ARTICLE IN PRESS. Nuclear Instruments and Methods in Physics Research A

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1 Nuclear Instruments and Methods in Physics Research A 66 (29) 7 77 Contents lists available at ScienceDirect Nuclear Instruments and Methods in Physics Research A journal homepage: Test of hadronic interaction models in GEANT4 at low energy using the BESIII data G.F. Cao a,b,,m.he a, H.M. Liu a, Z.Y. Deng a, Y. Yuan a, Y.T. Liang c, C.D. Fu a, Y. Liu a,b, C. Zhu a,b, W.D. Li a, Z.P. Mao a, K.L. He a a Institute of High Energy Physics, CAS, Beijing 49, China b Graduate University of Chinese Academy of Sciences, Beijing 49, China c Peking University, Beijing 1871, China article info Article history: Received 21 February 29 Received in revised form 24 March 29 Accepted 17 April 29 Available online 3 May 29 Keywords: Hadronic interaction Detector simulation GEANT4 BESIII abstract Using the experimental data recently collected at BESIII, we compare hadronic shower energy, profile and fake photons in the electromagnetic calorimeter with several hadronic models in GEANT4. We find that for pions and protons at low energy (o:7 GeV) the Bertini model with high precision neutron tracking (_HP) is the best among the hadronic models compared, though it takes more simulation time. For anti-proton, the GEANT4 simulation generates more annihilation than experimental data. & 29 Elsevier B.V. All rights reserved. 1. Introduction While the electromagnetic interaction is well understood and can be successfully simulated in some well-known Monte Carlo softwares, such as EGS [1], GEANT3 [2], GEANT4 [3], etc., the hadronic interaction, on the other hand, has to rely on some phenomenological models because the underlying theory QCD cannot make meaningful calculations at low energy domain. It is very important to validate the models by comparing them with experimental data and make sure that no significant systematic error comes from the use of a specific model in simulation. GEANT4 is a powerful simulation toolkit both for detector description and particle interaction. It provides many hadronic models for users to choose or combine based on incident particle type and its energy range. Among them there are three categories, data driven, theory driven, and parameterization driven models, available for different applications. Physics validation with GEANT4 has been carried out by many experiments, for instance, the four experiments at LHC [4], HARP [5], and BABAR [6]. However, most of these tests focus at high or intermediate energies ð45 GeVÞ. In this paper, we report the comparisons of GEANT4 hadronic models and the experimental Corresponding author at: Institute of High Energy Physics, CAS, Beijing 49, China. Tel.: ; fax: addresses: caogf@mail.ihep.ac.cn, cgf1122@sohu.com (G.F. Cao). data taken with the new BESIII detector [7] operating at the upgraded Beijing electron positron collider (BEPCII). For hadrons (most of them with momentum less than 1:8 GeV=c) produced at BESIII, the energy deposition, shower profile and fake photons produced in the calorimeter in data and Monte Carlo are presented, and simulation speeds of these models are also compared. The information is very helpful and useful not only for us to choose a best hadronic model in our experiment but also for developers to improve the models in the future. 2. The detector, simulation system and hadronic models The BESIII detector is a conventional solenoidal magnetic spectrometer that is described in detail in Ref. [7]. The main parts of the detector, from inner to outer, are beam pipe, main drift chamber (MDC), the time of flight (TOF) scintillation counters, the electromagnetic calorimeter (EMC), the super-conducting magnet coil, and the muon counter (MUC). The calorimeter (EMC) consists of 624 thallium-doped CsI crystals which are distributed at the barrel and two end-cap sections, covering 93% of 4p solid angle. There are a total of 44 rings of crystals along the beam direction (z-axis) in the barrel, each with 12 crystals, and six rings along radial direction in each end-cap, with different number of crystals in each ring. Each barrel crystal has a length of 28 cm (15X ), with a frontal face of 5 cm 5 cm and a rear face of 6:5cm 6:5 cm /$ - see front matter & 29 Elsevier B.V. All rights reserved. doi:1.116/j.nima

2 G.F. Cao et al. / Nuclear Instruments and Methods in Physics Research A 66 (29) Table 1 Physics lists and hadronic models. Physics lists p Proton Anti-proton BERT ( 4 GeV) BIC ( 4 GeV) CHIPS ( 4 GeV) _HP BERT ( 9.9 GeV) BERT ( 9.9 GeV) LE_GHEISHA ( 25 GeV) BERT ( 9.9 GeV) BERT ( 9.9 GeV) LE_GHEISHA ( 25 GeV) LE_GHEISHA ( 25 GeV) BIC ( 9.9 GeV) LE_GHEISHA ( 25 GeV) LE_GHEISHA ( 25 GeV) LE_GHEISHA ( 25 GeV) LE_GHEISHA ( 25 GeV) Events/.2 (GeV/c) 1 (π + ) Events/.2 (GeV/c) 1 (π - ) Events/ p (GeV/c) 4 (π + ) Events/.4 p (GeV/c) 4 (π - ) cos θ cos θ Fig. 1. Momentum and polar angular distributions of pions from cð2sþ!p þ p J=cðJ=c! e þ e Þ. Dots with error bars are data, and histograms are Monte Carlo (). Monte Carlo samples are normalized to the number of events in data. The time window of EMC electronics is 3 ms. The designed energy and position resolutions are 2.5% and 6 mm for gamma or electron at 1 GeV in barrel part, which plays an important role for physics study [8] at BESIII. The BESIII object-oriented simulation tool (BOOST) [9] was developed based on GEANT4 and is being tuned by experimental data. The geometry, material and magnetic field of the detector are well described in BOOST, the signal response (digitization) in each sub-detector, trigger simulation and background mixing are also seriously considered. With event generators and background data taken with random trigger, billions of Monte Carlo events have been generated for Monte Carlo tuning and physics study. For the time being, the comparisons of data and Monte Carlo are generally satisfactory. The GEANT4 toolkit provides or recommends several particle detector interaction packages (physics lists in GEANT4 s terminology) for different applications, users can choose one of them, combine them or even build their own based on the particle type and its energy range. A set of physics lists together with hadronic models used at low energy range are listed in Table 1. It should be pointed out that the same packages to simulate electromagnetic interaction and particle decay are used in all the physics lists, and the GEANT4 version used in this work is GEANT4.9. with patch 1 released in August 27. The parameterized LE_GHEISHA model is a modified version of the GHEISHA package used in GEANT3. The Bertini cascade (BERT) [1] and the binary cascade (BIC) [11] models are two theory-driven models. The high precision model (data driven, suffixed with HP), is specially designed for low energy neutron ðo2 MeVÞ tracking in detector. More detailed information about these models can be found in Ref. [12]. In this paper, all the physics lists (hadronic models) listed in Table 1 are compared with data. 3. Data samples and electromagnetic interaction validation Since the start of commissioning run in August 28, more than 1 M cð2sþ events have been collected with BESIII detector at

3 72 G.F. Cao et al. / Nuclear Instruments and Methods in Physics Research A 66 (29) 7 77 Events/.2 (GeV/c) (p) 1 5 Events/.2 (GeV/c) (p) p (GeV/c) p (GeV/c) (p) 4 (p) Events/ Events/ cos θ cos θ Fig. 2. Momentum and polar angular distributions of proton and anti-proton from cð2sþ!p þ p J=cðJ=c! p pþ. Dots with error bars are data, and histograms are Monte Carlo (). Monte Carlo samples are normalized to the number of events in data _HP Events/.2 Events/.2 Events/.2 Events/.2 Events/ _HP Events/.4 Events/.4 Events/.4 Events/.4 Events/ _HP _HP Fig. 3. Comparison between data (dots with error bars) and models (histograms) for electrons from cð2sþ!p þ p J=cðJ=c! e þ e Þ. Monte Carlo samples are normalized to the number of events in data.

4 G.F. Cao et al. / Nuclear Instruments and Methods in Physics Research A 66 (29) Events/ Events/ _HP Events/.2 8 _HP Events/.4 1 _HP _HP Events/ Events/ Events/ Events/ Events/ Events/ Fig. 4. Comparison between data (dots with error bars) and models (histograms) for positrons from cð2sþ!p þ p J=cðJ=c! e þ e Þ. Monte Carlo samples are normalized to the number of events in data. pffiffi BEPCII operating at cð2sþ resonance ð s ¼ 3:686 GeVÞ. The detector is calibrated using the Bhabha events ðe þ e! e þ e Þ at cð2sþ, and all the events from the data are fully reconstructed by the offline software [13]. In this paper, we use the information from the barrel calorimeter to compare the hadronic interaction between data and Monte Carlo, because currently the end-cap parts are not well calibrated due to the large beam related background. We select p, proton and anti-proton from the physics channels cð2sþ!p þ p J=cðJ=c! e þ e Þ and cð2sþ!p þ p J= cðj=c! p pþ. Because the sample purity is of the top priority, we apply stringent selection criteria without considering too much about the loss of efficiency. The purity of selected events is studied by comparing with a Monte Carlo sample of 2 M inclusive cð2sþ events, for cð2sþ!p þ p J=cðJ=c! e þ e Þ and cð2sþ! p þ p J=cðJ=c! p pþ, the background event levels are about.1% and.7%, respectively. For each physics channel and each physics list in Table 1, 3 Monte Carlo simulated events (mixed with real background) are generated. Like the real data, all the Monte Carlo raw data are reconstructed, and then selected with the same selection criteria. For data and Monte Carlo, the momentum (p) and polar angular (cos y) distributions of selected hadrons are shown in Figs. 1 and 2. Since different physics lists used in simulation give very similar distributions, we just use the simulated results in these two figures. We first compare the electromagnetic interaction between data and Monte Carlo by using the electrons and positrons (energy around 1.5 GeV) selected from cð2sþ!p þ p J=cðJ=c! e þ e Þ. The following four observable variables are chosen to characterize the behavior of a charged track in calorimeter: (1) Energy deposited in 5 5 crystals (matrix) around the seed in a shower, denoted by E5 5, where the seed is the crystal with the maximum energy in this shower, and a shower is defined as a cluster of crystals with energy deposition over a threshold (1 MeV). (2) Ratio of energy deposited in the seeded crystal and in 3 3 crystals around the seed, denoted by Eseed=E3 3, where E3 3 means the energy deposited in 3 3 crystals around the seed. (3) Ratio of energy deposited in 3 3 and 5 5 crystals around the seed, denoted by E3 3=E5 5. (4) Angle ðy fc Þ between a fake photon and a charged track. The vertex subtended by the angle is initial e þ and e interaction point. A shower is defined as a fake photon if it

5 74 G.F. Cao et al. / Nuclear Instruments and Methods in Physics Research A 66 (29) (χ 2 = 7.2) Events/.2 Events/.2 (χ 2 = 9.44) Events/.6 Events/ (χ 2 = 6.59) _HP _HP _HP (χ 2 = 9.) (χ 2 = 6.58) 3 (χ 2 = 8.9) Events/.2 Events/.2 (χ 2 = 8.32) Events/ (χ 2 = 1.9) (χ 2 = 22.78) 3 (χ 2 = 11.6) 2 (χ 2 = 9.11) (χ 2 = 8.94) Events/ (χ 2 = 18.15) Events/.6 Events/ (χ 2 = 3.13) (χ 2 = 5.73) (χ 2 = 7.83) _HP (χ 2 = 6.22) 8 (χ 2 = 1.24) (χ 2 = 17.33) (χ 2 = 2.1) Fig. 5. Comparison between data (dots with error bars) and models (histograms) for p þ from cð2sþ!p þ p J=cðJ=c! e þ e Þ, Monte Carlo samples are normalized to the number of events in data. does not match any charged tracks from MDC. For instance, y gp denotes the angle between a fake photon and a negatively charged pion. We use two variables (Items (2) and (3)) to describe the shower profile or transverse development in the calorimeter. In the BESIII experiment, some physics photons at very low energy (around several tens MeV) cannot be easily distinguished from fake photons. Most fake photons are produced from electronic noise and background, we have considered these in our simulation. These appear as a continuum background in the y fc distribution. There are still some fake photons from the splitting of hadronic showers, especially, when a hadronic shower scatters or spreads widely. These may appear as a peak in the small-angle part of the y fc distribution. If a splitting of a hadronic shower is misidentified as a physics photon, it is harmful to physics analysis. We usually use the angle cut ðy fc Þ to discard fake photons around the hadron track. The comparison results for electrons and positrons are presented in Figs. 3 and 4. The deposited energy in 5 5 crystals ðe5 5Þ is lower than the energy of the electron (around 1.5 GeV), because of energy leakage out of the crystals. We fit the electron energy spectrum in E5 5 with a Gaussian, the mean and width are and.78 GeV for data, and different simulations give almost same results and.83 GeV. We fit the electron E3 3=E5 5 distribution with a Novosibirsk function, the peak position and width are.977 and.9 for data, and.978 and.9 for different simulations. To remove the hadronic shower contamination (may be different for data and simulation, see next section), we exclude fake photons around pions (y gp o31) in the angle distributions in Figs. 3 and 4. We see very nice agreements between data and Monte Carlo. We are not surprised that different models give similar simulated results, because electrons and positrons have only electromagnetic interaction and the same standard electromagnetic simulation package in GEANT4 is used in these models. The general agreement

6 G.F. Cao et al. / Nuclear Instruments and Methods in Physics Research A 66 (29) (χ 2 = 9.23) Events/.2 Events/ (χ 2 = 8.43) Events/ (χ 2 = 23.42) (χ 2 = 18.34) 4 _HP 8 _HP _HP _HP (χ 2 = 6.2) 6 (χ 2 = 7.39) 3 (χ 2 = 33.3) (χ 2 = 3.56) (χ 2 = 1.78) (χ 2 = 1.68) (χ 2 = 7.51) Events/.2 Events/.2 Events/ (χ 2 = 12.3).2 Events/.6 Events/ (χ 2 = 31.84) (χ 2 = 29.16) 4 (χ 2 = 15.28) 3 (χ 2 = 21.3) (χ 2 = 41.37) 2.2 (χ 2 = 14.6) Events/.6 Events/ (χ 2 = 96.29) (χ 2 = 53.37) Fig. 6. Comparison between data (dots with error bars) and models (histograms) for p from cð2sþ!p þ p J=cðJ=c! e þ e Þ, Monte Carlo samples are normalized to the number of events in data. also indicates that our simulation system with GEANT4 is reliable. 4. Comparing data with hadronic models We still use the variables defined in Section 3 to compare data with Monte Carlo for hadrons. To make the comparison quantitative, we calculate w 2 to evaluate the difference between data and Monte Carlo and put the number in each of the following plots. Figs. 5 and 6 show the comparison results for p þ and p from cð2sþ!p þ p J=cðJ=c! e þ e Þ. In the plots of y gp þ=y gp, fake photons around p =p þ (y gp =y gp þo31) are excluded. In general, different physics lists simulate the energy deposition and the profiles very well both for p þ and p, except the profile of E3 3=E5 5 for p (shown in Fig. 6) in which simulations produce smaller showers than data. The small bumps (1 MeV) in E5 5 plots mainly come from the mismatching of a charged track with a fake photon which is split from hadronic interaction, because position resolutions of MDC and EMC would get worse for low momentum charged tracks. For the angle distribution of fake photons, most of physics lists tend to produce more photons near the hadron especially for p. Actually, when a p comes to stop in detector, a capture physics process may happen, this makes the results of p little bit different from p þ. Based on the comparison results of all plots, _HP is mostly close to data, partly because the secondary neutrons produced by hadrons are well considered in simulation. For protons from cð2sþ!p þ p J=cðJ=c! p pþ, the comparison results are shown in Fig. 7. In the plots of y gp, fake photons around pions (y gp o31) are excluded. From the plots of energy deposition, we can see a peak around.21 GeV which is produced mainly by electromagnetic interaction for a proton with kinetic energy around.6 GeV, all physics lists simulate the deposited energy well except. For the shower profile, each physics list is consistent with data. For fake photons, because the proton and anti-proton are nearly back to back in the event, we see more fake photons in the anti-proton direction (around 161)

7 76 G.F. Cao et al. / Nuclear Instruments and Methods in Physics Research A 66 (29) (χ 2 = 2.65) Events/.2 Events/ (χ 2 = 1.3) Events/ (χ 2 = 1.67) (χ 2 = 17.4) _HP _HP _HP _HP (χ 2 = 2.59) 1 (χ 2 = 1.24) 4 (χ 2 = 1.46) 4 (χ 2 = 2.76) Events/ (χ 2 = 1.42) Events/.1 Events/ (χ 2 = 3.32) (χ 2 = 15.31) (χ 2 = 2.8) 1 (χ 2 = 1.25) 4 (χ 2 = 2.16) 4 1 (χ 2 = 19.38) (χ 2 = 9.35) (χ 2 = 2.42) Events/.2 Events/ (χ 2 = 1.73) Events/.1 Events/ (χ 2 = 6.6) (χ 2 = 22.4) Fig. 7. Comparison between data (dots with error bars) and models (histograms) for proton from cð2sþ!p þ p J=cðJ=c! p pþ, Monte Carlo samples are normalized to the number of events in data. due to annihilation, _HP is also the best to match data compared with other models. Fig. 8 demonstrates the behavior of anti-proton in calorimeter from cð2sþ!p þ p J=cðJ=c! p pþ. In the plots of y g p, fake photons around pions (y gp o31) are excluded. All physics lists give similar energy deposition and shower profile. The distinct disagreements between data and simulation exist in deposited energy and shower profile. From the profile plots, we find that the Monte Carlo samples produce larger showers than data. The height of simulated electromagnetic peak is lower than data, but at the range of deposited energy from.3 to.9 GeV, the Monte Carlo samples have more anti-proton annihilation than data. We notice that the same routine is used in GEANT4 to deal with the anti-proton at rest in all physics lists. There are two possibilities to explain the disagreement, one is that the crosssection for anti-proton annihilation in GEANT4 is larger than expected, the other is that the GEANT4 simulation on annihilation is imperfect. We finally compare the simulation speeds under different physics lists, the average CPU time needed to simulate one event of the two physics channels are listed in Table 2. We can see that has the highest speed and _HP is the slowest compared with other models. The test is carried out on an IBM PC (2.33 GHz/2 GB). 5. Conclusion We have presented the comparisons between data and many hadronic models in GEANT4 for hadrons (p, proton and antiproton) with kinetic energy less than.7 GeV. This work concludes that the Bertini model with high precision neutron tracking (_HP) is the best to match the experimental data though it is also the slowest to simulate events among the physics lists compared. For anti-proton, the GEANT4 simulation produces more annihilation than data, indicating that the annihilation crossing section in GEANT4 is larger or the annihilation model needs to be improved. When this work came to an end, the new GEANT4.9.2 was released in December 28. For the time being, it is very difficult for us to select pure kaon, neutron and anti-neutron samples from physics channels with high statistics. We plan to test this new

8 G.F. Cao et al. / Nuclear Instruments and Methods in Physics Research A 66 (29) Events/4MeV Events/4MeV Events/4MeV Events/4MeV Events/4MeV 15 (χ 2 = 7.33) _HP 1 (χ 2 = 1.63) (χ 2 = 9.49) (χ 2 = 9.79) (χ 2 = 9.91) Events/.2 Events/.2 Events/.2 Events/.2 Events/ (χ 2 = 8.3) 2 (χ 2 = 1.8) 6 (χ 2 = 17.28) _HP _HP 8 _HP (χ 2 = 8.1) 2 (χ 2 = 8.76) 6 (χ 2 = 7.88) (χ 2 = 9.87) 2 (χ 2 = 11.3) 6 (χ 2 = 16.73) (χ 2 = 11.25) 2 (χ 2 = 13.13) 6 (χ 2 = 2.9) (χ 2 = 8.68) Events/.2 Events/.2 Events/.2 Events/.2 Events/ (χ 2 = 8.8) (χ 2 = 24.63) Fig. 8. Comparison between data (dots with error bars) and models (histograms) for anti-proton from cð2sþ!p þ p J=cðJ=c! p pþ, Monte Carlo samples are normalized to the number of events in data. Table 2 Comparison of simulation speeds (s/event). Physics lists cð2sþ!p þ p J=cðJ=c! e þ e Þ cð2sþ!p þ p J=cðJ=c! p pþ _HP release when more and more data at BESIII are available in the near future. Acknowledgments We would like to thank the GEANT4 collaboration for their continuous development on the simulation toolkit. We also thank the staff of BEPCII/BESIII for their hard efforts to run the new machine and detector. This work is partly supported by the Natural Science Foundation of China (NSFC) under Contract numbers and References [1] H. Hirayama, et al., The EGS5 code system, SLAC-R-73, 25. [2] CERN Program Library Long Writeup W513, CERN, [3] S. Agostinelli, et al., Geant4 Collaboration, Nucl. Instr. and Meth. A 56 (23) 25; J. Allison, et al., IEEE Trans. Nucl. Sci. NS-53 (1) (26) 27. [4] V.N. Ivanchenko, A. Ivanchenko, J. Phys. Conf. Ser. 119 (28) 3226; T. Koi, et al., AIP Conf. Proc. 896 (27) 21; C. Alexa, et al., AIP Conf. Proc. 867 (26) 463; A.E. Kiryunin, et al., Nucl. Instr. and Meth. A 56 (26) 278. [5] M.G. Catanesi, et al., HARP Collaboration, Phys. Rev. C 77 (28) [6] A. Khan, K. Schofield, D. Wright, in: IEEE Nuclear Science Symposium and Conference Record, Brunel University, vol. 2, 25, p [7] Y.F. Wang, Int. J. Mod. Phys. A 21 (26) [8] D.M. Asner, et al., September 28, arxiv: [9] Zi-Yan Deng, et al., HEP & NP 3 (5) (26) 371 (in Chinese) H.M. Liu et al., BESIII detector simulation with GEANT4, in: Talk Given at 12th GEANT4 collaboration workshop, Hebden Bridge, UK, 27 hhttp://indico.- cern.ch/conferencedisplay.py?confid=1311i. [1] M.P. Guthrie, et al., Nucl. Instr. and Meth. 66 (1968) 29 A. Heikkinen, et al., in: Proceedings of 23 Conference for Computing in High-Energy and Nuclear Physics (CHEP3), La Jolla, CA, 23. [11] G. Folger, et al., Eur. Phys. J. A 21 (24) 47. [12] Geant4 physics reference manual hhttp://geant4.web.cern.ch/geant4/ UserDocumentation/UsersGuides/PhysicsReferenceManual/fo/ PhysicsReferenceManual.pdfi. [13] W.D. Li et al., The offline software for the BESIII experiment, in: Proceedings of CHEP6, Mumbai, 26.