions overlap at low energies, which makes the distinction moredifficult. For this reason, only runs with beam momenta from 3 (4) to 10 GeV/c are considered forthe π ± (proton) analyses, as only for these was a reliable selection of hadrons possible.The pre-selection of hadron events is based on the Cherenkov threshold counters. In order tosuppress the muons without the help of a tail catcher, information based on the high granularity– 11 – E ne r g y pe r l a y e r [ M I P ] beam , p + e DataSimulation CALICE W-AHCAL
Layer number S i m u l a t i on / D a t a Figure 9: Longitudinal shower profile for 2 GeV e + : comparison of data with simulation. In thebottom part of the figure the ratio between the simulation and the data is shown. The grey bandshows the overall uncertainty.of the calorimeter is used. Algorithms are applied to identify tracks [17] and clusters [15] inthe calorimeters. A set of cuts on the number of found tracks and on their length, as well as onthe number of clusters and their position in the calorimeter, was developed. It was confirmed bycomparison with the Monte Carlo simulation that the applied cuts have no significant impact on thehadron events.The events which fulfil any of the following cuts are considered to be either muon-like or lateshowering hadrons: • A track segment is identified which ends in layer ≥
15, has a small angle with respect to thenormal incidence (cos φ ≥ . • At least two track segments are identified, which have a small angle (cos φ > . • At least one track segment is identified with hits in layer 29 or 30, and which traverses atleast ten layers; • Two clusters are found in the first and second half of the calorimeter, and they are aligned,i.e. the difference between their x and y positions is less than the size of the scintillator tileof 3 cm.About 45% of the events for hadrons with a beam momentum of 3 GeV/c and about 50% at10 GeV/c fulfil the criteria described above and are therefore rejected from the analysis.– 12 – nergy sum [MIP] . M I P ) (cid:215) en t r i e s (cid:229) E n t r i e s / ( = 3 GeV beam , p + p DataQGSP_BERT_HPFTFP_BERT_HP
CALICE W-AHCAL
Figure 10: Energy sum distribution for π + with a beam momentum of 3 GeV/c: comparison ofdata with selected GEANT4 physics lists. The pre-selection of pions based on Cherenkov threshold counters resulted in a sample with anelectron and proton contamination of less than 1%.The hadron energy sum distributions are non-Gaussian, with a high-energy tail, the effect beingmore pronounced at low energies, as exemplified in figure 10 for pions with a beam momentum of3 GeV/c. This shape is predicted by the selected GEANT4 physics lists.In order to measure the hadron energy resolution, we take the non-Gaussian shape of theenergy distributions into account by using: σ E E = RMSMean , (7.1)with RMS and Mean obtained directly from the histogram statistics. The dependence of the meanvisible energy on the available energy E available is shown in figure 11 (left), where E available is theenergy available for deposition in the calorimeter. In the case of a pion, E available is simply theparticle’s total energy [18]: E available = (cid:113) p + m π , (7.2)where m π = .
57 MeV/c is the pion mass. Data are compared with selected GEANT4 physicslists. In the bottom part of the figure 11 (left), the ratio between the simulation and data is shown.The best description is given by QGSP_BERT_HP, the deviations being of the order of 2% or better.As FTFP_BERT_HP shares the same physics model for particles with momenta up to 5 GeV/c, theagreement is equally good, but gets worse when switching to the Fritiof model. For both Bertini-based physics lists, a decrease of the energy ratio is observed for 10 GeV/c. This corresponds tothe transition to the Low Energy Parametrisation model for QGSP_BERT_HP. The RMS of thevisible energy distributions is shown as a function of the available energy in figure 11 (right), forthe different physics lists. For QGSP_BERT_HP and FTFP_BERT_HP the deviations are within10%. The simulated distributions are in general broader than those of the data.The energy resolution for π ± data is shown in figure 12. The data are fitted with the functiondefined in equation 6.4. The c -term is fixed by the spread (RMS) of the energy distribution in ran-– 13 – [GeV] available E M ean [ M I P ] + p DataQGSP_BERT_HPFTFP_BERT_HP
CALICE W-AHCAL [GeV] available E S i m u l a t i on / D a t a [GeV] available E R M S [ M I P ] + p DataQGSP_BERT_HPFTFP_BERT_HP
CALICE W-AHCAL [GeV] available E S i m u l a t i on / D a t a Figure 11: Left: Dependence of the mean π + visible energy on the available energy. Right: De-pendence of the RMS of the π + visible energy on the available energy. Data are compared withselected GEANT4 physics lists. In the bottom part of the figure the ratio between the simulationand the data is shown. The bands show the overall uncertainty. [GeV] available E R M S / M ean CALICE W-AHCAL
Data + p - p Figure 12: Energy resolution for the 2010 π ± W-AHCAL data, obtained with equation 7.1.The lines indicate a fit with the function givenin equation 6.4. The error bars show the overalluncertainty.
Energy sum [MIP] E n t r i e s Gaussian fit: 0.28 – = 260.59 m – = 50.64 s c – = 0.194 ms /E = E s – Mean = 263.05 0.19 – RMS = 55.32 0.001 – = 0.210 MeanRMS/E = E s CALICE W-AHCAL = 10 GeV beam , p + p Figure 13: Energy sum distribution for π + witha beam momentum of 10 GeV/c. The red lineindicates a fit with a Gaussian function in theregion ± · RMS around the mean (filled range).The energy resolutions obtained using the pa-rameters of the Gaussian fit, as well as usingthe histogram statistics, are indicated.domly triggered events inside the beam spill, considering all calorimeter cells. This term amountsto 71 MeV in the case of π − data, and to 70 MeV in the case of π + data.– 14 –able 3: Parameters of the energy resolution fits for the 2010 W-AHCAL π ± data. The c parameteris fixed. Parameter π − π + a [%] 63 . ± . . ± . b [%] 3 . ± . . ± . c [GeV] 0 .
071 0 . χ /ndf 0.4/6 0.5/6The parameters obtained with the energy resolution fit are given in Table 3. The stochastic termof ( . ± . ) % / (cid:112) E [ GeV ] is slightly worse than that of ( . ± . ) % / (cid:112) E [ GeV ] obtained forthe CALICE Fe-AHCAL [19]. However, a direct comparison of the pion resolutions measured withthe two detectors is difficult due to several reasons. Firstly, in the W-AHCAL case the spectra havehigh energy tails, as illustrated in figure 13. Hence a Gaussian fit would result in a too optimisticenergy resolution, as indicated in the same figure. In the Fe-AHCAL case, the energy spectraare fitted with a Gaussian function in a ± · RMS range around the mean value. Secondly, theFe-AHCAL data covered a much wider beam momentum range, from 10 to 100 GeV/c, comparedto the range of 3 to 10 GeV in the W-AHCAL case. The a and b parameters are anti-correlated,and poorly constrained with this low energy data, which is reflected in the large uncertainty of the b parameter.In order to judge the quality of the simulation concerning the spatial development of hadronshowers, comparisons of data with the Monte Carlo simulation were done for variables whichdescribe the shower development along the z -axis (longitudinally) and in the ( x , y ) plane (trans-versely). To study the longitudinal shower development, a variable called the energy weightedlayer number is defined as: (cid:104) N wl (cid:105) = ∑ i E i · layer i ∑ i E i (7.3)where E i is the hit energy in cell i , layer i is the layer number to which cell i belongs, and thesummation is done over all cells. This variable is sensitive to the longitudinal shower development:the mean energy weighted layer (cid:104) N wl (cid:105) will have a larger value for showers which develop deep inthe calorimeter than for early starting showers. The dependence of the mean energy weighted layernumber on the π + available energy is presented in figure 14, which contains also the ratio betweenthe simulation and the data. The observed disagreement is within ±
3% for both QGSP_BERT_HPand FTFP_BERT_HP.The longitudinal profile for π + with a beam momentum of 9 GeV/c is shown in figure 15 (left).In the central part the energy deposition is well reproduced by the simulation models considered.However, both models overestimate the energy depositions in the first and last calorimeter layersby up to 25%. The difference in the front part of the calorimeter cannot be related to an improperdescription of the material in the test beam, since the longitudinal profile of 2 GeV e + is welldescribed as shown in figure 9. The simulation models seem instead to predict an earlier showerstart than observed in the experimental data.The shower development in the transverse plane is studied by means of the so-called radial– 15 – [GeV] available E æ w l N Æ + p DataQGSP_BERT_HPFTFP_BERT_HP
CALICE W-AHCAL [GeV] available E S i m u l a t i on / D a t a Figure 14: Dependence of the mean energy weighted layer number of π + initiated show-ers on the available energy: comparison of data with selected GEANT4 physics lists.One layer corresponds to 0.13 λ I . In the bottom part of the figure the ratio between thesimulation and the data is shown. E ne r g y pe r l a y e r [ M I P ] CALICE W-AHCAL = 9 GeV beam , p + p DataQGSP_BERT_HPFTFP_BERT_HP
Layer number S i m u l a t i on / D a t a Radius [mm] ] E ne r g y den s i t y [ M I P / c m -3 -2 -1 CALICE W-AHCAL = 9 GeV beam , p + p DataQGSP_BERT_HPFTFP_BERT_HP
Radius [mm] S i m u l a t i on / D a t a Figure 15: Longitudinal (left) and radial (right) shower profiles of π + with a beam momentumof 9 GeV/c: comparison of data with selected GEANT4 physics lists. In the bottom part of thefigures the ratios between the simulations and the data are displayed. The bands show the overalluncertainty. – 16 –rofile. The procedure to measure this profile is the following: In order to reduce the influence ofthe varying detector granularity within one layer, the physical W-AHCAL cells are divided into vir-tual cells of 1 × [15]. In a next step, the energy in a given cell is distributed randomly amongthe 1 × virtual cells contained in the real cell. Then virtual rings, centred on ( x cog , y cog ),are built. The radii of these rings are multiples of the width of the smallest W-AHCAL tile, i.e.3 cm. Next the energy density, i.e. the energy contained in a given ring divided by the area of thering, is measured in MIP/cm in each ring. Finally, the radial profile is given by the distributionof the energy density (i.e., energy per unit area) as a function of the radial distance to the showercentre-of-gravity, defined as: r i = (cid:113) ( x i − x cog ) + ( y i − y cog ) , (7.4)where x i ( y i ) is the x ( y ) position of the centre of the cell i , and x cog and y cog are the centres-of-gravity in x and y for the whole calorimeter: x cog = ∑ i E i · x i ∑ i E i and y cog = ∑ i E i · y i ∑ i E i , (7.5)with E i being the hit energy in cell i .An example of a radial profile is given in figure 15 (right) for π + with a beam momentum of9 GeV/c. The deviations are at the level of 10% or smaller for QGSP_BERT_HP, which describesthe data better than FTFP_BERT_HP. The calorimeter response to protons differs from the response to pions mainly due to two ef-fects [20]: • The first effect is due to the differences in the energy available for deposition in the calorime-ter. For pions, it is given in equation 7.2. For protons, the available energy is: E available = E kin = (cid:113) p + m − m proton , (7.6)where m proton = .
27 MeV/c is the proton mass. This is relevant for the low energy rangeanalysed in this paper; • The second effect originates from the different fractions of π mesons produced in protonand pion-induced showers. As a consequence of baryon number conservation, which favoursthe production of leading baryons, one expects a smaller average number of π mesonsin proton showers, compared to pion showers. In the latter case, the leading particle maybe a π , due to the charge exchange reaction: π + n → π + p . This reaction is favouredby the large number of neutrons in tungsten, i.e. about 50% more neutrons than protons.A smaller number of π implies a smaller electromagnetic fraction in the shower. For anon-compensating calorimeter ( e / h > [GeV] available E M ean [ M I P ] Protons
CALICE W-AHCAL
Linear fit: 3.67 – u=2.73 0.72 – v=25.69 2/ndf=0.5/5 c [GeV] available E a v a il ab l e ) / E a v a il ab l e - E æ r e c E Æ ( -0.050.000.05 Figure 16: Dependence of the mean visi-ble proton energy Mean on the available en-ergy. The line indicates a fit with the functionMean = u + v · E available . The fit parameters arealso indicated. In the bottom part of the fig-ure, the residuals to the fit are displayed, with (cid:104) E rec (cid:105) [ GeV ] = (
Mean [ MIP ] − u ) / v . The greyband shows the overall uncertainty.
Energy sum [MIP]
200 400 600 . M I P ) (cid:215) en t r i e s (cid:229) E n t r i e s / ( = 10 GeV beam Protons, pDataQGSP_BERT_HPQGSP_BIC_HPFTFP_BERT_HP
CALICE W-AHCAL
Figure 17: The visible energy distribution ofprotons with a beam momentum of 10 GeV/c:comparison of data with selected GEANT4physics lists.The selection cuts for protons are the same as for pions, apart from the Cherenkov-based par-ticle identification. Only data with beam momenta from 4 to 10 GeV/c are included for the protonanalysis. For this momentum range, electrons and pions are rejected with high efficiency based onthe signals from the Cherenkov threshold counters [14], resulting in samples with negligible e + and π + contamination (less than 1%). The remaining muons were rejected as described in section 7.1.The procedure to measure the energy and resolution for protons is the same as for pions.The average calorimeter response for protons is shown as a function of the available beamenergy in figure 16. The residuals to a linear fit are shown in the bottom part of the same figure.The proton response is linear within the experimental uncertainties. The proton visible energydistribution is compared with the expectation from selected GEANT4 physics lists in figure 17 forthe 10 GeV/c case. The level of agreement between data and the simulation models is very good.The proton mean visible energy as a function of the available energy is compared for dataand the selected GEANT4 physics lists in figure 18 (left). As in the pion case, the best descrip-tion is given by the QGSP_BERT_HP physics list, the differences being less than 2%. For pro-tons, QGSP_BIC_HP also performs well, although the agreement becomes worse with increasingavailable energy. The RMS of the energy distribution is displayed as a function of the availableenergy in figure 18 (right). Several steps are observed in the ratio between simulation and the– 18 – [GeV] available E M ean [ M I P ] ProtonsDataQGSP_BERT_HPQGSP_BIC_HPFTFP_BERT_HP
CALICE W-AHCAL [GeV] available E S i m u l a t i on / D a t a [GeV] available E R M S [ M I P ] ProtonsDataQGSP_BERT_HPQGSP_BIC_HPFTFP_BERT_HP
CALICE W-AHCAL [GeV] available E S i m u l a t i on / D a t a Figure 18: Left: Dependence of the mean visible proton energy (cid:104) E vis (cid:105) on the available energy.Right: Dependence of the RMS of the proton energy distributions on the available energy. Theerror bands show the overall uncertainty. Data are compared with selected GEANT4 physics lists.In the bottom part of the figures the ratios between the different simulation models and the data areshown.data, corresponding to the transition from one simulation model to another. For example in theFTFP_BERT_HP physics list, the transition from the Bertini cascade to the FTFP model is be-tween 4 and 5 GeV. However, in all cases the deviations between simulation and data are smallerthan 10%.The proton energy resolution, obtained using equation 7.1, is presented in figure 19. The pa-rameters of the fit with the function given by equation 6.4 are also displayed. The noise term is fixedto the same value of 70 MeV as for the π + data. The stochastic term of ( . ± . ) %/ (cid:112) E [ GeV ] is comparable with the value obtained in the π + case, ( . ± . ) %/ (cid:112) E [ GeV ] . The main differ-ence is the constant term, which is higher: ( . ± . ) % for protons, compared to ( . ± . ) %for pions. This is compatible with expectations from simulations. QGSP_BERT_HP predicts astochastic term of about 62%, and a constant term of about 11%. For a better constraint on theconstant terms, it would be necessary to also include higher energy data in the fit.The dependence of the mean energy weighted layer number on the available energy is pre-sented in figure 20, together with the ratios of selected GEANT4 physics lists to the data. TheBertini-based models (QGSP_BERT_HP and FTFP_BERT_HP) show the best agreement withdata, the deviations being less than 3%. QGSP_BIC_HP, on the other side, predicts higher valuesthan observed, i.e. the showers start to develop later in the calorimeter, and the differences are in-creasing with the available energy. This behaviour can also be observed in the longitudinal showerprofiles for protons with beam momenta of 4 and 10 GeV/c presented in figure 21. The Bertini-based models give very similar results in both cases, and are close to data. The QGSP_BIC_HP– 19 – [GeV] available E R M S / M ean Fit: 3.1)% – a=(62.7 2.7)% – b=(11.6 c=70 MeV2/ndf=0.4/5 c Protons
CALICE W-AHCAL
Figure 19: Proton energy resolution defined asRMS/Mean, as a function of the available en-ergy. The grey band shows the overall uncer-tainty. The fit parameters are also indicated. [GeV] available E æ w l N Æ ProtonsDataQGSP_BERT_HPQGSP_BIC_HPFTFP_BERT_HP
CALICE W-AHCAL [GeV] available E S i m u l a t i on / D a t a Figure 20: Dependence of the mean energyweighted layer number for proton initiatedshowers vs. the available energy: comparisonof data with selected GEANT4 physics lists.One layer corresponds to 0.13 λ I . In the bottompart of the figure the ratio between the simula-tion and the data is shown.model predicts a reduced response in the first calorimeter part, and a somewhat later shower maxi-mum than observed in data.The radial shower profiles for protons with beam momentum of 4 and of 10 GeV/c are shownin figure 22. All selected physics lists are in agreement with the data in the 4 GeV/c case. For10 GeV/c, the best prediction is given by FTFP_BERT_HP, the deviations being less than 5%.However, all physics lists show in this case a dependence on the shower radius.
8. Comparison of the calorimeter response for different particle types
The calorimeter response to π + , protons and positrons is compared in figure 23 for data (left) andfor simulation (right). The upper part of the figures shows the reconstructed energy as a functionof the available energy. The filled line indicates a fit of the π + experimental data with the functionMean = u + v · E available , the fit parameters being given in table 4. The corresponding fit parametersfor protons and positrons are shown in figure 16 and in table 1. The values for pions and protonsare compatible, whereas the e + data show a slightly steeper slope. This behaviour is also predictedby the simulation. The bottom part of the figures shows the residuals from the linear fit of the– 20 –
10 15 20 25 30 E ne r g y pe r l a y e r [ M I P ] CALICE W-AHCAL = 4 GeV beam
Protons, pDataQGSP_BERT_HPQGSP_BIC_HPFTFP_BERT_HP
Layer number S i m u l a t i on / D a t a E ne r g y pe r l a y e r [ M I P ] CALICE W-AHCAL = 10 GeV beam
Protons, pDataQGSP_BERT_HPQGSP_BIC_HPFTFP_BERT_HP
Layer number S i m u l a t i on / D a t a Figure 21: Longitudinal shower profile for a proton with a beam momentum of 4 GeV/c (left) andof 10 GeV/c (right). Data are compared with selected GEANT4 physics lists. In the bottom partof the figures the ratios between the simulations and the data are displayed. The bands show theoverall uncertainties.
Radius [mm] ] E ne r g y den s i t y [ M I P / c m -3 -2 -1 CALICE W-AHCAL = 4 GeV beam
Protons, pDataQGSP_BERT_HPQGSP_BIC_HPFTFP_BERT_HP
Radius [mm] S i m u l a t i on / D a t a Radius [mm] ] E ne r g y den s i t y [ M I P / c m -3 -2 -1 CALICE W-AHCAL = 10 GeV beam
Protons, pDataQGSP_BERT_HPQGSP_BIC_HPFTFP_BERT_HP
Radius [mm] S i m u l a t i on / D a t a Figure 22: Radial shower profiles for a proton with a beam momentum of 4 GeV/c (left) and of10 GeV/c (right). Data are compared with selected GEANT4 physics lists. In the bottom part ofthe figures the ratios between the simulation and the data are shown.– 21 – M ean [ M I P ] + p protons + e CALICE W-AHCALData [GeV] available E a v a il ab l e E a v a il ab l e - E æ r e c E Æ -0.2-0.10.00.1 M ean [ M I P ] + p protons + e CALICE W-AHCALQGSP_BERT_HP [GeV] available E a v a il ab l e E a v a il ab l e - E æ r e c E Æ -0.2-0.10.00.1 Figure 23: Dependence of the mean visible energy (cid:104) E vis (cid:105) on the available energy for e + , π + andprotons, for data (left) and for QGSP_BERT_HP (right). In the e + case, the mean energy is obtainedfrom a fit, while for hadrons it is given by the statistical mean of the corresponding distribution.The filled line indicates a fit of the π + experimental data with the function Mean = u + v · E available .The dotted line indicates the extrapolation of the line to zero. The bottom part of the figures showsthe residuals from this fit, where (cid:104) E rec (cid:105) [ GeV ] = (
Mean [ MIP ] − u ) / v . The bands show the overalluncertainties.Table 4: Fit parameters of the dependence of the mean π + visible energy on the available energy.Parameter Value u [MIP] 3 . ± . v [MIP/GeV] 25 . ± . χ /ndf 0.9/6experimental π + data. The CALICE W-AHCAL response to positrons, pions and protons is verysimilar from 3 GeV onwards, the differences being smaller than ±
9. Summary
We presented a study of low momentum ( p beam ≤
10 GeV/c) e ± , π ± and proton-initiated showersin the CALICE tungsten-scintillator analog hadron calorimeter prototype. The analysis includesmeasurements of the energy resolution for the different particle types and studies of the showerdevelopment in the longitudinal and in the transverse plane. The energy resolution for hadronshas a stochastic term of approximately 62%/ (cid:112) E [ GeV ] and a constant term of the order of 7% to– 22 –1%. The modelling of the detector configuration and response is verified with electrons and showsexcellent agreement with the data.The hadron results are compared with the following GEANT π + , positrons and protons. Acknowledgments
We gratefully acknowledge the CERN technical staff: E. Richards, I. Krasin, D. Piedigrossi,D. Fraissard and R. Loos for the help in the W-AHCAL test beam. We also gratefully acknowledgethe DESY and CERN managements for their support and hospitality, and their accelerator staff forthe reliable and efficient beam operation. The authors would like to thank the RIMST (Zelenograd)group for their help and sensors manufacturing. This work was supported by the European Com-mission under the FP7 Research Infrastructures project AIDA, grant agreement no. 262025; by theBundesministerium für Bildung und Forschung, Germany; by the the DFG cluster of excellence‘Origin and Structure of the Universe’ of Germany; by the Helmholtz-Nachwuchsgruppen grantVH-NG-206; by the BMBF, grant no. 05HS6VHS1; by the Russian Ministry of Education andScience contracts 8174, 8411, 1366.2012.2, and 14.A12.31.0006; by MICINN and CPAN, Spain;by CRI(MST) of MOST/KOSEF in Korea; by the US Department of Energy and the US NationalScience Foundation; by the Ministry of Education, Youth and Sports of the Czech Republic un-der the projects AV0 Z3407391, AV0 Z10100502, LC527 and LA09042 and by the Grant Agencyof the Czech Republic under the project 202/05/0653; by the National Sciences and EngineeringResearch Council of Canada; and by the Science and Technology Facilities Council, UK.
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