Study of energy response and resolution of the ATLAS Tile Calorimeter to hadrons of energies from 16 to 30 GeV
Jalal Abdallah, Stylianos Angelidakis, Giorgi Arabidze, Nikolay Atanov, Johannes Bernhard, Romeo Bonnefoy, Jonathan Bossio, Ryan Bouabid, Fernando Carrio, Tomas Davidek, Michal Dubovsky, Luca Fiorini, Francisco Brandan Garcia Aparisi, Tancredi Carli, Alexander Gerbershagen, Hazal Goksu, Haleh Hadavand, Siarhei Harkusha, Dingane Hlaluku, Michael James Hibbard, Kevin Hildebrand, Juansher Jejelava, Andrey Kamenshchikov, Stergios Kazakos, Tomas Kello, Ilya Korolkov, Yuri Kulchitsky, Hadar Lazar, Nthabiseng Lekalakala, Jared Little, Romain Madar, Samuel Manen, Filipe Martins, Thabo Masuku, Irakli Minashvili, Tigran Mkrtchyan, Michaela Mlynarikova, Seyedali Moayedi, Stanislav Nemecek, Lawrence Nodulman, Robert Oganezov, Mats Joakim Robert Olsson, Mark Oreglia, Priscilla Pani, Alexander Paramonov, Ruth Pottgen, Tres Reid, Sergi Rodriguez Bosca, Andrea Rodriguez Perez, Rachel Christine Rosten, Puja Saha, Claudio Santoni, Laura Sargsyan, Douglas Michael Schaefer, Nikolay Shalanda, Andrew Caldon Smith, Alexander Solodkov, Oleg Solovyanov, Pavel Starovoitov, Evgeny Starchenko, Petr Tas, Viacheslav Tereshchenko, Sijiye Humphry Tlou, Michael Ughetto, Lea Uhliarova, Giulio Usai, Eduardo Valdes Santurio, Alberto Valero Biot, Guido Volpi, Tamar Zakareishvili, Pedro Diego Zuccarello
EEur. Phys. J. C manuscript No. (will be inserted by the editor)
Study of energy response and resolution of the ATLAS TileCalorimeter to hadrons of energies from 16 to 30 GeV
Jalal Abdallah , Stylianos Angelidakis , Giorgi Arabidze , NikolayAtanov , Johannes Bernhard , Rom´eo Bonnefoy , Jonathan Bossio , RyanBouabid , Fernando Carrio , Tomas Davidek , Michal Dubovsky , LucaFiorini , Francisco Brandan Garcia Aparisi , Tancredi Carli , AlexanderGerbershagen , Hazal Goksu , Haleh Hadavand , Siarhei Harkusha ,Dingane Hlaluku , Michael James Hibbard , Kevin Hildebrand ,Juansher Jejelava , Andrey Kamenshchikov , Stergios Kazakos , TomasKello , Ilya Korolkov , Yuri Kulchitsky , Hadar Lazar , NthabisengLekalakala , Jared Little , Romain Madar , Samuel Manen , FilipeMartins , Thabo Masuku , Irakli Minashvili , Tigran Mkrtchyan a,18 ,Michaela Mlynarikova , Seyedali Moayedi , Stanislav Nemecek ,Lawrence Nodulman , Robert Oganezov , Mats Joakim Robert Olsson ,Mark Oreglia , Priscilla Pani , Alexander Paramonov , Ruth Pottgen ,Tres Reid , Sergi Rodriguez Bosca , Andrea Rodriguez Perez , RachelChristine Rosten , Puja Saha , Claudio Santoni b,6 , Laura Sargsyan ,Douglas Michael Schaefer , Nikolay Shalanda , Andrew Caldon Smith ,Alexander Solodkov , Oleg Solovyanov , Pavel Starovoitov , EvgenyStarchenko , Petr Tas , Viacheslav Tereshchenko , Sijiye HumphryTlou , Michael Ughetto , Lea Uhliarova , Giulio Usai , Eduardo ValdesSanturio , Alberto Valero Biot , Guido Volpi , Tamar Zakareishvili ,Pedro Diego Zuccarello Department of Physics, University of Texas at Arlington, Arlington TX Physics Department, National and Kapodistrian University of Athens, Athens Department of Physics and Astronomy, Michigan State University, East Lansing MI Joint Institute for Nuclear Research, Dubna CERN, Geneva LPC, Universit´e Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand Department of Physics, McGill University, Montreal QC Enrico Fermi Institute, University of Chicago, Chicago IL Instituto de F´ısica Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Valencia Charles University, Faculty of Mathematics and Physics, Prague Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk School of Physics, University of the Witwatersrand, Johannesburg E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino Institut de F´ısica d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona Laborat´orio de Instrumenta¸c˜ao e F´ısica Experimental de Part´ıculas - LIP, Lisboa Kirchhoff-Institut f¨ur Physik, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg Department of Physics, Northern Illinois University, DeKalb IL Institute of Physics of the Czech Academy of Sciences, Prague High Energy Physics Division, Argonne National Laboratory, Argonne IL Alikhanyan National Science Laboratory, Yerevan Department of Physics and Astronomy, University of California Irvine, Irvine CA Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen Fysiska institutionen, Lunds universitet, Lund Ohio State University, Columbus OH Nevis Laboratory, Columbia University, Irvington NY Oskar Klein Centre, Stockholm High Energy Physics Institute, Tbilisi State University, TbilisiReceived: date / Accepted: date a r X i v : . [ phy s i c s . i n s - d e t ] F e b Abstract
Three spare modules of the ATLAS Tile Calorimeterwere exposed to test beams from the Super ProtonSynchrotron accelerator at CERN in 2017. The mea-surements of the energy response and resolution of thedetector to positive pions and kaons and protons withenergy in the range 16 to 30 GeV are reported. The re-sults have uncertainties of few percent. They were com-pared to the predictions of the Geant4-based simulationprogram used in ATLAS to estimate the response of thedetector to proton-proton events at Large Hadron Col-lider. The determinations obtained using experimentaland simulated data agree within the uncertainties.
Three spare modules of the Tile Calorimeter (TileCal)of the ATLAS experiment [1], two long-barrels and oneextended-barrel, were exposed to muons, electrons, pi-ons, kaons and protons with different energies and in-cident angles at test beams (TBs) in 2017 [2]. The roleof the hadron calorimetry in ATLAS is to measure theenergy and the angle of isolated hadrons and jets. Toachieve good performance, the study of the sub-detectorresponse to isolated hadrons is important. In this pa-per, the measurements of the calorimeter response andresolution to positive pions and kaons and protons, withenergies in the range 16-30 GeV are presented. Theresults are compared with the ones obtained analyz-ing simulated data produced using the ATLAS Geant4toolkit [3], [4] and [5]. The experimental setup includingthe beam line counters and the detector is described inSection 2. The data sets, the event selections and thereconstruction of the particle energies in the case ofexperimental and simulated data are presented in Sec-tions 3 and 4, respectively. The determinations of thecalorimeter responses and resolutions are discussed inSection 5. The results are compared with hadronic cas-cade model predictions in Section 6. The conclusionsare stated in Section 7. a Corresponding author e-mail: [email protected] b Corresponding author e-mail: [email protected]
ScanningTable
Ch3
Secondary Target 93m 38m 18.43m S1S2
Not drawn to scale Experimental area
BC1
Ch2 Ch1
Fig. 1: Schematic layout of the H8 beam line detectors.The distances of the beam line components and of theSecondary Target from the Scanning Table (on whichwas placed the TB calorimeter) setup are shown.Proton Synchrotron (SPS) accelerator, on a 100 mmthick T4 target made of beryllium (primary target). Us-ing Secondary Targets located at about 130 m down-stream of the T4 target, tertiary beams can be pro-duced. A large spectrometer constructed of four MainBend North Area dipole magnets is used for the mo-mentum definition. Beam particles can have energiesfrom 10 to 350 GeV. Beam intensity decreases dramat-ically at the low energies. To have mixed hadron en-riched tertiary beams, the Secondary Target is made ofcopper and has a thickness of 300 mm. Additionally, alead absorber (6 mm) is moved into the beam about270 m downstream of the target. It absorbs the elec-trons, while the hadrons mostly pass through it. Forelectron enriched tertiary beams, the Secondary Targetis made by aluminum and has a thickness of 400 mm.It is immediately followed by 6 mm of lead. The leadabsorber further downstream is moved out of the beamtrajectory.The layout of the beam line detectors is shown inFigure 1. The transverse beam profile was monitoredby the wire chamber BC1 [6]. Two scintillating coun-ters, S1 and S2 with an active surface of 5 × [7],were used in coincidence to trigger the data acquisi-tion (Physics Trigger) and to provide the trigger timing.These two detectors were also used to reject beam parti-cles interacting upstream of the detector. The Cherenkovcounters Ch1, Ch2 and Ch3 allowed identification ofbeam particles. The counters Ch1 and Ch3 distinguishelectrons and pions from kaons and protons. They werefilled with CO and He, respectively. The pressure val-ues set for the different beam energies are reported inTable 1. The Cherenkov counter Ch2 was also filled withCO . The higher pressure in Ch2 allows for separationof kaons from protons. More details can be found inRef. [7].2.2 The detectorThe TB setup, shown in Figure 2, consists of three spareATLAS modules [1] of TileCal, two long-barrels and Table 1: Cherenkov radiator materials and correspond-ing gas pressure values set for the different beam ener-gies.
Cherenkov Counter Ch1 Ch2 Ch3Radiator Material CO CO He E beam [GeV] Pressure [bar]16 0.19 0.75 2.618 0.19 0.75 2.620 0.19 0.75 2.630 0.3 2.0 2.6 zy x 𝜽 = 76° EBC65LBC65M0 CM0 ALBA65 . m Fig. 2: Schematic view of the TileCal modules asstacked on the scanning table at the H8 beam line. Thenames of the super-drawers and the direction and theinteraction point of the particle beams in the detectorare shown.one extended-barrel, stacked on a scanning table (seeFigure 1) that is capable of placing modules at differ-ent position and angle with respect to the incomingbeam particles. An extended-barrel (long-barrel) con-sists of one (two) super-drawer(s). In the figure they arenamed M0A and M0C (module at the bottom), LBA65 and LBC 65 (module in the middle) and EBC 65(module at the top). Some of the super-drawers wereequipped with different upgraded front-end electronicssystems proposed for the ATLAS LHC Phase-II oper-ations [8]. The super-drawers EBC 65 and M0 C wereequipped with the electronics installed currently in AT-LAS [1]. As shown in Figure 3, the modules have aperiodic structure of steel plates and scintillating tilesperpendicular to the z axis. Wavelength-shifting fibrestransmit light produced in the tiles to the PMs [9]. Ineach module a three-dimensional cell structure is de-fined by grouping optical fibres connected to the samePM [10]. In general two PMs read-out a cell and thesignals are summed up to provide the cell response. Astructure of three cell layers parallel to the z axis isobtained. The cell layers A, BC and D in half long- Fig. 3: Mechanical structure of a TileCal module, show-ing the slots in the steel for scintillating tiles and themethod of light collection by wavelength-shifting fibresto PMs. The holes for radioactive source tubes that tra-verse the module perpendicularly to the iron plates andscintillating tiles are also shown.barrel and A, B and D in extended barrel are shown inFigure 4.As in the ATLAS detector at LHC, the energy de-posited in a cell of the TB detector, E rawc , was deter-mined making use of the Optimal Fit method [11]. Thelinearity of the ADC’s is determined using the ChargeInjection System (CIS) [12]. The inter-calibration of thedifferent calorimeter cells was obtained by equalizingthe PM current induced by movable radioactive Cssources that cross every row of scintillating tiles nearthe edges (see Figure 3). Since the scintillating tile re-sponse depends on the impact point position of the par-ticle in the tile and on the tile size, correction factorswere applied for each layer of the calorimeter. Thosevalues were determined from 1990’s Test Beam data,which measured the response to muons impinging onthe calorimeter with a direction parallel to the z axis(see Figure 2), and from the measurements obtainedusing a Sr source [12]. The scale of the reconstructedcell energy, C EMc = 1.05 pC ⁄ GeV, was obtained usingelectron beams incident at the centre of each cell withan angle of 20 ◦ with respect to the cell surface normal.The estimated uncertainty is ∆C EMc = 2.4% [12]. Theanalysis of the muon and electron test beam data col-lected in the 2017 Test Beam [8] produced performanceresults that agree with the ones obtained using previousTBs [12] and with in-situ measurements in ATLAS [13].To be consistent, the Optimal Fit method [11] wasapplied also to reconstruct the energy deposited in thecells in the case of simulated events. The scale of the cellenergy measurements was obtained using the responseto simulated electrons
The energy deposited by the beam particles incidentthe detector, E raw , was determined as the sum of theenergy measured in the calorimeter cells.
500 1000 1500 mm0 A3 A4 A5 A6 A7 A8 A9 A10A1 A2BC1 BC2 BC3 BC5 BC6 BC7 BC8BC4D0 D1 D2 D3 A13 A14 A15 A16B9 B12 B14 B15D5 D6D4C10
B11 B13A12E4E3E2E1 beam axis =0,0 η ~~ z Fig. 4: Cell structure in half long-barrel (a) andextended-barrel (b) modules of the calorimeter. Solidlines show the cell boundaries formed by grouping opti-cal fibers from the tiles for read out by separate photo-multipliers. Also shown are dashed lines of fixed pseudo-rapidity η [1]. The results discussed in this paper were obtained ex-posing the TB calorimeter setup to enriched tertiarypositive hadron beams with energy, E beam , equal to 16,18, 20 and 30 GeV. As shown in Figure 2, the beamshit at the middle of the cell A3 of the super-drawerLBC65 with an azimuth angle φ = 0 and polar angle θ of about 76 ° , corresponding to a pseudo-rapidity val-ues η = 0.25 [1]. (see Figure 4). The angle from thecalorimeter module normal is equal to 14 degrees. Thenumbers of events collected during the data taking pe-riod are reported in Table 2 (Physics Trigger).3.1 Collimated single-particle eventsCollimated single-particle events were first selected us-ing beam detectors upstream of the TB calorimetersetup. The selection criteria on the beam line scintil-lating counters signals, E S1 and E S2 , were establishedmaking use of the responses of S1 and S2 to muons.Muon events were recognized by requiring an energydeposited in the module LBC65 compatible with theone deposited by a minimum ionizing particle. The re-tained events satisfy the criteria: E S1 < × E m.p.S1 ( µ ) (1)and E S2 < × E m.p.S2 ( µ ) (2) where the quantities E m.p.S1 ( µ ) and E m.p.S2 ( µ ) are themost probable (m. p.) values of the S1 and S2 muonsignal distributions respectively. The selection criteria,especially useful for electron studies, remove particlesthat initiated a shower upstream of the calorimeter,as well as multi-particle beam events. The number ofevents retained after the application of the criterion arereported in Table 2 (Selection 1.). Events with a beamTable 2: Numbers of experimental data events collectedand retained in the analysis selection steps for each ofthe four beam energies. The number of events identi-fied as electrons, pions, kaons and protons is reported.Selection criteria and determination of statistical un-certainties on the number of electrons and pions arediscussed in the text. E beam [GeV] 16 18Physics Trigger 694658 944460Selection 1. 656262 895863Selection 2. 552179 771513Selection 3. 501013 700590 e/π K/p ± ± ∓ ∓ E beam [GeV] 20 30Physics Trigger 1226756 1297099Selection 1. 1155580 1230470Selection 2. 935131 1069709Selection 3. 777386 983892 e/π K/p ± ± ∓ ∓ trajectory far away from the beam axis were rejectedbecause the beam particles might have scattered up-stream and therefore be off-energy. The beam chamberBC1 allows a determination of the transverse beam im-pact point coordinates, x BC1 and y BC1 . Gaussian func-tions were fitted to the distributions of each data set todetermine the peak values x peakBC1 and y peakBC1 respectively.The accepted events have the beam impact point coor-dinates inside the square surface of the trigger scintil-lating counters: | x BC1 − x peakBC1 | < . | y BC1 − y peakBC1 | < . . (4) The numbers of events retained after the application ofthis criterion are reported in Table 2 (Selection 2.).3.2 Identification of muons and electrons
The second set of criteria allows identifying pure sam-ples of hadrons. As already mentioned, at the consid-ered beam energies, muons are minimum ionizing par-ticles and deposit in the scintillating tiles energy muchsmaller than electrons and hadrons (see Figure 5). Themuon rejection was obtained requiring a reconstructedenergy in the detector (see Section 2.2) E raw (cid:105) E raw µ cut = 5 GeV. The selection criterion allows also a rejec-tion of spurious trigger events. The retained events arereported in Table 2 (Selection 3.). raw E ´ E v en t s
16 GeV hadrons 𝐸 𝝁 (a) raw E ´ E v en t s
18 GeV hadrons 𝐸 𝝁 (b) Fig. 5: Distributions of the energy E raw in GeV mea-sured in the calorimeter modules in the case of particlebeam energies equal to 16 GeV (a) and 18 GeV (b).The events were selected applying the selection criteriaup to Selection 2. (see Table 2). The muons and spuri-ous events were rejected in the analysis requiring E raw larger than E raw µ cut = 5 GeV, as shown in the histograms. As shown in Figure 6, the signals measured in Cherenkovcounters Ch1 and Ch3, S Ch1 and S Ch3 , respectively, al-low a separation of pions and electrons ( e/π ) from kaons K and protons p ( K/p ). The selection criteria in ADCcounts applied on the signals are reported in Table 3.The numbers of the identified events are reported inTable 2. As discussed in Section 3.3, the Ch2 measure-ments allow separating kaons and protons.The electron components in e/π samples were deter-mined statistically exploiting the difference of electro-magnetic and hadronic shower profiles in the calorime-ter modules [12]. Two separators, C long and C tot , wereused: Table 3: Selection criteria in S Ch1 , S Ch2 and S Ch3 sig-nals applied to identify e/π , K and p event samples forthe four particle beam energy data sets. The Cherenkovsignals are measured in ADC counts E beam e/π K p [GeV]16 S Ch1 ≥ S Ch1 < S Ch1 < S Ch3 ≥ S Ch3 ≤ S Ch3 ≤ S Ch2 ≥ S Ch3 ≤ S Ch1 ≥ S Ch1 ≤ S Ch1 ≤ S Ch3 ≥ S Ch3 ≤ S Ch3 ≤ S Ch2 ≥ S Ch3 ≤ S Ch1 ≥ S Ch1 ≤ S Ch1 ≤ S Ch3 ≥ S Ch3 ≤ S Ch3 ≤ S Ch2 ≥ S Ch3 ≤ S Ch1 ≥ S Ch1 ≤ S Ch1 ≤ S Ch3 ≥ S Ch3 < S Ch3 < S Ch2 ≥ S Ch3 ≤ Ch1 S [ A DC c oun t s ] C h3 S
18 GeV Hadrons
K/p e/ 𝜋 (a) Ch1 S [ A DC c oun t s ] C h3 S
30 GeV Hadrons
K/p e/ 𝜋 (b) Fig. 6: Scatter plots of the signals measured in theCherenkov counter Ch3, S Ch3 , as a function of the sig-nals measured in the Cherenkov counter Ch1, S Ch1 , inADC counts. The histograms were obtained analysingdata with beam energies equal to 18 GeV (a) and30 GeV (b). The events were selected applying selec-tion criteria summarized in Table 2, up to Selection 3.The cut values used to select kaon and proton,
K/p ,(left/bottom) and electron and pion, e/π , (right/top)events are shown. Colors are used in the plots to showthe cell contents.1. The shower profile parameter C long represents thefraction of the beam energy, E beam , deposited in thelayers A of the modules (see Figure 4) : C long = (cid:80) i =1 (cid:80) j =1 ( E rawc ) i,j E beam (5)where i = 1, 2 and 3 indicate the super-drawers M0C, LBC65 and EBC65 respectively. The parameter j runs over 3 contiguous cells of the three layers Aaround the cell hit by the beam and E rawc stands forthe energy measured in a cell (see Section 2.2). tot C l ong C
18 GeV hadrons (a) tot C l ong C
30 GeV hadrons (b)
Fig. 7: Scatter plot C long vs C tot of e/π sample eventsproduced by beams of particles with energies equal to18 GeV (a) and 30 GeV (b). Colors are used in the plotsto show the cell contents.2. The separator C tot measures the spread of the en-ergy E rawc deposited in the cells of the modules: C tot = 1 (cid:80) N cell i =1 [( E rawc ) i ] α × (cid:118)(cid:117)(cid:117)(cid:116) N cell N cell (cid:88) i =1 (cid:16) [( E rawc ) i ] α − N cell N cell (cid:88) i =1 [( E rawc ) i ] α (cid:17) (6)where N cell = 24 stands for the total number of con-tiguous cells, around the hit cell, considered for theshower profile estimate and the exponent α = 0.6was tuned using a Monte Carlo (MC) simulationprogram to achieve maximum electron pion separa-tion [12].Scatter plots, C long vs C tot , of e/π sample events ob-tained using beams of particles with E beam equal to 18and 30 GeV are shown in Figure 7. They can be com-pared with the ones in Figure 8 obtained using simu-lated electrons and pions events with the same beamenergies. In general the pions have small values of C long and C tot , while in the case of electrons, the parame-ters have larger values localized in narrower regions.Pion events with large C long and C tot values are due toshowers with large electromagnetic component.The analysis is based on the fact that electron (pion)C tot distributions are well described by one (two) Gaus-sian function. As an example, Figure 9 (a) shows theexperimental C tot distribution obtained using an en-riched electron beam with E beam = 20 GeV andC long ≥ C minlong = 0 .
6. The fit was performed in the re-gion C tot ≥ tot distributionsat 18 and 30 GeV are well described by one Gaussianfunction. Pion C tot distributions are best described bytwo Gaussian functions. The distributions of e/π dataevents with C long < C minlong = 0.6 and E beam equal to 18 tot C l ong C
18 GeV electrons (a) tot C l ong C
18 GeV pions (b) tot C l ong C
30 GeV electrons (c) tot C l ong C
30 GeV pions (d)
Fig. 8: Scatter plot C long vs C tot obtained using simu-lated 18 GeV electrons (a), 18 GeV pions (b), 30 GeVelectrons (c) and 30 GeV pions (d) beam. The colorbands represent the number of events in the bins. tot C E v en t s
20 GeV electronsExperimental dataFit to experimental data (a) tot C E v en t s
18 GeV electronsSimulated dataFit to simulated data (b) tot C E v en t s
30 GeV electronsSimulated dataFit to simulated data (c)
Fig. 9: Distributions of C tot obtained using experimen-tal electron-enriched beams of particles with an en-ergy equal to 20 GeV (a), and simulated electrons with E beam equal to 18 GeV (b) and 30 GeV (c). Fit Gaus-sian functions obtained using the method of the leastsquares are superimposed in red on the distributions.and 30 GeV, respectively, are shown in Figure 10. TwoGaussian contributions fit is shown. Individual Gaus-sian contributions are also presented. In Figure 11 C tot distributions of simulated pions with E beam equal to 18GeV (a) and 30 GeV (b) are shown. They are also well described by the sum of two Gaussian functions. The tot C E v en t s p
18 GeV e/Experimental dataTwo gaussian fitSingle gaussian contributions to the fit (a) tot C E v en t s p
30 GeV e/Experimental dataTwo gaussian fitSingle gaussian contributions to the fit (b) tot C E v en t s
18 GeV pionsSimulated dataTwo gaussian fitSingle gaussian contributions to the fit (c) tot C E v en t s
30 GeV pionsSimulated dataTwo gaussian fitSingle gaussian contributions to the fit (d)
Fig. 10: The blue histograms in (a) and (b) show C tot distributions of experimental e/π sample events withE beam equal to 18 GeV and 30 GeV, respectively. Sam-ples of pion events were selected requiring C long < beam equal to 18GeV and 30 GeV, respectively. Two Gaussian functionsfits, obtained using the method of the least squares, areoverlapped to the data (red dashed curves). Red dottedcurves show the individual Gaussian contributions.number of electrons in the four e/π samples were deter-mined considering C tot distributions of the events withC long ≥ C minlong = 0 .
6. Examples of such distributions ob-tained in the case of events produced by beams of parti-cle with energies equal to 18 GeV and 30 GeV are shownin Figure 12. Three Gaussian functions were fitted tothe experimental distributions using the method maxi-mum likelihood. The fit functions are superimposed onthe histograms in Figures 12 (a) and 12 (c). The indi-vidual Gaussian function contributions are also shown.The functions with the largest mean values µ describethe electron contributions. The numbers of the electronsreported in Table 2 are determined from the areas lim-ited by such functions. The statistical uncertainties areequal to the corresponding diagonal terms of the fit er-ror matrices. tot C E v en t s
18 GeV pionsSimulated dataTwo gaussian fitSingle gaussian contributions to the fit (a) tot C E v en t s
30 GeV pionsSimulated dataTwo gaussian fitSingle gaussian contributions to the fit (b)
Fig. 11: The black histograms show C tot distributionsobtained using simulated pions with E beam equal to 18GeV (a) and 30 GeV (b). The events were selected re-quiring C long < beam data set the number of pions reported in Table 2 wasestimated by subtracting the number of electron eventsobtained using the method described in Section 3.2.2from the number of events of the corresponding e/π sample. The Ch2 signal measurements allow a sepa-ration of kaons and protons in the K/p samples. Thescatter plots of the Ch2 signals, S Ch2 , in ADC countsunits vs the energy measured in the calorimeter, E raw ,obtained by analyzing data produced by beams of par-ticles with energies equal to 18 and 30 GeV, are shownin Figure 13. The S Ch2 selection values in ADC countunits are reported in Table 3. The obtained numbers ofkaons and protons are reported in Table 2.3.4 Reconstruction of the energy deposited in themodulesAs already discussed in Section 2.2, the energy E raw deposited by incident particles in the detector was ob-tained as the sum of the energy measured in the calorime-ter cells. In this study only cells with | E rawc | > σ noise were considered in the sum. For each run, the cell elec-tronics noise σ noise was determined using random eventscollected between beam bursts (Pedestal Triggers). Typ-ical noise values are of the order of 30 MeV.No corrections for dead material, containment and non-compensation effects were applied.Due to the electron contamination, as sketched inthe Figure 14, the pion energy distributions n π ( E raw ) tot C E v en t s / ( . )
18 GeV hadronsExperimental dataFit to experimental dataSingle gaussian contributions to the fit (a) tot C E v en t s / ( . )
18 GeV hadronsExperimental dataFit to experimental dataSingle gaussian contributions to the fit (b) tot C E v en t s / ( . )
30 GeV hadronsExperimental dataFit to experimental dataSingle gaussian contributions to the fit (c) tot C E v en t s / ( . )
30 GeV hadronsExperimental dataFit to experimental dataSingle gaussian contributions to the fit (d)
Fig. 12: The dotted histograms (a), (b) and (c), (d)represent the C tot distributions of e/π sample eventswith E beam equal to 18 GeV and 30 GeV respectively.The events were selected requiring C long ≥ µ describes the electron contamination.were obtained using, bin per bin, the formula n π ( E raw ) = n e/π ( E raw ) − N e f e ( E raw ) . (7)where n e/π ( E raw ) is the number of e/π events in theconsidered E raw bin, the electron distribution f e ( E raw )is normalized to 1 and the number of electrons, N e ,was determined using the procedure described in Sec-tion 3.2.2. Simulated electron distributions were usedin the analysis because experimental data are avail-able only for electron beam energy equal to 20 GeV.A comparison between the distributions obtained an-alyzing simulated and experimental electrons with thesame beam energy, direction and impact point is shownin Figure 15 (a) . Figures 16 to 19 show the E raw distri-butions obtained in the case of beams of pions, kaonsand protons with energies equal to 16, 18, 20 and 30GeV, respectively.
10 15 20 25 30 35 40 45 50 [GeV] raw E [ A DC c oun t s ] C h2 S
18 GeV Hadrons Kp (a)
10 15 20 25 30 35 40 45 50 [GeV] raw E [ A DC c oun t s ] C h2 S
30 GeV Hadrons Kp (b) Fig. 13: Scatter plot of the Ch2 signals, S Ch2 , in ADCcounts units, vs the energy measured in the calorimeter, E raw obtained analyzing K/p sample events producedby beams of particles with energy equal to 18 (a) and30 (b) GeV. The cut values applied in the analysis toselect kaon and proton events are shown. Colors areused in the plots to show the cell contents.Table 4: Numbers of simulated and retained pion, kaonand proton events for each beam energy value. Selectioncriteria used in the analysis are discussed in the text. E beam [GeV] 16 18 20 30Generated events 300000Pions 283222 285211 286574 291040Kaons 247559 253040 256514 269728Protons 292412 293891 294596 296532 The experimental results obtained using positive pi-ons and kaons and protons beams, with energies in therange 16–30 GeV, were compared to the predictionsof the Geant4-based ATLAS simulation program [3],[4] and [5]. The FTFP BERT ATL hadronic showeringmodel [14] was used in the simulation. This is the modelpresently being used in the simulation of the ATLASevents collected during the LHC Run 1 and Run 2. Thenumber of generated events for each experimental datapoint is reported in Table 4. The responses of the beamline detectors were not included in the simulation. Thedistributions of the transverse beam impact point coor-dinates in the detector were tuned to reproduce the onesmeasured using the BC1. The TB detector material andgeometry were fully described (see Ref. [4]). The mea-sured electronics noise in the different calorimeter cellsand the effects of photo-statistics (70 photo electron perGeV) in the PM signals, are included in the MC simula-tion. The simulated pion events were selected applyingthe C long and C tot cuts used in the analysis of exper- raw E E v en t s
16 GeV data p / e Experimental data e Simulated (a) raw E E v en t s
18 GeV data p / e Experimental data e Simulated (b) raw E E v en t s
20 GeV data p / e Experimental data e Simulated (c) raw E E v en t s
30 GeV data p / e Experimental data e Simulated (d)
Fig. 14: Distributions of the reconstructed energy E raw of the e/π samples events with E beam equal to 16 GeV(a), 18 GeV (b) 20 GeV (c) and 30 GeV (d). The bluedotted histograms correspond to the experimental data.The black histograms correspond to the expected distri-butions of the electrons contaminating the samples ob-tained using simulated events. The normalization pro-cedure is described in the text.imental data. The numbers of the retained events foranalyses are reported in Table 4. The shower energywas reconstructed using the same procedure applied inthe case of experimental data. The distributions of E raw obtained using simulated data are shown in Figures 16to 19 for beam energies equal to 16, 18, 20 and 30 GeVrespectively. The experimental and simulated E raw distributions ofpion, kaon and proton data are described reasonablywell around the peak values by a Gaussian function. Asin Ref. [12], the µ and σ parameters of Gaussian func-tions fitting the distributions in a region ± σ aroundthe peak values were used to estimate the measurementresponses (cid:104) E raw (cid:105) and resolutions σ raw . An iterative pro-cedure has been applied in order to get stable values ofthe parameters. The method of the least squares hasbeen used. The fit functions obtained analysing experi-mental data are superimposed to the corresponding dis-tributions in Figures 16 to 19. The fit results obtainedusing experimental and simulated data are reported in
10 15 20 25 30 35 40 [GeV] raw E E v en t s
20 GeV electronsExperimental dataSimulated dataHigh energy simulated dataLow energy simulated data (a) - - - - - z [ G e V ] r a w E
20 GeV electronsSimulated dataFit to the simulated data (b)
20 25 30 35 40 45 50 [GeV] raw E E v en t s
30 GeV electronsSimulated dataHigh energy simulated dataLow energy simulated data (c) - - - - - z [ G e V ] r a w E
30 GeV electronsSimulated dataFit to the simulated data (d)
Fig. 15: The black histograms in (a) and (c) show thedistributions of the reconstructed energy E raw obtainedanalysing simulated data obtained using electron beamswith E beam equal to 20 GeV and 30 GeV respectively.The blue dot distribution in (a) has been obtained us-ing experimental data. In (a) and (c) are also shownthe distributions obtained using “high energy events”(red dashed line) and “low energy events” (red dottedline) discussed in Section 5.1. The histograms (b) and(d) show the oscillation of the electron response due tothe sampling fraction variations as obtained using sim-ulated electrons with E beam equal to 20 GeV and 30GeV respectively. The dashed curves in red correspondto the fit of Eq. 10 to the data. The horizontal black linecorresponds to the electron mean energy, p (Eq.(10)).Table 5. The statistical uncertainties correspond to thesquare root of the corresponding diagonal term of thefit error matrix.5.1 Energy responses and resolutions normalized toincident beam energyEnergy response normalized to incident beam energy R (cid:104) E raw (cid:105) = (cid:104) E raw (cid:105) E beam (8)and energy resolution normalized to incident beam en-ergy R σ raw = σ raw E beam (9) Table 5: Energy response (resolution) obtained fittingGaussian functions to the experimental and simulated E raw distributions obtained using pions ( (cid:104) E raw (cid:105) ( π ) and( σ raw ( π ))), kaons ( (cid:104) E raw (cid:105) ( K ) and ( σ raw ( K )) and pro-tons ( (cid:104) E raw (cid:105) ( p ) and ( σ raw ( p ))) with different beam en-ergy. The statistical uncertainties correspond to the fitparameter uncertainties. (cid:104) E raw (cid:105) ( π ) E beam [GeV] Exp. Data Sim. Data16 12.678 ± ± ± ± ± ± ± ± σ raw ( π ) E beam [GeV] Exp. Data Sim. Data16 2.013 ± ± ± ± ± ± ± ± (cid:104) E raw (cid:105) ( k ) E beam [GeV] Exp. Data Sim. Data16 12.291 ± ± ± ± ± ± ± ± σ raw ( K ) E beam [GeV] Exp. Data Sim. Data16 2.168 ± ± ± ± ± ± ± ± (cid:104) E raw (cid:105) ( p ) E beam [GeV] Exp. Data Sim. Data16 11.511 ± ± ± ± ± ± ± ± σ raw ( p ) E beam [GeV] Exp. Data Sim. Data16 1.795 ± ± ± ± ± ± ± ± raw E E v en t s no r m a li z ed t o
16 GeV pionsExperimental dataSimulated dataFit to the experimental data (a) raw E E v en t s N o r m a li z ed t o
16 GeV kaonsExperimental dataSimulated dataFit to the experimental data (b) raw E E v en t s no r m a li z ed t o
16 GeV protonsExperimental dataSimulated dataFit to the experimental data (c)
Fig. 16: Distributions of the reconstructed energy E raw obtained analyzing pion (a), kaon (b) and proton (c)data with E beam = 16 GeV. The blue dotted histogramsrepresent the experimental data. Only statistical un-certainties are shown. The dashed curves in red corre-spond to the fit of a Gaussian function to the exper-imental data in a region ± σ around the peak value.The black histograms correspond to the predictions ofthe MC simulation.obtained for the different values of E beam are reportedin Table 6. In the case of experimental results, the firstuncertainty value corresponds to the statistical uncer-tainty. The systematic uncertainty, second value, wasobtained combining in quadrature the contributions ofthe seven sources discussed in the following. In the caseof simulated data only statistical uncertainties are re-ported. Seven sources of systematic uncertainties wereconsidered in the study:1. Systematic Uncertainty 1. affects only pion deter-minations. It corresponds to the statistical uncer-tainty on the determination of the number of elec-trons contaminating the e/π samples discussed inSection 3.2.2.2. As discussed in the same section the electron con-tamination was determined studying the C tot distri-butions of the e/π sample events with C long ≥ C minlong = 0.6. Results obtained with different values of C long were used for uncertainty estimations. SystematicUncertainty 2. values reported in Table 7 correspondto half of the differences of the determinations of R (cid:104) E raw (cid:105) and R σ raw obtained using C minlong = 0 . minlong = 0 . Table 6: Measured energy response (resolution) nor-malized to incident beam energy obtained using pions( R (cid:104) E raw (cid:105) ( π ) and ( R σ raw ( π ))), kaons ( R (cid:104) E raw (cid:105) ( K ) and( R σ raw ( K ))) and protons ( R (cid:104) E raw (cid:105) ( p ) and ( R σ raw ( p ))) ofdifferent beam energy obtained analyzing experimen-tal and simulated data. In the case of experimentaldata, statistical and systematic uncertainties are re-ported. The effects of the different sources of systematicsources discussed in the text were combined in quadra-ture. Only statistical uncertainties are reported in thecase of simulated data. R (cid:104) E raw (cid:105) ( π ) E beam [GeV] Exp. Data Sim. Data16 0.7924 ± ± ± ± ± ± ± ± ± ± ± ± R σ raw ( π ) E beam [GeV] Exp. Data Sim. Data16 0.1258 ± ± ± ± ± ± ± ± ± ± ± ± R (cid:104) E raw (cid:105) ( K ) E beam [GeV] Exp. Data Sim. Data16 0.7682 ± ± ± ± ± ± ± ± ± ± ± ± R σ raw ( K ) E beam [GeV] Exp. Data Sim. Data16 0.1356 ± ± ± ± ± ± ± ± ± ± ± ± R (cid:104) E raw (cid:105) ( p ) E beam [GeV] Exp. Data Sim. Data16 0.7195 ± ± ± ± ± ± ± ± ± ± ± ± R σ raw ( p ) E beam [GeV] Exp. Data Sim. Data16 0.1122 ± ± ± ± ± ± ± ± ± ± ± ± raw E E v en t s no r m a li z ed t o
18 GeV pionsExperimental dataSimulated dataFit to the experimental data (a) raw E E v en t s N o r m a li z ed t o
18 GeV kaonsExperimental dataSimulated dataFit to the experimental data (b) raw E E v en t s no r m a li z ed t o
18 GeV protonsExperimental dataSimulated dataFit to the experimental data (c)
Fig. 17: Distributions of the reconstructed energy E raw obtained analyzing pion (a), kaon (b) and proton (c)data with E beam = 18 GeV. The blue dotted histogramsrepresent the experimental data. Only statistical un-certainties are shown. The dashed curves in red corre-spond to the fit of a Gaussian function to the exper-imental data in a region ± σ around the peak value.The black histograms correspond to the predictions ofthe MC simulation.3. Effects due to the missmodeling of the C tot distri-butions used to determine the number of electronscontaminating the e/π samples was estimated com-paring the results obtained using three Gaussianfunctions fits (see Section 3.2.2) with the ones ob-tained using two Gaussian functions fits. The esti-mated percentage of electrons increases from a valueof 11% at 16 GeV up to 28% at 30 GeV. SystematicUncertainty 3. values, affecting only pion determi-nations, are reported in Table 7 for each of the fourbeam energy samples. It is equal to the differencesof the values of R (cid:104) E raw (cid:105) and R σ raw obtained usingthe two fitting functions.4. As discussed in Section 3.4 the experimental E raw distributions of pions were obtained using Eq. (7).In Figure 15 are shown electron distributions ob-tained in the case of simulated data with beam en-ergies equal to 20 and 30 GeV. Due to the regu-larly spaced scintillating tiles (see Figure 3) and thecompactness of electromagnetic showers, the elec-tron response varies with the periodicity of samplingfraction and thus depends on the coordinate of theimpact point of the beam particles along the frontface of the calorimeter module ( z ). In Figures 15 (b) raw E E v en t s no r m a li z ed t o
20 GeV pionsExperimental dataSimulated dataFit to the experimental data (a) raw E E v en t s N o r m a li z ed t o
20 GeV kaonsExperimental dataSimulated dataFit to the experimental data (b) raw E E v en t s no r m a li z ed t o
20 GeV protonsExperimental dataSimulated dataFit to the experimental data (c)
Fig. 18: Distributions of the reconstructed energy E raw obtained analyzing pion (a), kaon (b) and proton (c)data with E beam = 20 GeV. The blue dotted histogramsrepresent the experimental data. Only statistical un-certainties are shown. The dashed curves in red corre-spond to the fit of a Gaussian function to the exper-imental data in a region ± σ around the peak value.The black histograms correspond to the predictions ofthe MC simulation.and (d) is shown that the variation is reasonablywell described by a simple periodic function [12] E raw ( z ) = p [1 + p sin(2 πz/p ) + p ] . (10)The parameter p corresponds to the mean recon-structed energy. The relative amplitude of the os-cillation is described by p . The parameter p cor-responds to the periodic thickness as seen by thebeam at a given z value and p is a phase. Thebehavior is responsible of the two peak structureof the E raw distributions evident, in particular, inthe case of E beam = 30 GeV simulated data in Fig-ure 15 (c). The effects of the uncertainty on the dis-tribution of the z coordinates of the electron impactpoint on the determinations of R (cid:104) E raw (cid:105) and R σ raw was estimated using the E raw distributions of theevents with a z value corresponding to E raw > p ,“high energy events”, and E raw < p , “low energyevents”, respectively. The distributions are shown inFigures 15 (a) and 15 (c). Systematic Uncertainty4. values, reported in Table 7, correspond to half ofthe differences of the values obtained using the two raw E E v en t s no r m a li z ed t o
30 GeV pionsExperimental dataSimulated dataFit to the experimental data (a) raw E E v en t s N o r m a li z ed t o
30 GeV kaonsExperimental dataSimulated dataFit to the experimental data (b) raw E E v en t s no r m a li z ed t o
30 GeV protonsExperimental dataSimulated dataFit to the experimental data (c)
Fig. 19: Distributions of the reconstructed energy E raw obtained analyzing pion (a), kaon (b) and proton (c)data with E beam = 30 GeV. The blue dotted histogramsrepresent the experimental data. Only statistical un-certainties are shown. The dashed curves in red corre-spond to the fit of a Gaussian function to the exper-imental data in a region ± σ around the peak value.The black histograms correspond to the predictions ofthe MC simulation.distributions. This uncertainty affects only pion de-terminations.5. The 30 GeV scatter plot S Ch1 vs. S Ch3 in Figure 6shows two spots in the
K/p region. Their origin isnot clear. Systematic Uncertainty 5. values reportedin Table 7 correspond to the differences of the valuesof R (cid:104) E raw (cid:105) and R σ raw obtained using the events with S Ch1 ≤
400 [ADC counts] and S Ch1 ≤
250 [ADCcounts], respectively. Although the other three en-ergy data points do not show the two spot structure,a systematic uncertainty was determined also forthem using the described procedure with the sameselection criterion values.6. As it appears in Figure 13, proton S Ch2 distributionsshow large tails. Their origin is not understood. Sys-tematic Uncertainty 6. values in Table 7, correspondto the differences of the values of R (cid:104) E raw (cid:105) and R σ raw obtained using for each of the four proton beam en-ergies, the upper values of the S Ch2 signals of Ta-ble 3, and the ones obtained selecting the eventswith S Ch2 ≤ Ch2, the effect may not be visible. For this reasonthe systematic uncertainty obtained for protons isalso applied in kaon determinations.7. The effect of the uncertainty of the scale of the re-constructed cell energy ∆C EMc on the measurementswas also investigated. An estimation of the uncer-tainty on the energy response can be obtained usingthe formula: ∆ (cid:104) E raw (cid:105) EM = ∆C EMc (cid:115)(cid:88) i (cid:104) E raw c (cid:105) i (11)where ∆C EMc is equal to 2.4% (see Section 2.2) and (cid:104) E raw c (cid:105) i is the average energy deposited in the cell i . E beam is known at few per mile and one obtainsthe values of ∆ R (cid:104) E raw (cid:105) reported in Table 7 for thetwelve data points (Systematic Uncertainty 7.). Nosignificant dependence of the values on the beamenergies was found. The uncertainty on C EMc affectsin a negligible way the determinations of R σ raw .The effects of each of the seven considered sourcesof systematic uncertainties on the four energy determi-nations are correlated. The uncertainty in the energyresponse normalized to incident beam energy is domi-nated by the systematic effects due to cell response nonuniformity (Systematic Uncertainty 7.).The systematic uncertainties in Table 6 were ob-tained by combining in quadrature the effects of theseven sources reported in Table 7. Eleven values of thetwelve energy response normalized to incident beam en-ergy determinations have a total uncertainty smallerthan 1.4%. It is mainly defined by the uncertainty inthe calibration of the energy response of the relativelysmall part of the calorimeter involved in the study. Inthe case of kaons with E beam = 16 GeV, due to thelarge statistical error, the uncertainty on the determi-nation of R (cid:104) E raw (cid:105) , is equal to 2.4%. Nine of the twelvedeterminations of the energy resolution normalized toincident beam energy, R σ raw , have a total uncertaintysmaller than 1.9%. The uncertainty values of the deter-minations of R σ raw obtained in the case of 16 GeV pionand kaon and 18 GeV kaon beams are equal to 3.1%,20.3% and 10.4% respectively.The determinations of R (cid:104) E raw (cid:105) ( R σ raw ) as a func-tion of E beam (1 ⁄ (cid:112) E beam [GeV]) are reported in thehistograms of Figure 20 (Figure 21) . In the case ofexperimental results, statistical and systematic uncer-tainties are combined in quadrature. In the case of sim-ulated results only statistical uncertainty are shown. Table 7: Systematic uncertainties on the estimations of R (cid:104) E raw (cid:105) and R σ raw in percent. The pion measurementsare affected by the uncertainty on the number of elec-trons contaminating the e/π samples (Systematic un-certainties 1., 2. and 3.), on the E raw shape of the con-taminating electrons (Systematic uncertainty 4.). Thekaon and proton measurements are affected by the un-certainty on the Ch1 (Systematic uncertainty 5.) andCh2 (Systematic uncertainty 6.) selection criteria. Theuncertainty on the determination of the cell energy re-sponse non-uniformity, Systematic uncertainty 7., af-fects the determinations obtained for the three particlebeams. E beam [GeV] 16 18Syst. Beam R (cid:104) E raw (cid:105) R σ raw R (cid:104) E raw (cid:105) R σ raw Uncer. Part. [%] [%] [%] [%]1. π π π π K p - 0.031 0.011 0.0446. K p π K p E beam [GeV] 20 30Syst. Beam R (cid:104) E raw (cid:105) R σ raw R (cid:104) E raw (cid:105) R σ raw Uncer. Part. [%] [%] [%] [%]1. π π π π K p K p π K p ∆ (cid:104) E raw (cid:105) = (cid:104) E raw (cid:105)(cid:104) E rawMC (cid:105) − r a w E R PionsExperimental dataSimulated dataFit to the experimental dataFit to the simulated data
16 18 20 22 24 26 28 30 [GeV] beam E - r a w E D (a) [GeV] beam E r a w E R KaonsExperimental dataSimulated dataFit to the experimental dataFit to the simulated data
16 18 20 22 24 26 28 30 [GeV] beam E - - r a w E D (b) [GeV] beam E r a w E R ProtonsExperimental dataSimulated dataFit to the experimental dataFit to the simulated data
16 18 20 22 24 26 28 30 [GeV] beam E - - r a w E D (c) Fig. 20: Energy response normalized to incident beamenergy, R (cid:104) E raw (cid:105) , measured (blue dots) and predicted byMC simulation (black circles) as a function of beamenergy obtained in the case of pion (a), kaon (b) andproton (c) beams. The experimental uncertainties in-clude statistical and systematic effects combined inquadrature. Only statistical uncertainties affect sim-ulated results. The red dashed (black dotted) curvesare fits of the Eq. (22) to the experimental (simulated)data points. In case of experimental determinations thedashed blue strips display the correlated systematic un-certainties. In the bottom of the histograms are shownthe fractional differences ∆E (cid:104) raw (cid:105) defined in Eq. (12).The uncertainties include statistical and systematic ef-fects combined in quadrature.and ∆σ raw = σ raw σ rawMC − . (13)The results are reported in Table 8 where statisti-cal and systematic uncertainties are shown separately.The statistical uncertainties include the experimentaland simulated uncertainties combined in quadrature.The results are also shown in Figures 20 and 21 wherestatistical and systematic uncertainties are combined inquadrature.The average of the absolute values of the differenceof all the energy response (resolution) measurementsobtained using experimental and simulated data wasfound to be 1.1% (3.4%). In the case of the responsedeterminations and the resolution determinations of pi- beam E r a w s R PionsExperimental dataSimulated dataFit to the experimental dataFit to the simulated data [GeV] beam E - r a w sD (a) beam E r a w s R KaonsExperimental dataSimulated dataFit to the experimental dataFit to the simulated data [GeV] beam E - r a w sD (b) [GeV] beam E r a w s R ProtonsExperimental dataSimulated dataFit to the experimental dataFit to the simulated data [GeV] beam E - - r a w sD (c) Fig. 21: Energy resolution normalized to incident beamenergy, R σ raw , measured (blue dots) and predictedby MC simulation (black circles) as a function of1 ⁄ √ E beam obtained in the case of pion (a), kaon (b)and proton (c) beams. The experimental uncertaintiesinclude statistical and systematic effects combined inquadrature. Only statistical uncertainties affect sim-ulated results. The red dashed (black dotted) curvesare fits of the Eq. (30) to the experimental (simulated)data points. In case of experimental determinations thedashed blue strips display the correlated systematic un-certainties. In the bottom of the histograms are shownthe fractional differences ∆σ raw defined in Eq. (13). Theuncertainty includes statistical and systematic effectscombined in quadrature.ons and kaons, the differences are consistent within theuncertainties. The uncertainties of the proton resolu-tion determinations are about one order of magnitudesmaller.5.3 Comparison between pion, kaon and proton energyresponses and resolutionsThe values of the ratios R (cid:104) E raw (cid:105) ( K ) R (cid:104) E raw (cid:105) ( π ) (14) R σ raw ( K ) R σ raw ( π ) (15) Table 8: Comparison of the energy response (top) andresolution (bottom) obtained analyzing experimentaland simulated data in the case of pion, kaon and protonbeams with different beam energies. Statistical uncer-tainties (first value) and systematic uncertainties (sec-ond value) are reported.
Pions E beam ∆E raw = (cid:104) E raw (cid:105)(cid:104) E rawMC (cid:105) − ∆σ raw = σ raw σ rawMC − ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± E beam ∆E raw = (cid:104) E raw (cid:105)(cid:104) E rawMC (cid:105) − ∆σ raw = σ raw σ rawMC − ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± E beam ∆E raw = (cid:104) E raw (cid:105)(cid:104) E rawMC (cid:105) − ∆σ raw = σ raw σ rawMC − ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± R (cid:104) E raw (cid:105) ( p ) R (cid:104) E raw (cid:105) ( π ) (16) R σ raw ( p ) R σ raw ( π ) (17)obtained using experimental and simulated data are re-ported in Table 9. The statistical (first value) and thesystematic (second value) uncertainties are shown sep-arately in the case of experimental results. The system-atic uncertainty was obtained combining in quadraturethe contribution of the seven sources of systematic un-certainties discussed in Section 5.1 . The uncertainty onthe scale of the reconstructed cell energy, C EMc , affectsin a correlated way the reconstruction of the energydeposited in the modules by pions, kaons and protons.It follow that its effects on the energy response ratiodeterminations are negligible. In the case of simulateddata only statistical uncertainties are reported. The de-terminations are also shown as a function of E beam in Figure 22. In the case of results obtained analyzing ex-perimental data, the error bars were obtained combin-ing in quadrature statistical and systematic uncertain-ties. In the case of results obtained analyzing simulateddata only statistical uncertainty are shown.Table 9: Values of the ratios (14)–(17) obtained usingexperimental and simulated data produced by particleswith E beam equal to 16, 18, 20 and 30 GeV. In the caseof experimental determinations statistical (first value)and correlated systematic uncertainties (second value)are reported separately. Only statistical errors affect theMC determinations. R (cid:104) E raw (cid:105) ( K ) ⁄ R (cid:104) E raw (cid:105) ( π ) E beam [GeV] Experimental data Simulation data16 0.9694 ± ± ± ± ± ± ± ± ± ± ± ± R (cid:104) E raw (cid:105) ( p ) ⁄ R (cid:104) E raw (cid:105) ( π ) E beam [GeV] Experimental data Simulation data16 0.9079 ± ± ± ± ± ± ± ± ± ± ± ± R σ raw ( K ) ⁄ R σ raw ( π ) E beam [GeV] Experimental data Simulation data16 1.0769 ± ± ± ± ± ± ± ± ± ± ± ± R σ raw ( p ) ⁄ R σ raw ( π ) E beam [GeV] Experimental data Simulation data16 0.8918 ± ± ± ± ± ± ± ± ± ± ± ± In the considered E beam range, the measured ratiosof the kaon over pion energy responses is constant witha weighted average equal to 0.967 ± ± E beam = 16 GeV to0.941 ± E beam = 30 GeV. The val-ues of the ratios of the energy resolution determina-tions are constants. The weighted averages values are R σ raw ( K ) ⁄ R σ raw ( π ) = 0.95 ± R σ raw ( p ) ⁄ R σ raw ( π ) = 0.888 ±
16 18 20 22 24 26 28 30 [GeV] beam E R a t i o experimental data ) p ( raw E R / (K) raw E R experimental data ) p ( raw E R / (p) raw E R simulated data ) p ( raw E R / (K) raw E R simulated data ) p ( raw E R / (p) raw E R (a)
16 18 20 22 24 26 28 30 [GeV] beam E R a t i o experimental data ) p ( raw s R / (K) raw s R experimental data ) p ( raw s R / (p) raw s R simulated data ) p ( raw s R / (K) raw s R simulated data ) p ( raw s R / (p) raw s R (b) Fig. 22: (a) Ratios of the kaon and proton re-sponses over the pion ones as a function of E beam .The blue dots (black empty circles) show the ra-tios R (cid:104) E raw (cid:105) ( K ) ⁄ R (cid:104) E raw (cid:105) ( π ) obtained using experimen-tal (simulated) data. The blue full (black empty)squares show the ratios R (cid:104) E raw (cid:105) ( p ) ⁄ R (cid:104) E raw (cid:105) ( π ) obtainedusing experimental (simulated) data. (b) Ratios of thekaon and proton resolutions over the pion ones as afunction of E beam . The blue dots (black empty cir-cles) show the ratios R σ raw ( K )/ R σ raw ( π ) obtained us-ing experimental (simulated) data. The blue full (blackempty) squares show the ratios R σ raw ( p ) ⁄ R σ raw ( π ) ob-tained using experimental (simulated) data. In the caseof experimental results uncertainties include statisticaland systematic effects combined in quadrature. In thecase of simulated results only statistical uncertainty arereported. R (cid:104) E raw (cid:105) = (1 − F h ) + F h × ( eh ) − (18)where F h represents the non-electromagnetic energycomponent of showers induced by incident hadrons ofenergy E beam and e/h is the ratio between the responsesto the purely EM and hadronic components of showers.The measurements allow a determination of the ratiosof the non-electromagnetic energy component of show-ers induced by incident pions ( F h ( π )), kaons ( F h ( K ))and protons ( F h ( p )) for the same value of E beam . UsingEq. (18) one obtains F h ( K ) F h ( π ) = 1 − R (cid:104) E raw (cid:105) ( K )1 − R (cid:104) E raw (cid:105) ( π ) (19)and F h ( p ) F h ( π ) = 1 − R (cid:104) E raw (cid:105) ( p )1 − R (cid:104) E raw (cid:105) ( π ) (20)The determinations obtained using experimental andsimulated data are reported in Table 10. The statisti-cal (first value) and the systematic (second value) un-certainties are shown separately in the case of experi-mental results. The systematic uncertainties were ob-tained combining in quadrature the effects of the sevensources discussed in Section 5.1. In the case of simu-lated data, only statistical uncertainties are reported.Data show constant ratios F h ( K ) /F h ( π ). The weightedaverage numerical value is 1.13 ± ± F h ( p ) /F h ( π ) decreases from 1.351 ± ± E beam
16 GeV to 1.24 ± ± E beam
30 GeV.The ratio F h ( p ) /F h ( π ), as obtained in Refs. [17] and[18] from the copper/quartz-fiber calorimeter data [19],varies from 1.22 at 200 GeV to 1.15 at 370 GeV. InRef. [20], a constant value of F h ( p ) /F h ( π ) in the rangebetween 1.15 and 1.20 is predicted.The determinations of F h ( K ) /F h ( π ) and F h ( p ) /F h ( π ) as a function of E beam are also reportedin the histograms of Figure 23 (a) and (b) respectively.In the case of experimental results, statistical and sys-tematic uncertainties are combined in quadrature. Inthe case of simulated results only statistical uncertaintyare shown. Table 10: Values of the ratios F h ( K ) /F h ( π ) and F h ( p ) /F h ( π ) obtained using experimental and simu-lated data for the four values of the beam energies E beam . In the case of experimental determinations sta-tistical (first value) and correlated systematic (secondvalue) uncertainties are reported separately. Only sta-tistical uncertainties affects the MC determinations. F h ( K ) /F h ( π ) E beam [GeV] Experimental Data Simulated Data16 1.1165 ± ± ± ± ± ± ± ± ± ± ± ± F h ( p ) /F h ( π ) E beam [GeV] Experimental Data Simulated Data16 1.3512 ± ± ± ± ± ± ± ± ± ± ± ± In Groom’s parametrization, [20], [17] and [18], onehas F h = ( E beam E ) m − (21)where the quantity E is the energy at which mul-tiple pion production becomes significant and the pa-rameter m describes the relation between the averagemultiplicity of secondary particles produced in the col-lision and the fraction of energy going into π ’s in onecollision. One obtains R (cid:104) E raw (cid:105) = 1 + 1( E ) m − [( eh ) − − E beam ) m − . (22)and F h ( K ) F h ( π ) = E ( π ) m ( π ) − E ( K ) m ( K ) − × ( E beam ) m ( K ) − m ( π ) (23) F h ( p ) F h ( π ) = E ( π ) m ( π ) − E ( p ) m ( p ) − × ( E beam ) m ( p ) − m ( π ) (24)Fits of Eq. (23) to the histograms of Figure 23 (a)and of Eq. (24) to the histograms of Figure 23 (b) allowa determination of B K/π = E ( π ) m ( π ) − E ( K ) m ( K ) − , (25)
16 18 20 22 24 26 28 30 [GeV] beam E R a t i o experimental data ) p ( h F / (K) h F simulated data ) p ( h F / (K) h F Fit to the experimental dataFit to the simulated data (a)
16 18 20 22 24 26 28 30 [GeV] beam E R a t i o experimental data ) p ( h F / (p) h F simulated data ) p ( h F / (p) h F Fit to the experimental dataFit to the simulated data (b)
Fig. 23: (a) F h ( K ) /F h ( π ) as a function of E beam ob-tained using experimental, blue dots, and simulateddata, black empty circles. (b) F h ( p ) /F h ( π ) as a func-tion of E beam obtained using experimental, blue dots,and simulated data, black empty circles. In the caseof experimental results uncertainties include statisticaland systematic effects combined in quadrature. In thecase of simulated results only statistical uncertainty areshown. The dashed (dotted) red curves are fits of thefunctions (23) and (24) to the experimental (simulated)data points. In case of experimental determinations thedashed red strips display the correlated systematic un-certainties. C K/π = m ( K ) − m ( π ) (26)and B p/π = E ( π ) m ( π ) − E ( p ) m ( p ) − , (27) C p/π = m ( p ) − m ( π ) (28)respectively. The fit curves to the experimental and sim-ulated data are show in the figure. The strips display thecorrelated systematic uncertainties ∆ syst. F h ( K ) /F h ( π )(Figure 23 (a)) and ∆ syst. F h ( p ) /F h ( π ) (Fig. 23 (b)).They are defined by the curves obtained fitting Eq. (23)(Eq. (24)) to the points F h ( K ) /F h ( π ) ± ∆ syst. F h ( K ) /F h ( π )( F h ( p ) /F h ( π ) ± ∆ syst. F h ( p ) /F h ( π )). All the fits wereperformed using as uncertainties the statistical uncer-tainties of the determinations. The values of the pa-rameters obtained in the fits are reported in Table 11.The first uncertainty value is the statistical uncertainty.It corresponds to the square root of the correspondingdiagonal term of the fit error matrix. The systematicuncertainty (second uncertainty value) is equal to halfof the differences of the determinations obtained fittingEq. (23) to the points F h ( K ) /F h ( π ) ± ∆ syst. F h ( K ) /F h ( π ) and Eq. (24) to the points F h ( p ) /F h ( π ) ± ∆ syst. F h ( p ) /F h ( π ). In the table,the χ probability values of the fits performed to thecentral points are reported. In the case of the fits tosimulated data the probabilities are very small.Table 11: Values of the parameters B K/π (Eq. (25))and C K/π (Eq. (26)) obtained fitting Eq. (23) to theexperimental and simulated values of F h ( K ) /F h ( π ) asa function of E beam shown Figure 23 (a). Values of theparameters B p/π (Eq. (27)) and C p/π (Eq. (28)) ob-tained fitting Eq. (24) to the experimental and sim-ulated values of F h ( p ) /F h ( π ) as a function of E beam shown Figure 23 (b). In the case of experimental dataresults, statistical and systematic uncertainties are re-ported. Only statistical uncertainties appear in the caseof simulated data results. The χ probability values ofthe fits are reported. Experimental data Simulated data B K/π ± ± ± C K/π ± ± ± χ prob. 0.944 1 . × − Experimental data Simulated data B p/π ± ± ± C p/π -0.137 ± ± ± χ prob. 0.311 8 . × − The values of B K/π and C K/π obtained using ex-perimental and simulated data agree within two sigmas.The values of B p/π and C p/π obtained using experimen-tal and simulated data differ significantly.Fits of Eq. (22) to the determinations of R (cid:104) E raw (cid:105) asa function of E beam (see Figure 20) allow a determina-tion [17] of m and A = 1( E ) m − [( eh ) − − . (29)The fit curves to the experimental and simulated de-terminations are reported in the figure. The strips dis-play correlated systematic uncertainties ∆R E raw syst. . Theyare bounded by the curves obtained fitting Eq. (22) tothe points R E raw ± ∆R E raw syst. . All the fits were performedusing as uncertainties the statistical uncertainties of thedeterminations. The obtained values of A and m arereported in Table 12. The first uncertainty value is thestatistical uncertainty. It corresponds to the square rootof the diagonal term of the error matrix. The system-atic uncertainty (second uncertainty value) is equal tohalf of the differences of the determinations obtainedfitting Eq. (22) to the points R E raw ± ∆R E raw syst. . In the table the χ probability values of the fits performed tothe central points are reported. In the case of the fitsto kaon and proton simulated data the probabilities arevery small.Table 12: Values of the parameters A (Eq. (29)) and m obtained fitting Eq. (22) to the experimental and simu-lated energy response normalized to incident beam en-ergy, R E raw , as a function of E beam . The fit functionsare overlapped to the determinations in Figure 20. Inthe case of experimental data results statistical and sys-tematic uncertainties are reported. Only statistical un-certainties appear in the case of simulated data results.The χ probability values of the fits are reported. PionsExperimental data Simulated data A -0.2612 ± ± ± m ± ± ± χ prob. 0.004 0.238KaonsExperimental data Simulated data A -0.2481 ± ± ± m ± ± ± χ prob. 0.981 2 . × − ProtonsExperimental data Simulated data A -0.5041 ± ± ± m ± ± ± χ prob. 0.632 4 . × − The values of m obtained using pions, kaons andprotons data without making any assumption on thevalues of e/h and E are: 0.919 ± ± ± ± ± ± m around 0.87 are expected. The determi-nations can be compared with previous pion measure-ments summarized in [17].To compare the results discussed in this paper withthe ones obtained previously using pions beams withenergy in the range 10-350 GeV and incident in the Tile-Cal modules at η = 0.35 [12], Eq. (22) was fitted to thepion determinations fixing E = 1 GeV. The obtainedvalues e/h = 1.3535 ± m = 0.9187 ± ± ± E beam can be parametrizedaccording to R σ raw = a √ E beam ⊕ b. (30)where the first term describes the fluctuations on thenumber of particle produced in the showers, the secondterm describes the non-uniformity of the cell responseand the symbol ⊕ indicates the sum in quadrature. Inthe considered beam energy range the noise contribu-tion is negligible (see Section 3.4).The curves in Figure 21 were obtained fitting Eq. (30)to the experimental and simulated determinations of R σ raw as a function of 1 / (cid:112) E beam [GeV]. The strips inthe figure display correlated systematic uncertainties ∆R σ raw syst. . They are defined by the curves obtained fit-ting Eq. (30) to the points R σ raw ± ∆R σ raw syst. . All thefits were performed using as uncertainties the statisti-cal uncertainties of the determinations. The resultingvalues of a and b are reported in Table 13. The statisti-cal uncertainty (first uncertainty value) is equal to thesquare root of the corresponding diagonal term of thefit error matrix. The systematic uncertainty (second un-certainty value) is equal to half of the differences of thedeterminations obtained fitting Eq. (30) to the points R σ raw + ∆R σ raw syst. and R σ raw − ∆R σ raw syst. . In the table the χ probability values of the fits performed to the centralvalues are reported.The values of a obtained analyzing pions and kaonsare consistent inside the large uncertainties of about4%. The value obtained using protons is 14% smaller.The constant term b is about 5% and equal for the threeparticle beams. Analyses of simulated events producedvalues of a
10% smaller than the ones obtained usingexperimental data. The determinations of the constantterms b are 30% larger.The values of a and b obtained analyzing pion dataare consistent within about 2.6 sigmas with the resultsobtained in a previous study [12]. The results described in this paper were obtained byexposing three modules of the ATLAS Tile Calorime-ter to positive pion and kaon and proton beams withenergies equal to 16, 18, 20 and 30 GeV and incidentat the centre of the front face of a calorimeter modulecell with an angle of 14 degrees from the normal. Two Table 13: Values of the parameters a and b obtainedfitting Eq. (30) to the experimental and simulatedfractional resolution values R σ raw obtained using pi-ons ( π ), kaons ( K ) and prtons ( p ) as a function of1 ⁄ (cid:112) E beam [GeV] (see Figure 21). In the case of exper-imental data results, statistical and systematic uncer-tainties are reported. Only statistical uncertainties ap-pear in the case of simulated data results. The χ prob-ability values of the fits are reported. Previous pion [12]results are also shown ( π old). Experimental data a [% GeV − / ] b [%] χ prob. π ± ± ± ± K ± ± ± ± p ± ± ± ± π old 52.9 ± ± a [% GeV − / ] b [%] χ prob.Pions 42.25 ± ± ± ± ± ± Cherenkov counters in the beam line made it possibleto identify pions, kaons and protons. The effects of elec-trons contaminating the pion samples in reconstructingthe pion energy were determined by exploiting the dif-ference of electromagnetic and hadronic shower profilesin the detector.The main purpose of the study is to compare themeasured energy of the particles with the predictions ofthe Geant4-based simulation program used in ATLASto simulated jets produced in proton-proton collisionsat the Large Hadron Collider.Eleven (Nine) determinations of the twelve energyresponses (resolutions) normalized to incident beam en-ergy have a total uncertainty smaller than 1.4% (1.9%).In the case of kaons with E beam = 16 GeV, due to thelarge statistical error, the uncertainty on the determi-nation of R (cid:104) E raw (cid:105) , is equal to 2.4%. The uncertaintyvalues of the determinations of R (cid:104) σ raw (cid:105) obtained in thecase of 16 GeV pion and kaon and 18 GeV kaon beamsare equal to 3.1%, 20.3% and 10.4% respectively.Determinations of all the energy responses and ofthe pion and kaon energy resolutions obtained usingexperimental and simulated data agree within the un-certainties. The average of the absolute values of thedifferences of all the energy response measurements wasfound to be 1.1% with an average total uncertainty of1.4%. The average difference of all the resolution mea-surements was found to be 3.4%. The average total un- certainty of pion and kaon (proton) resolution measure-ments is 5.6% (0.6%).In the considered E beam range, the measured ratiosof the kaon over pion energy responses is constant witha weighted average equal to 0.967 ± ± E beam = 16 GeV to0.941 ± E beam = 30 GeV. The val-ues of the ratios of the energy resolution determina-tions are constants. The weighted averages values are R σ raw ( K ) ⁄ R σ raw ( π ) = 0.95 ± R σ raw ( p ) ⁄ R σ raw ( π ) = 0.888 ± F h ( π ), F h ( K ) and F h ( p ) and to the non-compensatingnature of the detector. Data show constant ratios F h ( K ) /F h ( π ). The weighted average numerical valueis 1.13 ± ± F h ( p ) /F h ( π ) decreases from 1.351 ± ± E beam
16 GeV to 1.24 ± ± E beam
30 GeV.As discussed in Section 6.1 the fraction of non–electromagnetic energy deposited by incident particlescan be expressed in terms of the parameters m and E [GeV]. The ratio between the responses to the purelyEM and hadronic components of showers e/h describesthe non-compensation nature of the calorimeter.. Thevalues of m obtained using experimental (simulated) pi-ons, kaons and protons data are 0.919 ± ± ± ± ± ± a ⁄ (cid:112) E beam [GeV] and a constant terms b (see Section6.2). The values of a [% GeV − / ] obtained analysingpions, kaons and protons are 47 ± ± ± ± ± ± b [%] values are 5.0 ± ± ± ± ± ± References
1. ATLAS Collaboration, JINST , S08003 (2008). DOI10.1088/1748-0221/3/08/S080032. CERN EN Engineering Department. H8 beam line.URL http://sba.web.cern.ch/sba/BeamsAndAreas/resultbeam.asp?beamline=H8
3. S. Agostinelli, et al., Nucl. Instrum. Meth. A , 250(2003). DOI 10.1016/S0168-9002(03)01368-84. J. Allison, et al., IEEE Trans. Nucl. Sci. , 270 (2006).DOI 10.1109/TNS.2006.8698265. D. Costanzo, A. Dell’Acqua, A. Di Simone, M. Gal-las, A. Nairz, A. Rimoldi, J. Boudreau, V. TSu-laia, ATLAS detector simulation: status and out-look. Tech. Rep. ATL-SOFT-PUB-2005-004. CERN-ATL-SOFT-PUB-2005-004. ATL-COM-SOFT-2005-008,CERN, Geneva (2005). URL https://cds.cern.ch/record/916030
6. J. Spanggaard, Delay Wire Chambers - A Users Guide.Tech. Rep. SL-Note-98-023-BI, CERN, Geneva (1998).URL http://cds.cern.ch/record/702443
7. B. Di Girolamo, A. Dotti, V. Giangiobbe, P. Jo-hansson, L. Pribyl, M. Volpi, Beamline instrumen-tation in the 2004 combined ATLAS testbeam.Tech. Rep. ATL-TECH-PUB-2005-001. ATL-COM-TECH-2005-001, CERN, Geneva (2005). URL http://cds.cern.ch/record/831497
8. ATLAS Collaboration, Technical Design Report for thePhase-II Upgrade of the ATLAS Tile Calorimeter. Tech.Rep. CERN-LHCC-2017-019. ATLAS-TDR-028, CERN,Geneva (2017). URL http://cds.cern.ch/record/2285583
9. M. Crouau, P. Grenier, G. Montarou, S. Poirot,F. Vazeille, Characterization of 8-stages HamamatsuR5900 photomultipliers for the TILE calorimeter. Tech.Rep. ATL-TILECAL-97-129. ATL-L-PN-129, CERN,Geneva (1997). URL http://cds.cern.ch/record/683595
10. J. Abdallah, et al., JINST , P01005. 26 p (2007)11. A. Valero, The ATLAS TileCal Read-Out Drivers SignalReconstruction. Tech. Rep. ATL-TILECAL-PROC-2009-004, CERN, Geneva (2009). URL http://cds.cern.ch/record/1223960
12. P. Adragna, et al., Nucl. Instrum. Meth.
A606 , 362(2009). DOI 10.1016/j.nima.2009.04.00913. ATLAS Collaboration, The European Physical JournalC (12), 987 (2018). DOI 10.1140/epjc/s10052-018-6374-z. URL https://doi.org/10.1140/epjc/s10052-018-6374-z
14. H.W. Bertini, M.P. Guthrie, Nucl. Phys.
A169 , 670(1971). DOI 10.1016/0375-9474(71)90710-X15. S. Abdullin, et al., Eur. Phys. J.
C60 , 359 (2009). DOI10.1140/epjc/s10052-009-1024-0. [Erratum: Eur. Phys.J.C61,353(2009)]16. R. Wigmans, Int. Ser. Monogr. Phys. , 1 (2000)17. D.E. Groom, Nucl. Instrum. Meth. A (2), 633 (2007).DOI https://doi.org/10.1016/j.nima.2006.11.070. URL
18. D.E. Groom, Nucl. Instrum. Meth. A (3), 638 (2008).DOI https://doi.org/10.1016/j.nima.2008.05.045. URL
19. N. Akchurin, S. Ayan, G. Bencze, K. Chikin, H. Cohn,S. Doulas, I. Dumanoˇglu, E. Eskut, A. Fenyvesi, A. Fer-rando, M. Fouz, O. Ganel, V. Gavrilov, Y. Gershtein,C. Hajdu, J. Iosifidis, M. Josa, A. Kayis, A. Khan,S. Kim, V. Kolosov, S. Kuleshov, A. Kuzucu-Polatoz,J. Langland, D. Litvintsev, J.P. Merlo, J. Molnar,A. Nikitin, Y. Onel, G. ¨Oneng¨ut, D. Osborne, N. ¨Ozde¸sKoca, H. Ozt¨urk, A. Penzo, E. Pesen, V. Podrasky,A. Rosowsky, J. Salicio, C. Sanzeni, R. Sever, H. Sil-vestri, V. Stolin, L. Sulak, J. Sullivan, A. Ulyanov,S. Uzunian, G. Vesztergombi, R. Wigmans, D. Winn,1R. Winsor, A. Yumashev, P. Zalan, M. Zeyrek, Nucl.Instrum. Meth. A (2), 380 (1998). DOI https:/ / doi . org / 10 . 1016 / S0168 - 9002(98 ) 00021 - 7. URL
20. T. Gabriel, D. Groom, P. Job, N. Mokhov, G. Steven-son, Nucl. Instrum. Meth. A (2), 336 (1994). DOIhttps://doi.org/10.1016/0168-9002(94)91317-X. URL(2), 336 (1994). DOIhttps://doi.org/10.1016/0168-9002(94)91317-X. URL