Characterisation of different stages of hadronic showers using the CALICE Si-W ECAL physics prototype
CALICE Collaboration, G. Eigen, T. Price, N.K. Watson, A. Winter, Y.Do, A.Khan, D.Kim, G. C. Blazey, A. Dyshkant, K. Francis, V. Zutshi, K. Kawagoe, Y. Miura, R. Mori, I. Sekiya, T. Suehara, T. Yoshioka, J. Apostolakis, J. Giraud, D. Grondin, J.-Y. Hostachy, O. Bach, V. Bocharnikov, E. Brianne, K. Gadow, P. Göttlicher, O. Hartbrich, D. Heuchel, F. Krivan, K. Krüger, J. Kvasnicka, S. Lu, O. Pinto, A. Provenza, M. Reinecke, F. Sefkow, S. Schuwalow, Y. Sudo, H.L. Tran, P. Buhmann, E. Garutti, S. Laurien, D. Lomidze, M. Matysek, G.W. Wilson, D. Belver, E. Calvo Alamillo, M.C. Fouz, H. García Cabrerai, J. Maríni, J. Navarrete, J. Puerta Pelayo, A. Verdugo, L. Masetti, M. Chadeeva, M. Danilov, M. Gabriel, L. Emberger, C. Graf, Y. Israeli, F. Simon, M. Szalay, H. Windel, M.S. Amjad, S. Bilokin, J. Bonis, D. Breton, P. Cornebise, P. Doublet, A. Gallas, J. Jeglot, A. Irles, H. Li, J. Maalmi, R. Pöschl, A. Thiebault, F. Richard, D. Zerwas, M. Anduze, V. Balagura, E. Becheva, V. Boudry, J-C. Brient, R. Cornat, E. Edy, G. Fayolle, F. Gastaldi, H. Videau, S. Callier, F. Dulucq, Ch. de la Taille, G. Martin-Chassard, L. Raux, N. Seguin-Moreau, J. Cvach, M. Janata, M. Kovalcuk, I. Polak, J. Smolik, et al. (6 additional authors not shown)
CCALICE-PUB-2019-002
Characterisation of different stages of hadronicshowers using the CALICE Si-W ECAL physicsprototype
The CALICE Collaboration
G. Eigen a , T. Price b , N.K. Watson b , A. Winter b , Y.Do c , A.Khan c , D.Kim c , G.C. Blazey d , A. Dyshkant d , K. Francis d , V. Zutshi d , K. Kawagoe e , Y. Miura e , R. Mori e ,I. Sekiya e , T. Suehara e , T. Yoshioka e , J. Apostolakis f , J. Giraud g , D. Grondin g ,J.-Y. Hostachy g , O. Bach h , V. Bocharnikov h , E. Brianne h , K. Gadow h , P. G¨ottlicher h ,O. Hartbrich h,1 , D. Heuchel h , F. Krivan h , K. Kr¨uger h , J. Kvasnicka h,s , S. Lu h , O. Pinto h ,A. Provenza h , M. Reinecke h , F. Sefkow h , S. Schuwalow h , Y. Sudo h , H.L. Tran h ,P. Buhmann i , E. Garutti i , S. Laurien i , D. Lomidze i , M. Matysek i , G.W. Wilson j ,D. Belver k , E. Calvo Alamillo k , M.C. Fouz k , H. Garc´ıa Cabrera k , J. Mar´ın k ,J. Navarrete k , J. Puerta Pelayo k , A. Verdugo k , L. Masetti l , M. Chadeeva m,n ,M. Danilov m,n , M. Gabriel o , L. Emberger o , C. Graf o , Y. Israeli o , F. Simon o , M. Szalay o ,H. Windel o , M.S. Amjad p,2 , S. Bilokin p,3, ∗ , J. Bonis p , D. Breton p , P. Cornebise p ,P. Doublet p,4 , A. Gallas p , J. Jeglot p , A. Irles p , H. Li p,5 , J. Maalmi p , R. P¨oschl p, ∗∗ ,A. Thiebault p , F. Richard p , D. Zerwas p , M. Anduze q , V. Balagura q , E. Becheva q ,V. Boudry q , J-C. Brient q , R. Cornat q,6 , E. Edy q , G. Fayolle q , F. Gastaldi q , H. Videau q ,S. Callier r , F. Dulucq r , Ch. de la Taille r , G. Martin-Chassard r , L. Raux r ,N. Seguin-Moreau r , J. Cvach s , M. Janata s , M. Kovalcuk s , I. Polak s , J. Smolik s , V. Vrba s ,J. Zalesak s , J. Zuklin s , D. Jeans t , N. van der Kolk u , T. Peitzmann u a University of Bergen, Inst. of Physics, Allegaten 55, N-5007 Bergen, Norway b University of Birmingham, School of Physics and Astronomy, Edgbaston, Birmingham B15 2TT, UK c Department of Physics, Kyungpook National University, Daegu, 702-701, Republic of Korea d NICADD, Northern Illinois University, Department of Physics, DeKalb, IL 60115, USA e Department of Physics and Research Center for Advanced Particle Physics, Kyushu University, 744 Motooka,Nishi-ku, Fukuoka 819-0395, Japan f CERN, 1211 Gen`eve 23, Switzerland g Laboratoire de Physique Subatomique et de Cosmologie - Universit´e Grenoble-Alpes, CNRS/IN2P3, Grenoble, France h DESY, Notkestrasse 85, 22607 Hamburg, Germany i Universit¨at Hamburg, Physics Department, Institut f¨ur Experimentalphysik, Luruper Chaussee 149, 22761 Hamburg,Germany j University of Kansas, Department of Physics and Astronomy, Malott Hall, 1251 Wescoe Hall Drive, Lawrence, KS66045-7582, USA k CIEMAT, Centro de Investigaciones Energ´eticas, Medioambientales y Tecnol´ogicas, Madrid, Spain l Institut f¨ur Physik, Universit¨at Mainz, Staudinger Weg 7, 55099 Mainz, Germany m P. N. Lebedev Physical Institute, Russian Academy of Sciences, 117924 GSP-1 Moscow, B-333, Russian Federation n National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) 31, Kashirskoye shosse,115409 Moscow, Russian Federation o Max-Planck-Institut f¨ur Physik, F¨ohringer Ring 6, 80805 Munich, Germany ∗ Corresponding author: [email protected] ∗∗ Corresponding author: [email protected] Now at University of Hawaii at Manoa, High Energy Physics Group, 2505 Correa Road, HI, Honolulu 96822, USA Now at Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK Now at IPHC Strasbourg, 23 rue du loess, BP28, 67037 Strasbourg cedex 2 Now at IUT d’Orsay (Universit´e Paris-Sud), Plateau de Moulon, 91400 Orsay, France Now at South China Normal University, 55 Zhong Shan Da Dao Xi, Tianhe District, 510631 Guangzhou, Guangdong,China Now at Laboratoire de Physique Nucl´eaire et de Hautes Energies (LPNHE), UPMC, UPD, CNRS/IN2P3, 4 PlaceJussieu, 75005 Paris, France a r X i v : . [ phy s i c s . i n s - d e t ] S e p Laboratoire de l’Acc´elerateur Lin´eaire, CNRS/IN2P3 et Universit´e de Paris-Sud XI, Centre Scientifique d’OrsayBˆatiment 200, BP 34, 91898 Orsay CEDEX, France q Laboratoire Leprince-Ringuet (LLR) – ´Ecole Polytechnique, CNRS/IN2P3, 91128 Palaiseau, France r Laboratoire OMEGA – ´Ecole Polytechnique-CNRS/IN2P3, 91128 Palaiseau, France s Institute of Physics, The Czech Academy of Sciences, Na Slovance 2, 18221 Prague 8, Czech Republic t Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tsukuba, Japan u Institute for Subatomic Physics, Utrecht University/Nikhef, 3584CC Utrecht, The Netherlands
Abstract
A detailed investigation of hadronic interactions is performed using π − -mesons with energies in therange 2–10 GeV incident on a high granularity silicon-tungsten electromagnetic calorimeter. The datawere recorded at FNAL in 2008. The region in which the π − -mesons interact with the detector mate-rial and the produced secondary particles are characterised using a novel track-finding algorithm thatreconstructs tracks within hadronic showers in a calorimeter in the absence of a magnetic field. Theprinciple of carrying out detector monitoring and calibration using secondary tracks is also demon-strated. Contents1 Introduction 22 The Si-W ECAL physics prototype 33 Data and Monte Carlo samples 4
The design of particle detectors at future high-energy physics experiments and, in particular, atlinear colliders is oriented towards the usage of Particle Flow Algorithms (PFA) for the event recon-struction. These algorithms aim to achieve good jet energy resolution by reconstructing individualparticles and hence require high granularity calorimeters [1, 2, 3].2he primary objective of the CALICE (Calorimeter for the Linear Collider Experiment) collabo-ration is the development, construction and testing of highly granular hadronic and electromagneticcalorimeters for future particle physics experiments.A detailed study of the calorimeter response to particle interactions is necessary to verify existingMonte Carlo simulation models and to build reliable PFA. This implies the precise simulation andreconstruction of the interaction of neutral and charged hadrons using the subsequent particle cascade.This article presents a detailed study of π − -meson interactions in the CALICE Silicon-TungstenElectromagnetic Calorimeter (Si-W ECAL) physics prototype [4]. The Si-W ECAL was tested atFermi National Accelerator Laboratory (FNAL) in 2008 using a beam of π − -mesons in the energyrange from 2 to 10 GeV. The highly granular structure of the Si-W ECAL enables both a detailedmeasurement of hadronic showers in terms of integral observables [5, 6] as well as deeper studiesof the interactions between hadrons and the absorber material, such as the characterisation of theinteraction region and the analysis of secondaries emerging from the interaction. The tracks producedby these secondaries are reconstructed using a new simple track-finding algorithm. The resultingobservables are used to compare data with predictions from several geant4 simulation models [7, 8].The analysis complements studies presented in [9] and [10] for tracking in CALICE prototypes ofhadronic calorimeters.
2. The Si-W ECAL physics prototype
The Si-W ECAL physics prototype has a sandwich-like structure comprising 30 layers of silicon asthe active material, alternating with tungsten as the absorber material. The active layers are made ofSi wafers segmented in 1 × pads. As shown in Fig. 1, each wafer consists of a square of 6 × × ×
18 cm . Figure 1:
A schematic view of the Si-W ECAL physics prototype.
The Si-W ECAL is subdivided into three modules of ten layers. The tungsten depth per layer is1.4 mm (0.4 radiation lengths, X ) in the first module, 2.8 mm in the second and 4.2 mm in the third.The total thickness corresponds to 24 X and about one nuclear interaction length λ I . Therefore morethan half of the hadrons are expected have a primary interaction within the detector volume. A moredetailed description of the prototype can be found in Ref. [4].For the analysis presented in this article it is convenient to introduce a unit grid based on the Si-W3CAL pad identifiers according to (cid:126)x = ( x, y, z ) = x = 0 .. y = 0 .. z = 0 .. , (1)where pad counting starts in the bottom right pad, see Fig. 1. Distances in this grid are measured in grid units , g . u .
3. Data and Monte Carlo samples
The test beam measurements were carried out at the Fermilab Test Beam Facility , FTBF, at FNALin May and July 2008. A schematic overview of the beam line is given in Fig. 2. The Si-W ECAL wasplaced in front of two other CALICE physics prototypes, the analogue hadronic calorimeter (HCAL)[11] and a TailCatcher [12]. In both steel is used as absorber. Sensors are scintillator tiles (HCAL)or scintillator strips read out by silicon-photomultipliers. The beam-line also included wire chambers(WC1-3), drift chambers (DC1-4) and scintillator counters of different sizes, named T100(A,B), VETO,T20x20 and T10x10(A,B). The latter two cover an area of 10 ×
10 cm each and are used for triggeringon beam particles analysed for this article. Finally, two Cherenkov detectors for particle identificationare located upstream of the Wire Chamber 1. Figure 2:
Plan view of the beam line at FNAL. Distances (not to scale) are in mm.
The chosen coordinate system is right-handed with the z -axis pointing along the beam directionand the y -axis being vertical. The data analysed in this article comprise runs with π − -mesons withenergies of 2, 4, 6, 8 and 10 GeV. Monte Carlo simulations were carried out within the Mokka framework [13], which provides thegeometry interface to geant4 . There are several models of hadronic interactions available within geant4 that are combined into simulation models. Each hadronic interaction model has its owntheoretical basis valid mainly in a specific energy range of hadrons. In this analysis, three simulationmodels contained in geant4
Version 10.1 are compared with the data: • ftfp bert uses the Bertini Cascade Model [14] and the Fritiof String Model [15, 16] where thefirst is used for hadron energies below and the second for hadron energies above 4.5 GeV; Fermilab Test Beam Facility web page: qgsp bert uses the Bertini Cascade Model at energies below, and the Fritiof String Model forenergies above 9.9 GeV. The Fritiof String Model replaces the LHEP parametrisation that wasemployed until Version 9.6 of geant4 ; • qbbc uses also the Bertini Cascade Model for energies below and the Fritiof String Model forenergies above 9.9 GeV but interpolates in a larger transition region (for protons and neutronsbelow 1.5 GeV the Binary Cascade Model [17] is used).The validity ranges of hadronic interaction models in the three simulation models are illustratedin Fig. 3. More information about these and other simulation models can be found in Ref. [18]. FTFP_BERTQGSP_BER T QBB
C 2 4 6 8 10 12
BERTINI CASCADEBERTINI CASCADEBERTINI CASCADE FRITIOF STRING MODEL
Energy [GeV]
FTFP_BERTQGSP_BER T QBB
C 2 4 6 8 10 12
BICBertini Cascade ModelBertini Cascade ModelBertini Cascade Model Fritiof String Model FritiofFritiof
Energy [GeV]
Figure 3:
Illustration of the validity ranges of the three tested geant4 hadronic interaction models as contained in geant4
Version 10.1.
The FNAL π − test beam is contaminated with µ − and e − , in particular at lower energies. At 2GeV the beam contains about 5% π − -mesons and 70% electrons. Events are triggered using the signalsfrom the two scintillator counters T10x10A and T10x10B upstream of the Si-W ECAL and π − -mesonsare identified by using Cherenkov counters. The response of the Si-W ECAL to charged particleswas calibrated with a 32 GeV µ − beam [19] and the deposited energy is converted into units of mostprobable energy depositions, called MIP hereafter, by particles with behaviour that is approximatelyminimally ionising. The deposited energy measured in a pad is called hit.To select π − -meson showers, data and simulation samples are required to satisfy similar criteria tothose of Refs. [6, 20], as below: • Selection criteria are applied to reject multi-particle events caused by beam impurities or productsof decays or upstream interactions of beam particles; • A lower threshold of 0.6 MIP is chosen to remove noise hits in the Si-W ECAL; • A hit is classified as being isolated if all the 26 pads in the surrounding cube (in g.u.) haveno signal above the noise threshold. The analysis presented in this article uses the non-isolatedhits that remain after this removal. The term ‘hits‘ will continue to be used to indicate onlynon-isolated hits in the following. • A total of at least 25 hits in the Si-W ECAL is required to remove particles with large incidentangle; 5
For the event selection the hit coordinates x hit and y hit are defined in the coordinate frameaccording to Fig. 2. The barycentres of the transverse coordinates ¯ x hit and ¯ y hit of the hits arecalculated as: ¯ x hit = (cid:88) hits x hit E hit (cid:88) hits E hit and ¯ y hit = (cid:88) hits y hit E hit (cid:88) hits E hit , (2)where E hit is the energy of a hit in MIP units, and the sums run over all hits in the calorimeter.The event is accepted if −
50 mm < ¯ x hit <
50 mm and −
50 mm < ¯ y hit <
50 mm to reduce lateralshower leakage; • Initially, the interaction layer i is identified as the first of three consecutive layers for which E i > E cut , E i +1 > E cut and E i +2 > E cut . (3)with E i being the total energy of layer i ;This simple condition is inefficient at low energies and is extended by the following relative energyincrease E i + E i +1 E i − + E i − > F cut and E i +1 + E i +2 E i − + E i − > F cut . (4)The variables E cut and F cut are free parameters with empirical values of eight MIP and six,respectively. It is argued in [6] and references therein that these values optimise the selectionefficiency in the energy range relevant for the present study. The event is selected if 5 < i <
15 tosuppress electron contamination and to ensure secondaries that extend over several layers afterthe interaction.
4. The track-finding algorithm
The track-finding algorithm reconstructs forward-scattered tracks from the interaction between the π − -meson and the absorber material in the absence of a magnetic field.The algorithm consists of three stages: • identification and removal of interaction region; • clusterisation of energy deposits; • formation of track-like clusters;The entire algorithm is carried out in the grid units introduced in Sec. 2. A typical inelastic hadronic interaction in the Si-W ECAL creates a shower with an interactionregion and tracks of long-lived particles emerging from it. The interaction region is created by particlessuch as electrons, photons and low-momentum hadrons that have a short distance of flight in theabsorber material of the Si-W ECAL.In the present analysis the interaction region is defined by all hits that have at least six neighbouringpads with a signal above the noise threshold. For the minimal value of six pads a interaction region iswrongly identified in only 1% of single muon events. Muon events are used to estimate the fraction ofevents in which this procedure incorrectly identifies an interaction region. For the minimal value of six(five) pads, an interaction region is found in 1% (10%) of muon events. Increasing the minimal value toseven neighbouring pads with hits further reduces the fraction of events with a fake interaction regionbut does not alter the results presented below in Sec. 5.6 a) Before removing the interaction region. (b)
After removing the interaction region.
Figure 4:
Event display of a π − -meson interaction with an energy of 10 GeV (a) before and (b) after removal of theinteraction region. Smaller cubes are pads that are part of the interaction region and are not processed by the track-finding algorithm. In this event the hits in the first ten layers are classified as hits left by the incoming π − -meson. Figure 4a displays an event after applying noise and isolated hits filters and Fig. 4b is the sameevent after removal of the interaction region, illustrating that the interaction region is the startingpoint for secondary tracks.
During the clusterisation step the energy deposits that are not assigned to the interaction regionare grouped into clusters according to topological criteria.
Cluster Cluster Considered hit(x n , y n , z n ) zxy Search region for considered hit
Figure 5:
Illustration of the clusterisation step. The Si-W ECAL hits are represented by blue cubes, and the searchregion for adjacent hits is indicated by red cubes. The blue arrows point in the direction of the clusterisation flow.
The steps of the clusterisation algorithm are described below, with reference to Fig. 5.7. The separation of tracks improves with increasing distance from the interaction layer. Therefore,the search for hits to seed a cluster begins in the layers that have largest z and continues in thedirection of decreasing z . Typically, seeding hits are found in the last layer of the detector;2. A hit can only be attributed to one cluster. This condition excludes double counting of hits. Arandom choice of seeding hits shows that effects arising from ambiguities in the assignment ofhits to clusters such as the order in which clusters are created, are negligible;3. For the clusterisation a nearest-neighbour clustering scheme is applied where for each newlyassociated hit with coordinates ( x n , y n , z n ), the algorithm finds nearby hits with the followingconditions: • a neighbour hit should have a z coordinate within [ z n − , z n ] g. u. ; • the transverse coordinates of neighbouring hits is searched within ranges [ x n − , x n + 1]and [ y n − , y n + 1].The search region for nearby hits is visualised in Fig. 5 as a ‘red cube’ with 3 × × Secondary long-lived charged particles from hadronic interactions can leave straight, MIP-like tracksin the detector. The goal of the classification of the clusters obtained in the previous step is thus toselect track-like clusters.The classification algorithm executes the following steps:1. Calculate the number of hits, N hits , in a cluster and reject all clusters with only two hits asresidual noise clusters2. Calculate the length l ∈ R of the considered cluster as the maximal distance between anypair of hits that are in the cluster. For example the lower cluster in Fig. 5 has a length of (cid:112) ∆ y n + ∆ z n = √
25 + 1 ≈ . . u . ;3. Reject a cluster with a length of less than l cut = 2 g . u . . This corresponds to the minimal lengthof a track-like cluster with 3 hits;4. Compute the following observable ξ = lN hits − εN hits , (5)as a measure for the eccentricity of the cluster. The first term of Eq. 5 is motivated by the lineardependence of N hits − l , illustrated in Fig. 6. The second term introducesa free parameter ε as an ad hoc correction to increase the efficiency for selecting clusters that donot match the nominal ‘pencil-like‘ topology, as explained below. The value ε = 0 .
03 was chosenafter visual inspection of a few tens of events for pion energies of 10 GeV in an event display.The chosen value is a compromise between a too small value at which also muon tracks wouldget assigned more than one track and too large values at which even for electrons the algorithmwould result in one single track. The choice made for 10 GeV is also adequate for the otherenergies relevant for this analysis. For a detailed discussion see Refs. [21] and [22] ;5. If ξ ≥
1, a cluster is considered as track-like. Otherwise, the cluster is classified as two inseparabletracks.Due to effects such as multiple scattering, residual detector-noise, δ -rays or the residual arbitrarinessin the assignment of hits to clusters, the reconstructed tracks are in general not exactly pencil-like.The correction term εN hits in the definition of ξ serves to keep a cluster as track-like even if it haslarge N hits and its form is not strictly pencil-shaped, i.e. l/ ( N hits − < [g. u.] - h i t s N QGSP_BERT - p
10 GeV
Figure 6:
Correlation between N hits − and cluster length l in g.u. for a sample of simulated pion interactions withan energy of 10 GeV using the qgsp bert simulation model. Clusters inside the red parabola are rejected by means ofEq. 5. To guide the eye a black line for N hits − l is also included in the figure. A cluster is classified as being produced by the incoming π − -meson if it starts in the first moduleof the Si-W ECAL and if it has a small polar angle with respect to the z -axis. An example of a clusterproduced by an incoming π − -meson is visible in Fig. 4b. Clusters assigned to the incoming π − -mesonare discarded in the following analysis. The remaining track-like clusters are merged into tracks if therelative angle θ c between these clusters fulfils the condition sin θ c < .
15, optimised using the polarangle distribution of secondary particles in simulated π − -meson interactions.For a sample of single, isolated 6 GeV muons, the track-finding algorithm finds a single track witha 99.7% efficiency.
5. Results
Observables characterising the interaction region and secondary particles are measured in data andare compared with predictions of the three geant4 simulation models introduced in Sec. 3.2. Theaverage values of observables are also used to make quantitative comparisons. After pre-selectionthe data have a residual contamination of 8.8% (1.5%) double π − -meson events at 2 GeV (10 GeV)beam energy [6]. Therefore, for comparison with data all simulation samples were produced with anadmixture of double π − events. For average values of observables, correction factors are extractedfor each Monte Carlo sample by comparing the results of contaminated samples with those from puresamples. To account for residual contamination, the averages of the data are multiplied by final correction factors. This final correction factors are given by the arithmetic mean of correction factorsof the three considered simulation models. The final correction factors are between 0.99 and 1.01and their uncertainties are much less than one percent. The total systematic error never exceeds twopercent and is dominated by two other sources of systematic uncertainties that have been studied.These are the lowering of the MIP threshold from the nominal 0.6 to 0.4 and the uncertainty on theabsolute MIP energy scale [9] that has been varied by ± The first estimator to characterise the interaction of π − -mesons with the absorber material is thefraction f IR = E IR E tot (6)9here E IR is the energy deposited in the interaction region and E tot is the total energy deposited inthe Si-W ECAL .Figure 7 compares the distribution of f IR in data with the three simulation models. The lowestbin of these histograms corresponds to the fraction of events for which no interaction region is foundby the algorithm. The rest of the distribution can be approximately described by a skewed normaldistribution. The mean value of f IR is shifted towards larger values in data with respect to simulation.Qualitatively, this observation suggests a different repartition of the deposited energy between thedense interaction region and the sparser parts of the shower in data and the simulation models.Figure 8 shows the average value of f IR , (cid:104) f IR (cid:105) , as a function of beam energy for beam energiesof 2, 4, 6, 8 and 10 GeV. Only events in which an interaction region has been detected are includedin (cid:104) f IR (cid:105) . An increase of (cid:104) f IR (cid:105) with increasing beam energy from 43% to around 64% is observed.Qualitatively, this is expected as number of particles increases with increasing energy but also theelectromagnetic component of the hadronic shower becomes increasingly important for higher energiesof the interacting π − -meson. All three simulation models underestimate the energy fraction by about10–15% while the slope is reproduced to a much better level. IR f E n t r i e s ( no r m a li s ed t o un i t y ) - - -
10 1 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (a) IR f E n t r i e s ( no r m a li s ed t o un i t y )
10 GeV FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (b)
Figure 7:
The f IR distribution for energies of 2 GeV (a) and 10 GeV (b) of the beam energy as observed in data(points with error bars) and for the three simulation models, qgsp bert , ftfp bert and qbbc . The double π − -mesonbackground for each of the three models is also shown. The first bin contains events without a detected interactionregion. All histograms are normalised to unit area. Error bars represent statistical uncertainties only. eam energy [GeV] > I R < f FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC
CALICE
Figure 8:
The average fraction (cid:104) f IR (cid:105) as a function of the beam energy for data (black points with grey shaded errorband) and the three simulation models. Error bars represent statistical errors. The error band is the sum in quadratureof the systematic error and the statistical error. Only events for which an interaction region has been detected areincluded in (cid:104) f IR (cid:105) . The lateral radius r IR of the detected interaction region is a measure of the spatial extension of theinteraction region. It is defined as: r IR = 1 N IRhits (cid:88) hit ∈ IR (cid:112) (¯ x IR − x hit ) + (¯ y IR − y hit ) , (7)where the sum runs over the hits in the interaction region, here labelled by IR, and N IR hits is the numberof hits in the interaction region. In Eq. 7 ¯ x IR and ¯ y IR are the transverse coordinates of the barycentreof the interaction region, which in analogy with Eq. 2, are defined as:¯ x IR = (cid:88) hit ∈ IR x hit E hit (cid:88) hit ∈ IR E hit and ¯ y IR = (cid:88) hit ∈ IR y hit E hit (cid:88) hit ∈ IR E hit . (8)Distributions of r IR for data and the predictions of the three simulation models are displayed inFig. 9 for π − -meson energies of 2 and 10 GeV. In both cases, the measured interaction region is widerthan the predictions by the simulation models. Figure 10 displays the dependence of the average r IR , (cid:104) r IR (cid:105) , on the beam energy for the data and the three simulation models. Again, only events inwhich an interaction region has been detected are included in (cid:104) r IR (cid:105) . The lateral size of the interactionregion increases with increasing beam energy. This trend is the same for data and for the simulationmodels. The interaction region measured in data is about 10% wider than those predicted by the threesimulation models, all of which yield similar distributions.11 [mm] IR r E n t r i e s ( no r m a li s ed t o un i t y ) - - - -
10 1 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (a) [mm] IR r E n t r i e s ( no r m a li s ed t o un i t y )
10 GeV FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (b)
Figure 9:
The r IR distribution for energies of 2 GeV (a) and 10 GeV (b) of the beam energy. Other details follow thoseof Fig. 7. Beam energy [GeV] > [ mm ] I R < r FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC
CALICE
Figure 10:
The average radius (cid:104) r IR (cid:105) as a function of the beam energy. Other details follow those of Fig. 8. The final tracks are composed from segments that are given by clusters, as described in Sec. 4.2.This motivates studying the total number of clusters, N clusters , reconstructed in each event by thetrack-finding algorithm. This observable is independent of details of the track-finding algorithm sinceit depends neither on the ε parameter value nor on other free parameters of the classification algorithm.Note that in all following discussion, only events in which an interaction region has been detected areconsidered. Figure 11 compares the distribution of N clusters in data with the predictions of the three geant4 simulation models for incoming π − -mesons with energies of 2 and 10 GeV. The data aredescribed well by the simulation albeit being slightly shifted towards higher values.12igure 12 shows the dependence of the average number of clusters, (cid:104) N clusters (cid:105) , on the beam energyfor data and the simulation models. The predictions of the models are systematically below data at allenergies. The largest deviation is about 7%. The agreement tends to improve with increasing beamenergy and is best at 10 GeV. clusters N E n t r i e s ( no r m a li s ed t o un i t y ) - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (a) clusters N E n t r i e s ( no r m a li s ed t o un i t y )
10 GeV FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (b)
Figure 11:
Number of clusters for energies of 2 GeV (a) and 10 GeV (b) of the beam energy. Only events for which aninteraction region has been detected have been included. Other details follow those of Fig. 7.
Beam energy [GeV] > c l u s t e r s < N FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC
CALICE
Figure 12:
The average number of clusters (cid:104) N clusters (cid:105) as a function of the beam energy. Other details follow those ofFig. 8. The N tracks distributions are given in Fig. 13 for data and the three simulation models for energiesof 2 and 10 GeV of the incoming π − -mesons, respectively. Data and simulation are in good agreement,although at 10 GeV the simulation predicts a narrower spread in N tracks than data.13igure 14 shows the dependence of (cid:104) N tracks (cid:105) on the beam energy for data and the simulation models.With increasing beam energy the centre-of-mass energy available for the π -tungsten scattering increaseswith the square-root of the beam energy according to fixed target kinematics. It is therefore expectedthat the number of outgoing tracks increases correspondingly. This is indeed observed in data andsimulation. The approximately linear increase at smallest energies flattens out towards higher beamenergies. The extension of the interaction zone also increases with energy, see for example Sec. 5.2.This makes it more and more difficult to reconstruct clean tracks in the finite volume of the Si-WECAL. The simulation models are in agreement with the data at beam energies of 2 GeV and 10 GeVand underestimate the number of secondary tracks by up to 7% at intervening energies. tracks N E n t r i e s ( no r m a li s ed t o un i t y ) - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (a) tracks N E n t r i e s ( no r m a li s ed t o un i t y )
10 GeV FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (b)
Figure 13:
Number of secondary tracks for energies of 2 GeV (a) and 10 GeV (b) of the beam energy. Other detailsfollow those of Fig. 11.
Beam energy [GeV] > t r a cks < N FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC
CALICE
Figure 14:
The average number of secondary tracks (cid:104) N tracks (cid:105) as a function of the beam energy. Other details followthose of Fig. 8. .5. Number of hits per track The number of hits per track N thits is an essential characteristic of the reconstructed tracks. Thehistograms of N thits for 2 and 10 GeV beam energy are shown in Fig. 15. The distributions obtainedfor data and Monte Carlo are in good agreement with each other.Figure 16 shows the dependence of (cid:104) N thits (cid:105) on the beam energy for data and the simulation models.Data and simulation agree within 5%. For energies greater than 4 GeV all simulation models are,however, systematically above the data. Note that the average number of hits slightly decreases withincreasing energy. The increasing size of the interaction zone limits the space available for trackreconstruction. This observation is, therefore, consistent with the flattening of the number of tracksobserved in Sec. 5.4. thits N E n t r i e s ( no r m a li s ed t o un i t y ) - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (a) thits N E n t r i e s ( no r m a li s ed t o un i t y )
10 GeV FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (b)
Figure 15:
Number of hits per reconstructed track for energies of 2 GeV (a) and 10 GeV (b) of the beam energy. Otherdetails follow those of Fig. 11. eam energy [GeV] > h i t s t < N FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC
CALICE
Figure 16:
The average number of hits per reconstructed track (cid:10) N t hits (cid:11) as a function of the beam energy. Other detailsfollow those of Fig. 8. Due to the high granularity of the Si-W ECAL further tracking observables such as the polar( θ ) and azimuthal ( φ ) angles of secondary tracks become available. Both angles are measured in theright-handed coordinate frame defined in Sec. 3.1 with θ measured relative to the z -axis. The trackdirection is calculated from the position of the first and the last hit of the track along the z -axis.Figures 17 and 18 display histograms of the φ and θ angles, respectively, for 2 and 10 GeV datatogether with corresponding corresponding results from simulation models. When corrected for thestaggering of the detector layers in x [4], the pad coordinates of the Si-W ECAL define a grid witha step width of about 1 cm in the lateral direction. This leads to a discretisation of the measuredtrack direction. In particular, in the case of the azimuthal angle φ , values that are a multiple of π / φ is isotropic as expected. The bulk of the tracks arescattered in polar angles θ less than π / θ angle, (cid:104) θ (cid:105) , which can be interpreted as a measure of the collimationof the secondary particles, is shown in Fig. 19 as a function of the beam energy. Here tracks withpolar angles smaller than π / (cid:104) θ (cid:105) has only a weak dependence onthe beam energy but shows the tendency to decrease with increasing energy as expected due to theincrease of the boost transferred to the secondary particles. The simulation models reproduce the datawithin a few percent, albeit the boost is less visible.16 [rad] f E n t r i e s ( no r m a li s ed t o un i t y ) - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (a) [rad] f E n t r i e s ( no r m a li s ed t o un i t y )
10 GeV FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (b)
Figure 17:
Comparison of the azimuthal angle φ of secondary tracks for energies of 2 GeV (a) and 10 GeV (b) of theincoming π − -mesons. Other details follow those of Fig. 11. [rad] q E n t r i e s ( no r m a li s ed t o un i t y ) - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (a) [rad] q E n t r i e s ( no r m a li s ed t o un i t y )
10 GeV FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double
CALICE (b)
Figure 18:
The polar angle θ of secondary tracks for energies of 2 GeV (a) and 10 GeV (b) of the incoming π − -mesons.Other details follow those of Fig. 11. eam energy [GeV] > [ r ad ] q < FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC
CALICE
Figure 19:
The truncated mean polar angle (cid:104) θ (cid:105) of secondary tracks as a function of the beam energy. Only tracks withpolar angles less than π / have been selected. Other details follow those of Fig. 8. At energies relevant for this study, the secondaries that create sizeable tracks cross the detectorvolume behaving in a similar manner to minimally ionising particles. This fact may be exploited as anin situ calibration of the detector, or at least to monitor the response of individual detector regions.For this specific study the selection criteria of events and tracks are modified as follows: • events are required to have more than one track and an interaction region to suppress soft inelasticscattering interactions at lower energies; • reconstructed tracks must have a length l ≥ l/N hits > . • Reconstructed tracks must have a polar angle θ < . E tdep for beam energies of 2and 10 GeV. Both distributions peak at around 1 MIP as expected for straight MIP-like tracks. Theoverlaid fit is a Landau distribution convolved with a Gaussian resolution function, describing the datawell. The tighter selection criteria reduce considerably the event sample at 2 GeV. As a consequence,the statistical uncertainty of the fit is large for the 2 GeV sample.Figure 21 presents the dependence of the most probable value (MPV) of the energy deposition insecondary tracks on beam energy. The MPV is about 1.05, which is compatible with the fact that theselected tracks cross the detector pads at a small angle. It can be seen that the detector response isboth uniform within 1–2% for the analysed energy range in data and reproduced by the simulationmodels within 1–2%. 18 [MIP] tdep E E n t r i e s ( no r m a li s ed t o un i t y ) - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double Fit
CALICE (a) [MIP] tdep E E n t r i e s ( no r m a li s ed t o un i t y )
10 GeV FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC bkg - p QGSP_BERT double bkg - p FTFP_BERT double bkg - p QBBC double Fit
CALICE (b)
Figure 20:
Energy deposition by secondary tracks observed in data (points with error bars) and for the three simulationmodels for beam energies of 2 GeV (a) and 10 GeV (b). The spectra are fit by the convolution of a Landau distributionwith a Gaussian resolution function. The double π − -meson background for the three models is shown by the grey dashed,dotted and dash-dotted histograms, respectively. All histograms are normalised to unity. Error bars represent statisticaluncertainties only. Beam energy [GeV] [ M I P ] t dep M o s t p r obab l e E FNAL 2008 - p QGSP_BERTFTFP_BERTQBBC
CALICE
Figure 21:
MPV of the Landau fit to the E t dep distributions of the ‘pencil-like‘ secondary tracks as a function of the beamenergy for π − data (black points with error bars) in comparison to the three simulation models. Error bars representthe statistical fit uncertainty. The algorithm has selected particles with approximately minimally ionising behaviour. The uniformresponse supports the idea that the secondary tracks can be used for the in situ monitoring of thecalibration. 19 . Summary and outlook
This study reveals the large potential of the CALICE Si-W ECAL physics prototype to obtaina detailed picture of the interactions of hadrons with matter. The article describes basic ideas andthe application of a new simple track-finding algorithm for the Si-W ECAL. This algorithm allowsfor the reconstruction of tracks produced by secondary particles created in the interaction of hadronswith the absorber material, and hence to study the interaction region of hadron showers in the Si-WECAL. The track-finding algorithm produces a new set of observables, based on reconstructed tracksof secondary particles and the interaction region of the hadronic cascades.Data recorded in test beams at FNAL in 2008 using π − -mesons with energies between 2 and10 GeV are compared with predictions from the simulation models qgsp bert , ftfp bert and qbbc as implemented in geant4 Version 10.1. The agreement between data and simulation varies withbeam energy and the chosen physics observable. In most cases data and simulation models agreewithin 10% without revealing a clear preference for one of the chosen simulation models.The largest discrepancy between data and the simulation models is observed for the depositedenergy in and the radius of the interaction region. The measured energy deposition in the interactionregion is up to 15% higher than predicted by the Monte Carlo simulation. The distributions of thenumber of secondary tracks and the number of hits per track for data are described well by thesimulation models. The distribution of the polar angle of the reconstructed tracks in the simulationagrees with data within 3–4 % and the distribution of azimuthal angles is reproduced well by thesimulation models in spite of the non-trivial detector geometry.Future work should aim at transferring the insights about the interaction region and the secondariesemerging from it to the optimisation of Particle Flow Algorithms.A tighter track selection leads to long tracks by particles that show approximately minimallyionising behaviour. The detector response determined using these tracks is stable to about 1–2% overthe tested energy range and shows good agreement with simulation. This observation can be exploitedas a starting point for a feasibility study of an in situ calibration (or at least a regular monitoring ofthe detector) by means of the selected tracks.
Acknowledgements
We gratefully acknowledge the DESY, CERN and FNAL managements for their support and hos-pitality, and their accelerator staff for the reliable and efficient beam operation. This work was sup-ported by the FWO, Belgium; by the Natural Sciences and Engineering Research Council of Canada;by the Ministry of Education, Youth and Sports of the Czech Republic; by the P2IO LabEx in theframework ’Investissements d’Avenir’ managed by the French National Research Agency (ANR) un-der Grant Agreements ANR-10-LABX-0038 and ANR-11-IDEX-0003-01; by the ’Quarks and Leptons’Programme of CNRS/IN2P3 France; by the Alexander von Humboldt Stiftung (AvH), Germany; bythe Bundesministerium f¨ur Bildung und Forschung (BMBF), Germany; by the Deutsche Forschungs-gemeinschaft (DFG), Germany; by the Helmholtz-Gemeinschaft (HGF), Germany; by the I-COREProgram of the Planning and Budgeting Committee, Israel; by the Nella and Leon Benoziyo Centerfor High Energy Physics, Israel; by the Israeli Science Foundation, Israel; by the National ResearchFoundation of Korea; by the Korea-EU cooperation programme of National Research Foundation ofKorea, Grant Agreement 2014K1A3A7A03075053; by the Netherlands Organisation for Scientific Re-search (NWO); by the Science and Technology Facilities Council, UK; by the Nuclear Physics, ParticlePhysics, Astrophysics and Cosmology Initiative, a Laboratory Directed Research and Developmentprogram at the Pacific Northwest National Laboratory, USA.
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