Impact of the choice of physics list on GEANT4 simulations of hadronic showers in tungsten

Transcription

1 CERN - European Organization for Nuclear Research LCD-Note Impact of the choice of physics list on GEANT4 simulations of hadronic showers in tungsten P. Speckmayer CERN, Switzerland February 12, 2010 Abstract The development of pion induced showers in a large block of matter (tungsten, lead, iron) is simulated for pions from 1 to 50 GeV. Two GEANT4 physics lists (QGSP BERT and QGSP BERT HP) are compared. The deposited energy at each step of the simulation is identified as visible, invisible or escaped. It will be shown, that for tungsten in most of the hadronic showers more than 90% of the energy is deposited visibly if QGSP BERT is used. This fraction drops to only 0% for QGSP BERT HP. The latter fraction is similar to lead, even when QGSP BERT is used for the simulation. The impact of this behaviour on the energy resolution of a sampling calorimeter with scintillator as active material is shown. Although more energy is deposited visibly for QGSP BERT than for QGSP BERT HP, the reconstructed energy resolution is about 5 to 10% percent better for the latter.

2 1 Introduction The development of pion showers in a large block of matter are simulated for pions from 1 to 50 GeV. The showers are fully contained and analysed on the step level of the simulation 1). The deposited energy is categorized into visible, invisble and escaped energy (see 2).The ratio of visible energy to the energy of the incoming particles is shown. The main aim of this study is to assess the beaviour of the two physicslists QGSP BERT and QGSP BERT HP for tungsten. Lead is chosen for comparison since it is a high-z material (as tungsten) which has been used in hadronic calorimeters before and where Monte Carlo simulation to data comparisons have been undertaken and the simulation has been validated. Iron has been used as material with a Z much below those of tungsten for the comparison of exemplary events. 2 Definitions The energy deposits of each simulation step have been recorded and classified in three types: visible energy denotes energy which is deposited by ionization 2). escaped energy is the energy of particles which leave the world volume 3). invisible energy is energy which is deposited due to other processes than ionization. Typically invisible energy deposits are the binding energy of atomic nuclei which are broken up by strong interactions. 3 Simulation setup For the simulation the software framework model Mokka[1] (version 0-0 patch03) was used. The detector simulation was performed using GEANT4[2, 3] (version 9.1, patch01). A particle gun 4) has been placed in the center of a block of tungsten or lead with the dimensions m 3 where 5 m of tungsten correspond to about 50 nuclear interaction lengths. Tenthousand π + with energies in the range from 1 to 50 GeV have been emitted in z-direction. The two physics-lists 5) QGSP BERT and QGSP BERT HP have been chosen for the simulation. QGS is the abbreviation of quark gluon string[4] model, P stands for precompound, BERT for Bertini cascade model[5, ] and HP indicates, that a high precision neutron tracking model is used. QGSP BERT has been chosen, since it is recommended by the GEANT4- collaboration[] ) for calorimetry in high energy physics. QGSP BERT HP has been chosen to 1 A step is the smallest unit of simulation. Each step is limited by a physics process. The deposited energy and the energies of the primary and the secondary particles are known. 2 Note, that visible energy does not imply, that this energy deposit can be measured. Only visible energy which is deposited in active calorimeter layers (e.g. scintillator layers) can be measured. In the first set of the simulation setup no active layers are forseen. 3 Spatial limit of the simulation. 4 A virtual source for particles in GEANT4 simulation. Direction, energy and particle type of the emitted particle can be chosen freely by the user. 5 A physics-list is a consistent set of physical processes which describe the interaction of particles with matter[2]. Recommendation from

3 10k π +, tungsten, QGSP_BERT E visible /E π +,beam E π +,beam [GeV] Figure 1: The hadronic shower development of 10k π + in tungsten, simulated using the physicslist QGSP BERT. The fraction of the visibly deposited energy divided by the true energy of the incoming particles is shown as a function of the true, total energy of the incoming particles. The colour palette indicates the number of events in the respective bins. compare the default treatment of neutrons with a high precision neutron tracking model for the tungsten case. 4 Simulation Results 4.1 Tungsten, simulated with QGSP BERT In figure 1 the fraction of the visible energy divided by the true energy of the incoming particle is shown as a function of the true particle energy. Three areas can be distinguished in the plot. The first from 1 GeV up to around 10 GeV, the second from 10 GeV up to 25 GeV and a third starting from 12.5 GeV up to 50 GeV. These regions correspond to the three dominant physics models in the QGSP BERT physics list. The Bertini cascade (BERT) is applied up to around 10 GeV, the low energy parametrization (LEP) is used from 10 GeV up to around 25 GeV and the quark gluon string (QGS) model is applied above 12.5 GeV. There is a small transition region between BERT and LEP and a larger one between LEP and QGS. In these transition regions one of the models is chosen at random to compute the interaction with matter. The steps which can be seen between the models are thus clearly non-physical artefacts of the simulation. A second feature of the simulation of tungsten with QGSP BERT is the high fraction of visibly deposited energy. In the BERT and the QGS region, almost all of the showers deposit more than 3

4 E visible /E π +,beam 10k π +, lead, QGSP_BERT E π +,beam [GeV] Figure 2: The hadronic shower development of 10k π + in lead have been simulated with the physics-list QGSP BERT. The fraction of the visibly deposited energy divided by to the true total energy of the incoming particles is shown as a function of the true energy of the incoming particles (E π +,beam). The color encoding shows the number of particlesin the respective bins. 90% of their energy by ionization (visibly), which seems unlikely for a high-z material such as tungsten. 4.2 Lead, simulated with QGSP BERT Similarly to tungsten, lead is a high-z material. Lead has been used frequently in calorimeters and the interaction of hadrons with lead has been studied in more detail than with tungsten. Hence, in this study lead has been chosen for comparison. Figure 2 shows the fraction of the visibly deposited energy devided by the true energy of the incoming particles as a function of the true particle energies for lead. It can be seen, that compared to tungsten the distribution of the fraction of visible divided by true energy is much broader. While the fraction is above 90% for tungsten it is only above around 0% for lead (rising with larger true energies). The clear steps between the BERT, LEP and QGS region in tungsten can barly be seen in lead. The simulations with lead suggest, that the result of the simulation of tungsten is non-physical and cannot be trusted. 4

5 E visible /E π +,beam 10k π +, tungsten, QGSP_BERT_HP E π +,beam [GeV] Figure 3: The hadronic shower development of 10k π + in tungsten have been simulated with the physics-list QGSP BERT HP. The fraction of the visibly deposited energy divided by to the true total energy of the incoming particles is shown as a function of the true, total energy of the incoming particles. The color encoding shows the number of particles. 4.3 Tungsten, simulated with QGSP BERT HP At strong interactions of hadrons with tungsten nuclei typically many neutrons emerge. The reason for the large deviation of the visible energy in tungsten from the range expected from simulations with lead can be attributed to an incorrect treatment of the neutrons. This can be shown by simulating with the QGSP BERT HP physics-list, where a high precision neutron tracking model is used. In figure 3 the fraction of visible deposited energy divided by the true energy of the incoming particles as a function of the true particle energies is shown for tungsten. Unlike the visible energy fraction of tungsten simulated with QGSP BERT, using the high precision model (QGSP BERT HP) the width of of the visible energy fraction is broad (above 0%) and thus in the same range as for lead. 5 Analyis Looking at the energies deposited at each step of the GEANT4 simulation one can observe that the difference of the visibly deposited energy mainly originates from the number of neutrons which are captured in the absorber material. In tungsten the number of neutrons which are created is similar, but many more neutrons are captured with QGSP BERT than with QGSP BERT HP. The reason for this is a less accurate description of the cross section for neutron capture in 5

6 QGSP BERT where the high precision neutron tracking model is not used. Each of these neutron captures produces two photons with a sum of roughly 8 MeV. Although this is only a small amount of energy compared to the beam energies in the range of several GeV, the large number of neutrons leads to a considerable impact on the visible energy. At strong interactions of hadrons with the nuclei of the matter, neutrons are set free. The binding energy which is used to free these neutrons contributes to the invisible energy and cannot be measured. But if such a neutron is later captured by a nucleus, the binding energy is used to create two photons. In that case the invisible energy is transformed back to visible energy and could in principle be measured again. 5.1 Exemplary events On the basis of the analysis of exemplary single pion events, the difference between the high precision neutron tracking and the default treatment of neutrons is shown: In an event where the shower development of one 4 GeV pion in tungsten was simulated with QGSP BERT a total energy of 1205 MeV was created at the production of photons due to neutron capture. This can be compared to only 11 MeV which were created in one 4 GeV pion shower simulated with QGSP BERT HP. For comparison lead and iron were simulated with QGSP BERT. There, photons with 232 MeV total energy (lead) and 38 MeV were created (iron). All other stages of the shower development (e.g. first strong interaction) have been compared as well, but the deviation of the amount of visible and invisible energy deposited there in tungsten, lead and iron was small compared to the effect seen with the neutron capture process. 5.2 Effect of physics list differences on the reconstructed energy resolution In the simulations described above, a large block of matter was considered where the full hadronic shower was contained. The deposited energy at each step of the simulation is known. There, visible, invisible and escaped energy can be defined. However to measure the visible energy readout-elements have to be present. In a sampling calorimeter, layers of the passive absorber material are interleaved with layers of active material (typically light material such as scintillator or gas). The amount of energy which is measured depends therefore on the ratio of the visible energy deposited in the active material compared to the total deposited energy in active and passive layers. From the measured energy, the true energy of the incoming hadrons can be estimated. For the energy reconstruction the energy and topology of the hadronic shower have been used[8]. The mean escaped energy in the simulations presented here is about 1% of the energy of the incoming particle. Figure 4 shows the energy resolution which has been obtained depending on the physics-list which has been used for simulation. It can be seen, that the energy resolution for the simulations done using the high precision neutron tracking (QGSP BERT HP) is (almost) always slightly better by about 5 to 10%. The difference is getting smaller for thicker passive layers.

7 E true =[3,43]GeV /E true ) reco RMS 90 (E E true =40±3 GeV physics-list material w passive QGSP_BERT tungsten 1.5 cm QGSP_BERT_HP tungsten 1.5 cm QGSP_BERT tungsten 1.0 cm QGSP_BERT_HP tungsten 1.0 cm QGSP_BERT tungsten 0.5 cm QGSP_BERT_HP tungsten 0.5 cm length [cm] Figure 4: Effect of the differences of QGSP BERT and QGSP BERT HP on the reconstructed energy resolution. The graphs with filled markers are obtained with QGSP BERT and the graphs with non-filled markers are obtained with QGSP BERT HP. The numbers above the markers (,, 8, 9) denote the length of the calorimeter in units of nuclear interaction length of the calorimeter material. The energy resolution for the simulations done with QGSP BERT HP are (almost) always slightly better than of those done with QGSO BERT. The difference is about 5 to 10%, getting smaller for thicker passive layers. At λ calorimeter length for a passive layer thickness of 1.5 cm the resolution obtained with QGSP BERT HP is actually slightly worse than that obtained with QGSP BERT. This deviation from the general behaviour can be attributed to the limited statistics used for training the neuronal network and for the evaluation of the particular energy ranges[8]. The worse energy resolution in the case of QGSP BERT can be explained with the relatively frequent neutron capture which takes place farther away from the core of the shower and spatially weakly correlated with the shower development. This halo of relatively low energetic photons which is produced changes the shower topology slightly. This impacts negatively on the predictive quality of the variables used to describe the shower topology[8]. Summary and Conclusions Using GEANT4 It has been shown, that for tungsten in most of the hadronic showers more than 90% of the energy is deposited visibly if QGSP BERT is used. This fraction drops to only 0% for QGSP BERT HP. The latter fraction is similar to simulations for lead using QGSP BERT. The neutron capture process has been identified as the reason for this difference of the simulations with two physics lists. The evaluation of the two physics lists on the energy resolution

8 of a sampling calorimeter with scintillator as active material show, that although more energy is deposited visibly for QGSP BERT than for QGSP BERT HP, the reconstructed energy resolution is about 5 to 10% percent better for the latter. The amount of visibly deposited energy with QGSP BERT is unphysically high for tungsten and the agreement of the QGSP BERT HP simulations of tungsten agree qualitatively with the better validated QGSP BERT simulations of lead. It is therefore recommended to use QGSP BERT HP for tungsten calorimeter simulations although considerably more computing time is necessary for the simulations. A validation of the simulations of hadronic showers in tungsten using a prototype calorimeter in a testbeam is necessary. Acknowledgements I want to thank the GEANT4-team for their explanations of the details of the physics lists and their underlying models. Many thanks as well for the fruitful discussions with Wolfgang Klempt and his help with the analysis of the verbose output of GEANT4. References [1] P. Mora de Freitas and V. H. Detector Simulation with Mokka/Geant4 : Present and Future. In International Workshop on Linear Colliders (LCWS 2002). JeJu Island, Korea, [2] S. Agostinelli et al. Geant4 A Simulation Toolkit. Nucl. Instrum. Methods Phys. Res., Sect. A, vol. 50(3) pp , [3] J. Allison et al. Geant4 developments and applications. IEEE T. Nucl. Sci., vol. 53(1) pp , 200. [4] G. Folger and J. P. Wellisch. String parton models in Geant4. In CHEP-2003-MOMT008. La Jolla, California, [5] H. W. Bertini. Low-energy intranuclear cascade calculation. Phys. Rev., vol. 131(4) pp , 193. [] A. Heikkinen, N. Stepanov, and J. P. Wellisch. Bertini intra-nuclear cascade implementation in Geant4. In CHEP-2003-MOMT008, vol. MOMT008. La Jolla, California, [] The GEANT4 collaboration. GEANT4, recommended physics lists. Website: geant4.org/geant4/support/physicslists/referencepl/usecases.shtml, [8] P. Speckmayer and C. Grefe. Comparison of performance of hadronic tungsten and steel sampling calorimeters. LCD-Note ,