arXiv:1202.3661v4 [astro-ph.HE] 29 May 2012 uncreain,ad arneeg pcr r studied are PACS spectra paper. energy this sum, in energy muon and, hadron of correlations, shower, size hadron muon distri- of size, number size electron shower bution, distribution, maximum, number shower muon of shower, depth viz. aeesfrpoo n rnpiaisi h nryrange energy the in primaries iron pa- and 10 (EAS) showers proton air for extensive rameters several with an 1.99, II-03 EPOS QGSJET models, interaction hadronic representative tr.Mroe,sm fteeprmtr ietemuon maximum the like shower parameters of these depth of content, the some compare Moreover, and param- EAS test eters. these to studying obser- by possible models at is interaction available particles it of Hence, number level. different vation and shapes lateral fur- are uncertainties these task. difficult of ther Estimation un- theoretical [2]. large certainties to subject hadronic is of production modeling attained multi-particle accelerator, the man-made above the by pro- understood; energy well interaction of reasonably electro-weak are modeling the cesses to While due interactions. and HE experiments in- large-scale fluctuations statistical in to volved due mainly uncertainties atic mass particles. primary arriving the the on of mea- conclusions composition with draw simulation can from one surements predictions relate the needed. to are comparing simulations But reliable By shower more air the mass, detailed done. and and and be algorithms energy energy can primary to of particle observables primary reconstruction the the the of par- EAS, [1]. mass ground the showers various of of air distribution ticles and of number development the From the high-energy of during processes interactions complex on the depends of measurements understanding shower the air ra- from primary derived of properties diation obser- of at interpretation The particles level. secondary vation of from information derived registered be the to known the have particle regarding particles primary Information generating shower secondary showers(EAS). air of extensive as cascades resulting sphere aea hp t.as eedo h aso rmr cos- primary of mass the on depend also etc. shape lateral nvriy uaai NI.Poe 1935490 e-mai 43920, 94355 91 + Phone: Phon INDIA. [email protected] INDIA. Guwahati, Assam, University, Nalbari, Tihu, [email protected] e-mail: College, 15996, 94350 Tihu +91 Physics, of 17 ne Terms— Index Abstract— ieethdoi neato oespeitdifferent predict models interaction hadronic Different system- from suffer simulations from predictions Again atmo- Earth’s the into enter rays cosmic High-energy .C hkra(orsodn uhr swt h Departmen the with is author) (Corresponding Thakuria C. C. .Bra sPoesri h eateto hsc,Gauhati Physics, of Department the in Professor is Boruah K. - 65.d 13.85.Tp 96.50.sd, : 10 oprsno PSadQSE-Ii EAS in QGSJET-II and EPOS of Comparison 19 eV nti okw opr h rdcin ftwo of predictions the compare we work this In sn OSK-90 h A parameters EAS The CORSIKA-6990. using arncitrcinmdl,EAS, models, interaction hadronic .Introduction I. iuainuigCORSIKA using Simulation hbnC.Taui,adK Boruah K. and Thakuria, Ch. Chabin X max h expected the , X max e: d l: t 1] IYL21[3,[4,ad EU .2[15], EAS for time 4.12 a VENUS at model and, one [14], choose can simulation. [13], we which 2.1 from SIBYLL [12], r noprtdit h GJTI- oe,wihis which model, QGSJET-II-3 Pomeron- the as effects into interaction described incorporated non-linear be are This can effects interactions. with Pomeron These interact en- and high other. overlap At each strongly regime. cascades energy high that parton at ergies assumption each true not of the is independent which on other, occur based exchanges interactions is Pomeron hadronic scheme individual energy cor- QGSJET high a for very [19]. importance of extreme treatment of be rect di- to Pomeron proved enhanced and by agrams described be “semi- nucleus-nucleus can The processes treat hard” [18]. [12], so-called to [11], interac- the approach. generalized Pomeron to using “semi-hard” energy been processes “semi-hard” collisions high has and nuclear interactions of It and model hadronic tions. String of Quark-Gluon [17] the [16], proach II-03 QGSJET A. pa- are respectively impact parameters large impact at dominant. small at rise) and energy rameter, high hard (with describing exchange interactions Pomeron “semi-hard” Pomeron sections. “hard” regime cross and, energy exchange, diffractive high and the contri- in inelastic, important However, total, giving to domain energy butions dominant low are are relatively and rise at exchanges, energy and Pomeron “soft” slow , as and “semi-hard” described in- parameters , interactions impact “soft” large non-perturbative into volving Soft classified Pomerons. be “hard” cas- can gluons) Pomeron & The (quarks cades, partons of microscopic [17], scattering. to [16], multiple corresponds SIBYLL in approach Reggeon exchange and, Gribov’s Pomeron QGSJET, the on EPOS, based DPMJET, to are are models adopted. interaction be hadronic accelerators, consistent made and man the reliable by attainable energy the above oes aeyDME .5[] PS19 7,[8], HE [7], seven 1.99 are EPOS [6], there other any [5], 2.55 ne DPMJET or CORSIKA-6990 the namely photon In in models, EAS hadron, of by particle. evolution initiated 4-Dimensional atmosphere the simulate to i as eve rmre ed naeae oaflatter a to average, of value on lower lead, and primaries distribution Heavier rays. mic GJT[0 sa diino rbv ego ap- Reggeon Gribovs of addition an is [10] QGSJET collisions hadron-hadron/nucleus-nucleus explain To OSK 3,[]i ealdMneCroprogram Carlo Monte detailed a is [4] [3], CORSIKA X us .7[] GJT0C[0,QSEI. [11], QGSJETII.3 [10], QGSJET-01C [9], 3.97 I PS19 n GJTII-03 QGSJET and 1.99 EPOS II. X max n oemuons. more and 1 2

based on the assumption that corresponding effects are

dominated by “soft” partonic processes. Re summation of QGSII-3 + FLUKA Proton 1010 essential enhanced contributions corresponding to particu- QGSII-3 + FLUKA Iron lar final states of the interaction from uncut diagrams (rep- EPOS1.99 + FLUKA Proton EPOS1.99 + FLUKA Iron

resenting the elastic scattering), and from various unitarity e cuts of enhanced Pomeron diagrams for all orders, yields 109 the final state. QGSJET II-03 is based on the obtained solutions, explicitly treating the corresponding effects in

individual hadronic (nuclear) collisions [12], [19]. 108

B. EPOS 1.99 Number of N

107 EPOS [7] is a newly developed model emerging from VENUS [15] and neXus models [9]. EPOS is a parton 17 17.5 18 18.5 19 model, with many binary parton-parton interactions, each Primary Energy lgE (eV) 0 one creating a parton ladder. EPOS is a quantum me- chanical model of multiple scattering approach based on Fig. 2 partons and strings. Both the process of the particle pro- Average electron shower size Vs log of primary energy duction, and the process of cross section calculations are consistent with the conservation of energy in EPOS. How- D. Moun Number ever for other models energy conservation is not considered for cross section calculations [20]. In EPOS 1.99 reduc- Muons are produced mainly by decay of charged pions tion of the proton-nucleus cross section is done for better and kaons in a wide energy range. Usually they are not correlation between the number of muons and the number produced directly on the shower axis. Multiple Coulomb of electrons at ground based measurement [21], scattering occurred in the atmosphere and in the shield- [22]. ing of the detector may change the initial direction of the muon. It is known that the reconstruction of the longi- tudinal development of the muon component provides the C. FLUKA 2011 information similar to that obtained with the fluorescence In CORSIKA apart from seven high energy interac- technique, but in the energy range above that accessible by tion models there are three low energy models, namely the detection of fluorescence light [28]. Thus muon com- GHEISHA [23], UrQMD [24], and FLUKA [25]. The Fluka ponent of EAS provides a powerful key for primary mass hadron-nucleon interaction models are based on resonance measurement and as well as provides information regard- production and decay below a few GeV , and on the Dual ing hadronic interactions. In some experiment like KAS- Parton model above. Two models are used also in hadron- CADE, truncated muon size is calculated by integrating nucleus interactions [26], [27]. muons between 40m and 200m. Instead of total num- ber of muons, truncated muon size is considered for EAS study [29]. The range of muon truncation is from 140m- 360m in KASCADE Grande.

900 EPOS1.99+FLUKA (p) 850 QGSII-3+FLUKA (P) E. Depth of Shower max EPOS1.99+FLUKA (Fe)

800 QGSII-3+FLUKA (Fe) The depth of shower maximum contains the information

) about the mass of the primary CR initiating the shower 2 750 as well as about the properties of hadronic interactions

700 involved in the process of cascade evolution. The average

> (g/cm value Xmax depends on the primary energy E and on the max 650 number of nucleons A of the primary as given in the Eq.1,

1.99 and QGSJET II-3. All together 12,000 showers are

QGSII-3 + FLUKA Proton generated. QGSII-3 + FLUKA Iron EPOS1.99 + FLUKA Proton 108 EPOS1.99 + FLUKA Iron

µ QGSII-3 + FLUKA Proton QGSII-3 + FLUKA Iron EPOS1.99 + FLUKA Proton

h EPOS1.99 + FLUKA Iron 7 10 105 Number of Muons N

106 104

17 17.5 18 18.5 19

Primary Energy lgE (eV) Total Nubmer of N 0 E >100GeV Fig. 3 h

103 Average muon number Vs log of primary energy 16.5 17 17.5 18 18.5 19 19.5 Primary Energy lg(E eV) 0 Fig. 5

QGSII-3 + FLUKA Proton hadron no Vs log of Primary Energy QGSII-3 + FLUKA Iron

tr EPOS1.99 + FLUKA Proton µ EPOS1.99 + FLUKA Iron

107

108 QGSII−3+FLUKA Proton QGSII−3+FLUKA Iron

EPOS1.99+FLUKA Proton

6 Gev EPOS1.99+FLUKA Iron 10 h E Σ

107 Number of Truncated Muons N

105 16.5 17 17.5 18 18.5 19 19.5 Primary Energy lgE (eV) 0

6 Fig. 4 Hadron enegy sum 10 Average truncated muon number Vs log of primary energy

8 8.5 9 9.5 10 Primary Energy lg(E /Gev) 0 where ER10 is known as elongation rate and Xinit is Fig. 6 the depth of first interaction [31]. Another sensitive pa- hadron energy sum Vs log of Primary Energy rameter is σXmax , expressing quantitatively the shower to shower fluctuations of Xmax . It depends mainly on the cross section and less strongly on the elasticity. This makes fluctuations in Xmax , a good parameter to study hadronic cross sections at ultra-high energies.[30] IV. Results The average of Depth of maximum X for the two III. Simulation max models are plotted as function of energy in Figures 1. It The shower simulations are performed using CORSIKA- is seen that heavier primary produces shower maximum at 6990. Hadronic interactions at low energies(E < 80 GeV ) lower depth compared with lighter primary as expected. are modelled using the FLUKA-2011 code. High Energy The average total number of electrons(Ne), muons(Nµ), tr interactions are treated with EPOS 1.99 and QGSJET II- truncated muons(Nµ ), hadrons (Eh > 100GeV ), and sum 3. Vertical showers initiated by primary protons and iron of energies of all the hadrons(Eh > 100GeV ) registered at nuclei are simulated. Observation level is taken at the sea the ground level for the interaction models EPOS 1.99 and level. US standard atmosphere and default magnetic field QGSJET II-03 are plotted as a function of energy in Fig- in CORSIKA are taken. 1000 showers are simulated each ures 2, 3, 4, 5, and 6 respectively. for three primary energies 1017 , 1018, and 1019eV , two It is seen that, both models yield a linear dependence of primary masses(p & Fe) and for two HE models EPOS these components with energy in Log-Log scale. 4

QGSII-3+FLUKA QGSII-3 + FLUKA h Proton primary Entries 1000 Mean 5.336 EPOS 1.99 + FLUKA EPOS1.99+FLUKARMS 0.09315 102 102 2 10 RMS 0.05133 17 18 h__3__3 19 10 Ev 10 Ev Entries 1001 10 Ev h__1__1 Mean 6.382 Entries 1002 RMS 0.04641 Mean 5.459

RMS 0.04122 102

10 10 10

10 Number Of Showers

1019eV 18 17 10 eV Number of Showers 10 eV 1 1 1 5.3 5.35 5.4 5.45 5.5 5.55 5.6 5.65 5.7 6.25 6.3 6.35 6.4 6.45 6.5 6.55 6.6 7.15 7.2 7.25 7.3 7.35 7.4 7.45 7.5 7.55 µtr tr number of muons lg N number of muons lg Nµ number of muons lg Nµtr 1 Iron Primary 4.8 4.9 5 5.15.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.37.4 7.5 7.6 7.7 number of muons lg Nµtr Fig. 8 Fig. 7 Distribution of the number of truncated muons for iron Distribution of the number of truncated muons for proton primary primary

QGS II-3 + FLUKA Mean 7.29 Proton Primary EPOS 1.99 + FLUKA TABLE I 102

Slope of Xmax and Intercept

Model Slope of Xmax Intercept & Primary ER10 error Xinit error EPOS − p 58.3690 ±1.64891 -303.488 ±29.7108 10 QGSII − p 47.5875 ±0.24876 -125.219 ±4.48227 EPOS − Fe ± ±

62.9539 1.55497 -491.491 28.0169 Nubmer of Showers

17 QGSII − Fe 55.2977 ±0.23593 -354.504 ±4.25079 10 Ev 1018 Ev 1019 Ev

1 6.8 7 7.2 7.4 7.6 7.8 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 number of electons lg Ne A. Dependence of Xmax with primary Energy Fig. 9 Distribution of the number of electrons for proton primary The value of Xmax and also the slope of the curve for proton primary for EPOS 1.99 is slightly higher than that of QGSJET II-03. Again, for iron primary also the slope of the curve has higher value for EPOS 1.99, while the values hadron energy for the two models considered in the chosen of Xmax are nearly equal for both the models. primary energies for proton and iron primaries. However for muons (Fig. 3, 4) differences between the predictions The fitted values of the slope ER10 and intercept Xinit are given in the Table I. of the two models are significant. The number of muons is larger for EPOS1.99 model as compared to QGSJET II-03 for both the primaries. From the figure 3, it is seen that there is very little overlap in the region bounded by p & B. Primary Energy Correlations Fe primaries for two models considered. However, for trun- From Figures 2 through 6, it is seen that, there is no sig- cated muons (in the range 40m-200m) there is no overlap 18 nificant differences in the electron shower size and sum of beyond 10 eV (Figure 4). For Eh > 100GeV hadrons, to- tal number for both proton & iron primaries are found to TABLE II be significantly more for EPOS than that for QGSJET II-3 Average Truncated Muon Number and RMS value (Figure 5). However, considering the sum total of energies Energy/Model Proton Primary Iron Primary of all the hadrons (Eh > 100GeV ), there is no significant tr tr (eV ) < lg(Nµ ) > RMS < lg(Nµ ) > RMS difference between the two models (Figure 6). 1017 − QGSII 5.33582 0.09227 5.45870 0.04113 1017 − EPOS 5.42664 0.10664 5.52427 0.04210 1018 − QGSII 6.26616 0.09035 6.38253 0.04637 1018 − EPOS 6.37158 0.09563 6.47433 0.04434 C. Distribution of truncated muon numbers and electron 1019 − QGSII 7.21209 0.08441 7.31510 0.05116 numbers 1019 − EPOS 7.31632 0.09665 7.41770 0.04526 tr Distributions of truncated muon numbers lg(Nµ ) for TABLE III proton and iron primaries are plotted in Figure 7 and 8. It tr Average Electron Number and RMS value is seen that EPOS1.99 yields higher value of lg(Nµ ) than Energy/Model Proton Primary Iron Primary QGSJET II-03. The mean & s.d. of these distributions (eV ) < lg(Ne) > RMS < lg(Ne) > RMS are tabulated in Table II, and significance test done (C). 1017 − QGSII 7.28989 0.14648 7.05567 0.08888 17 Distributions of electron numbers lg(Ne) for proton and 10 − EPOS 7.27924 0.15111 6.99535 0.09171 1018 − QGSII 8.40937 0.11724 8.21039 0.07825 iron primaries are plotted in Figure 9 and 10. It is seen that 1018 − EPOS 8.42408 0.11274 8.18449 0.07497 EPOS1.99 produces slightly less numbers of electrons for 1019 − QGSII 9.50743 0.09597 9.34173 0.06344 energy 1017eV for iron primary, but at 1019eV, EPOS1.99 19 − 10 EPOS 9.54035 0.08953 9.34330 0.06105 produces slightly more electrons as tabulated in Table III, Chabin Ch. Thakuria: COMPARISON OF EPOS AND QGSJET-II IN EAS SIMULATION USING CORSIKA 5

QGSMean 7.056 II-3 + FLUKA 102 EPOS 1.99 + FLUKA Iron Primary 0.2 Proton

0.15 Iron

10 e 0.1

0.05 19 Nubmer of Showers 10 eV

18 1017 Ev 10 Ev 1019 Ev 0 1018eV 1 6.8 7 7.2 7.4 7.6 7.8 8 8.2 8.4 8.6 8.8 9 9.2 9.4 number of electons lg Ne -0.05 1017eV Fig. 10 -0.1 Distribution of the number of electrons for iron primary Relative deviation of N -0.15

-0.2

10 6 7 10 QGSII-3 + FLUKA Proton 10 10 Average number of muons Nµtr QGSII-3 + FLUKA Iron EPOS1.99 + FLUKA Proton Fig. 12 EPOS1.99 + FLUKA Iron e Relative deviation of the number of electrons Vs average 109 number of truncated muons

108 5.3 < lg(Nµtr) < 5.55 103 Number of electrons N

102 107

-1 10 × 5 6 × 6 7 × 7 2 10 10 2 10 10 2 10 Gev Number of muons Nµtr h 1

Fig. 11 dn/dE QGSII-3 +FLUKA Proton -1 Number of electrons Vs number of truncated muons 10 QGSII-3Mean 1.544 +FLUKA Iron EPOS1.99 +FLUKA Proton -2 10 EPOS1.99 +FLUKA Iron and significance test done(C). 1 2 3 4 5 6 hadon enegy lg(E /Gev) h D. Electron to muon correlation Fig. 13 17eV The average number of electrons as a function of the hadron energy distribution (10 ) number of truncated muons are plotted in figure 11 for the two models. Slopes of all the curves are almost 1018eV , and 1019eV primary for both the models consid- equal. To emphasize the differences between the model ered are displayed in the Figures 13, 14, and 15 respec- predictions, relative deviation in the model prediction tively. There are apparently no distinguishable differences. EPOS1.99 with respect to the QGSJET II-3 prediction, EPOS − QGS QGS All the four data plots are overlapped to each-other with (Ne Ne )/Ne is plotted against the mean of QGS EPOS their error-bars. Nµ and Nµ in Figure 12. It is seen that for pro- ton primary, EPOS1.99 predicts slightly less (about 2%) electrons for 1017eV proton-induced showers, slightly more V. Summary 18 (about 3%) electrons for 10 eV and about 8% more elec- Although Xmax , shower size, hadron energy sum, 19 trons for 10 eV primary energy. But for iron primary hadron energy distribution shows no significant difference 17 18 19 at 10 eV , 10 eV , and, 10 eV , EPOS 1.99 yields about between the two HE models EPOS 1.99 (FLUKA) and 12% lesser, about 6% lesser and nearly equal ( difference QGSJET II-3 (FLUKA); muon number, hence electron is less than 1%) numbers of electrons as compared with to muon correlation shows incompatibility between them. QGSJET II-3 predictions. EPOS 1.99 (FLUKA) predicts more muons than QGSJET II-3 (FLUKA) which is known widely since its inception E. Variation in hadron component [22]. This difference is explained as more (anti-)baryon Total average number hadrons with energy Eh > production in EPOS leads to more muons in EAS [22]. 100GeV , for both primary masses & at all the three en- More (anti-)baryon generations in forward region result ergies show significant difference between the two models larger fraction of energy in the hadronic cascades and lesser (D). Energy spectrum of registered hadrons for 1017eV , in the electromagnetic cascades (more muon to electron ra- 6

[5] D. Heck, J. Knapp, J.N. Capdevielle, G. Schatz, and T. Thouw, Report FZKA 6019 (1998), Forschungszentrum Karlsruhe; 6.25 < lg(Nµtr) < 6.5 available from 104 http://www-ik.fzk.de/corsika/physics description/corsika phys.html [6] J. Ranft, Phys. Rev. D51 (1995) 64; preprint hep-ph/9911213 and hep-ph/9911232 (1999) 103 [7] K. Werner, F. M. Liu and T. Pierog, Phys. Rev. C 74 (2006)

-1 044902 102 [8] K. Werner, and T. Pierog, arXiv:0707.3330v1[astro-ph]. Gev h [9] H.J. Drescher, M. Hladik, S. Ostapchenko, T. Pierog, and K. Werner, Phys. Rep. 350 (2001) 93 (preprint hep-ph/0007198 10 dn/dE (2000)) QGSII-3 + FLUKA Proton [10] N.N. Kalmykov, S.S. Ostapchenko, and A.I. Pavlov, Nucl. Phys. 1 QGSII-3 + FLUKA Iron B (Proc. Suppl.) 52B (1997) 17 EPOS1.99Mean 1.547 + FLUKA Proton [11] S.S. Ostapchenko, Nucl. Phys. B (Proc. Suppl.) 151 (2006) 143- EPOS1.99 + FLUKA Iron 10-1 147; Phys. Rev. D 74 (2006) 014026 [12] S. Ostapchenko AIP Conf. Proc. 928 (2007) pp-118. 1 2 3 4 5 6 [13] R.S. Fletcher, T.K. Gaisser, P. Lipari, and T. Stanev, Phys. hadron energy lg (E Gev) Rev. D50 (1994) 5710; J. Engel, T.K. Gaisser, P. Lipari, and T. h Stanev, Phys. Rev. D46 (1992) 5013 Fig. 14 [14] R. Engel, T.K. Gaisser, P. Lipari, and T. Stanev, Proc. 26th Int. hadron energy distribution (1018eV ) Conf., Salt Lake City (USA), 1 (1999) 415; E.-J. Ahn, R. Engel, T.K. Gaisser, P. Lipari, and T. Stanev, Phys. Rev. D80 (2009) 094003 [15] K. Werner, Phys. Rep. 232 (1993) 87 [16] V.N. Gribov, Sov. Phys. JETP 26 (1968) pp-414. 7.1 < lg(Nµtr) < 7.45 [17] V.N. Gribov, Sov. Phys. JETP 29 (1969) pp-483. 105 [18] S. Ostapchenko, Phys. Rev. D 83, 014018 (2011), (preprint arXiv:1010.1869v2) 104 [19] S. Ostapchenko, (preprint arXiv:hep-ph/0412332) [20] M. Hladik, H. J. Drescher, S. Ostapchenko, T. Pierog, 103 and K. Werner et al., Phys. Rev. Lett. 86, 3506 (2001), -1 arXiv:hep-ph/0102194. 2 Gev 10 [21] T. Pierog, Iu. Karpenko, S. Porteboeuf,and K. Werner, h arXiv:1011.3748v1[astro-ph.HE] 10 [22] K. Werner, and T. Pierog, Proc. 31st ICRC, LODZ 2009 dn/dE QGSII-3 +FLUKA Proton [23] H. Fesefeldt, Report PITHA-85/02 (1985), RWTH Aachen 1 EPOS1.99+FLUKA Proton [24] S.A. Bass et al., Prog. Part. Nucl. Phys. 41 (1998) 225; M. Bleicher et al., J. Phys. G: Nucl. Part. Phys. 25 (1999) 1859; -1 Mean 1.414 QGSII-3 + FLUKA Iron 10 http://urqmd.org/ EPOS1.99+FLUKA Iron -2 [25] A. Fass`o, A. Ferrari, S. Roesler, P.R. Sala, G. Battistoni, F. 10 Cerutti, E. Gadioli, M.V. Garzelli, F. Ballarini, O.Ottolenghi, A. 1 2 3 4 5 6 7 Empl and J. Ranft, The physics models of FLUKA: status and hadron energy lg (E Gev) h recent developments, Computing in High Energy and Nuclear Physics 2003 Conference (CHEP2003), La Jolla, CA (USA), Fig. 15 19 March 24-28, 2003 (paper MOMT005); eConf C0303241 (2003); hadron energy distribution (10 eV ) arXiv:hep-ph/0306267; http://www.fluka.org/references.html [26] A. Ferrari, P.R. Sala, A. Fass‘, and J. Ranft, FLUKA: a multi- particle transport code, CERN-2005-10 (2005),INFN/TC 05/11, SLAC-R-773. tio in the EAS) for EPOS prediction. Also hadron(Eh > [27] G. Battistoni, S. Muraro, P.R. Sala, F. Cerutti, A. Ferrari, S. 100GeV ) shower size prediction by EPOS 1.99 (FLUKA) Roesler, A. Fass, J. Ranft, The FLUKA code: Description and benchmarking, Proceedings of the Hadronic Shower Simulation yields higher values irrespective of primaries considered as Workshop 2006, Fermilab 68 September 2006, M. Albrow, R. compared to that by QGSJET II-3 (FLUKA). Modifica- Raja eds., AIP Conference Proceeding 896, 31-49, (2007) tions may be needed for one, or, both of the models con- [28] P. Doll et al. Nucl. Phys. B (Proc. Suppl.) 196 (2009) 305308 [29] T. Antoni et.al. Nucl. Instr and Meth A 513, pp 490-510 (2003) sidered herein by comparing the model predictions with [30] Ralf Ulrich, Ralph Engel , and Michael Unger Phys. Rev. D. 83, experimental data. 054026 (2011) [31] P.K.F. Grieder, Extensive Air Showers , DOI:10.1007/978-3- VI. Acknowledgements 540-76941-5−20 The authors thankfully acknowledge UGC for com- Appendix putational infrastructure support under SAP and C.C. A. Statistical Test Thakuria acknowledges UGC for fellowship under FDP. A. Z-test results for Xmax distribution (Table IV) References The null hypothesis is [1] W.D. Apel et al., J. Phys. G.: Nucl. Part. Phys. 36 (2009) H0 = There is no difference between the two samples 035201, DOI:10.1088/0954-3899/36/3/035201 [2] D. d’Enterria, R. Engel, T. Pierog, S. Ostapchenko, K. Werner, (QGSJET II-03 data and EPOS1.99 data). Astro. Part. Phys. 35, (2011), pp 98-113 [3] J.N. Capdevielle et al., Report KfK 4998 (1992), Kern- forschungszentrum Karlsruhe B. Z-test results for ER10 and Xinit (Table V) [4] D. Heck and J. Knapp, Report FZKA 6097 (1998), Forschungszentrum Karlsruhe; available from The null hypothesis is http://www-ik.fzk.de/˜heck/publications/ H0 = There is no difference between the parameters for Chabin Ch. Thakuria: COMPARISON OF EPOS AND QGSJET-II IN EAS SIMULATION USING CORSIKA 7

TABLE IV data). Z statistics for Xmax n Energy/Primary Xmax Dist (eV ) Z Inference TABLE VII 17 10 − P roton 1.81 Not Significant Z statistics for total hadron number (Eh > 100GeV ) 17 10 − Iron 3.00 Moderately Significant n 18 Energy/Primary N Dist 10 − P roton 4.41 Significant h 1018 − Iron 0.28 Not Significant (eV ) Z Inference 17 1019 − P roton 8.65 Highly Significant 10 − P roton 4.07 Significant 19 10 − Iron 3.83 Moderately Significant 1017 − Iron 21.09 Highly Significant 1018 − P roton 8.91 Highly Significant 1018 − Iron 6.52 Highly Significant QGSJET II-03 and EPOS1.99 . 19 10 − P roton 13.25 Highly Significant 1019 − Iron 15.59 Highly Significant TABLE V

Z statistics for ER10 and Xinit

Parameter ER10 and Xinit &Primary Z Inference ER10 − P roton 6.466 Significant ER10 − Iron 4.981 Significant Xinit − P roton 5.933 Significant Xinit − Iron 4.834 Significant

It is seen that the parameters ER10 and Xinit describing Xmax (Equation 2), show significant differences for EPOS and QGSJET II, irrespective of the primaries.

tr C. Z-test results for Nµ and Ne distributions (Table VI) The null hypothesis is H0 = There is no difference between the two samples (QGSJET II-03 data and EPOS1.99 data).

TABLE VI tr N Z statistics for Nµ and Ne dist s tr n n Energy/Primary Nµ Dist Ne Dist (eV ) Z Inference Z Inference 1017 − P roton 20.36 Highly 1.60 Not Significant Significant 1017 − Iron 35.22 Highly 14.93 Highly Significant Significant 1018 − P roton 25.34 Highly 2.86 Moderately Significant Significant 1018 − Iron 45.25 Highly 7.56 Significant Significant 1019 − P roton 25.68 Highly 7.93 Significant Significant 1019 − Iron 47.50 Highly 0.56 Not Significant Significant

Average truncated muon number shows highly signif- icant difference between the two models. For the aver- age electron number, for lower energy(1017eV ) high sig- nificance for iron primary, but no significant difference for proton primary is seen, whereas at higher energy(1019eV ), no significance for iron, but significant differences for pro- ton primary is observed ( Table VI).

D. Z-test results for total hadron number (Eh > 100GeV ) (Table VII)

The null hypothesis is H0 = There is no difference be- tween the two samples (QGSJET II-03 data and EPOS1.99