Pierog, T

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29th International Cosmic Ray Conference Pune (2005) 7, 103106Dependence of the longitudinal shower profile on the characteristics ofhadronic multiparticle productionT. Pierog , M. Alekseeva, T. Bergmann , V. Chernatkin, R. Engel , D. Heck ,N.N. Kalmykov, S. Ostapchenko , M. Unger and K. Werner(a) Forschungszentrum Karlsruhe, Postfach 3640, D-76021 Karlsruhe, Germany(b) Skobeltsyn Institute of Nuclear Physics, Moscow State University, Leninskie Gory 1, 119992, Moscow, Russia(c) SUBATECH, Universite de Nantes, EMN, IN2P2/CNRS, Nantes, FrancePresenter: R. Engel (Ralph.Engel@ik.fzk.de), ger-engel-R-abs2-he14-oralThe new hybrid simulation code CONEX is used to study longitudinal shower profiles and their dependence onthe applied hadronic interaction model. In addition to the mean depth of shower maximum, we also investigatethe model dependence of different estimators for the total shower energy. The large differences of modelextrapolations to ultra-high energy are significantly reduced if the calorimetric energy of shower and energydeposit at shower maximum are considered.1. IntroductionAt shower energies above 	 eV, the longitudinal shower profile can be determined from measurements ofthe fluorescence light signal produced in the atmosphere. The number of produced fluorescence photons isexpected to be directly proportional to the ionization energy deposit of the shower particles. Therefore, thefluorescence technique allows not only the determination of the depth of shower maximum but also the directmeasurement of the calorimetric energy of an air shower – the energy that is transferred to em. particles andfinally converted to ionization energy. Traditionally, assuming a mean energy deposit per particle, measuredfluorescence light profiles are converted to shower size curves that are then compared with theoretical predic-tions. However, it is much more natural to calculate and compare energy deposit profiles as they are first of alldirectly related to the number fluorescence photons and secondly do not depend on the simulation thresholds[1].In this paper we use the hybrid cascade code CONEX [2] to simulate realistic energy deposit profiles of a largenumber of showers (about 1000 showers per energy value) to compare the predictions of different hadronicinteraction models.2. Shower depth of maximumThe mean depth of maximum of a hadron-induced shower is closely related to the description of high-energyhadron production. In Fig. 1 we compare the predictions obtained with CONEX for neXus 3.97 [3], QGSJET 01[4], and Sibyll 2.1 [5]. GHEISHA 2002 [6] is used as low-energy model for interactions below 80 GeV lab.energy. All three high-energy interaction models differ significantly in their predictions. For example, in thecase of Sibyll and QGSJET there are two counter-acting effects that nearly cancel each other. The cross sec-tion of Sibyll is much larger than that of QGSJET, leading to a higher first interaction point. At the same timethe larger elasticity of Sibyll causes a shift the shower development deeper into the atmosphere. In the caseof neXus and QGSJET the differences arise due mainly to the different secondary particle distributions. Thecross section of neXus and QGSJET are very similar, however, neXus predicts more high-energy secondarypions.104 T. Pierog et al.Energy      (eV)1710 1810 1910 2010 2110)2>       (g/cmmax<X50060070080090010001100120013001400HiRes-MIAHiResYakutsk 2001Fly’s EyepFeγQGSJET 01Sibyll 2.1neXus 3.97 no MFγ from Southγ from Northγ no LPM no MFγ)2      (g/cmmaxX700 800 900 1000 1100 1200 1300 1400 1500 1600maxdP/dX-410-310-210neXus 3.97 proton no MFγ from Southγ from NorthγFigure 1. Left: mean depth of shower maximum of hadronic showers for three different interaction models. Also shownare photon-induced showers for different directions to the local geomagnetic eld (MF). The references to the experimentaldata are given in [7]. Right: comparison of the distribution of the depth of maximum of photon- and proton-inducedshowers at  eV.The mean depth of maximum of photon-induced showers is strongly influenced by the Landau-Pomeranchuk-Migdal (LPM) effect and depends on the relative direction of the shower axis to the geomag. field. At highenergy, photons can produce an em. shower already well above the atmosphere by interacting with the Earth’smagnetic field. In Fig. 1 this is illustrated by showing the predictions for photon showers of  at the southernAuger detector coming from the north (weak mag. field effect) and from the south (strong mag. field effect).For reference, also calculations without mag. field and without both LPM effect and mag. field are shown.As many exotic models for ultra-high energy cosmic rays predict a large fraction of photons at high energy, itis interesting to compare the 	 distributions of protons and photons. In Fig. 1 (right) these distributions areshown at ﬀﬁﬃﬂ eV. A significant fraction of photon showers (those that either pre-shower in the geomag. field orhave a high-energy hadronic interaction in the early shower development) cannot be distinguished from protonshowers on the basis of ﬃ only.3. Primary energy estimationThe calorimetric energy of a shower, ! #" , is defined as the depth-integral of the ionization energy depositprofile. Integrating numerically the simulated profiles and accounting for muons and hadrons at large depth[8], we calculate the calorimetric energy of showers for a “perfect” measurement. In Fig. 2 (left) the correctionfactor $&%')(+*ﬃ(#,-  #" is shown with which the calorimetric energy has to be multiplied to obtain the primaryparticle energy. The black lines are the mean conversion factors averaged over the predictions of all threemodels considered here and averaged over proton and iron primaries. The ratio of the total to calorimetricenergy is directly related to the number of consecutive hadronic interactions (number of generations) that pionsundergo before they decay. In each of these interactions about 1/3 of the secondary particles are neutral pionsthat transfer all of their energy to the electromagnetic shower component. Since the typical energy at whichpions decay is about /.1023 GeV, the number of generations increases with increasing primary energy. Asthe number of generations also influences the number of muons produced in a shower, there is a close relationbetween the number of muons and the calorimetric energy. Both the factor $ and the predicted number ofmuons in high energy showers are bigger for QGSJET than Sibyll.Dependence of the longitudinal shower prole 4#454 105/eV)tot(E10log17 17.5 18 18.5 19 19.5 20 20.5cal/EtotE11.051.11.151.21.251.3pFeγQGSJET 01Sibyll 2.1neXus 3.97mean/eV)tot(E10log17 17.5 18 18.5 19 19.5 20 20.5Relative Uncertainty00.010.020.030.040.050.060.070.080.090.1Tot. Syst. error (quad. sum))γTot. Syst. error (incl. Stat. errorMass Syst. error)γMass Syst. error (incl. model error (Proton)model error (Iron)Figure 2. Left: mean value and RMS of the ratio of primary particle energy to calorimetric energy, shown for differentmodels and primary particles. Right: relative uncertainty in energy reconstruction implied by the use of a conversion factorbetween the calorimetric and total energies that is averaged over models and primary particle types.The uncertainty in reconstruction of the primary energy, assuming perfect calorimetric energy determination, isshown in Fig. 2 (right). We distinguish here between the statistical error due to shower-to-shower fluctuationsand the systematic error due to differences implied by not knowing the cosmic ray composition and by differentassumptions on hadronic interactions. The blue curves (triangles) show the systematic uncertainty one wouldhave due to different interaction models if the composition were either only proton or only iron. The greycurve (stars) shows the statistical shower-to-shower uncertainty in total energy reconstruction, again assumingthat the primary particle type is known. The green curve (filled circles) shows the systematic uncertainty if thecomposition is hadronic (in the range between proton and iron) but not known. It is calculated by applyingthe mean conversion factor $ shown as the second black line in the l.h.s. figure. The red curve (filled squares)shows the total systematic error: the uncertainty due to the model dependence for a fixed composition isadded quadratically to the uncertainty due to the unknown composition. If one considers the case of having asignificant fraction of photons as primary particles, the curves with open symbols have to be used to estimatethe uncertainties. They represent the composition-related and total systematic uncertainties if the conversionfactor is calculated as average over proton, iron, and photon primaries.The shower size at maximum is also well correlated with the primary energy and can be used as energy es-timator. Motivated by the primary observable of fluorescence technique experiments, we show in Fig. 3 thefactor by which the energy deposit at shower maximum has to be scaled to obtain the primary shower energy.Compared to the calorimetric energy, the energy deposit at shower maximum is subject to larger shower-to-shower fluctuations. On the other hand, the predictions are less model- and composition dependent over awide energy range. In particular at about ﬀ	687 9 eV the conversion from the energy deposit to total energy isnearly independent of the primary particle type, including photons, and the assumed interaction model. Notethe different behaviour of photon-induced showers due to the smaller muon number and the interplay betweenthe LPM effect and mag. pre-showering.The uncertainty in reconstruction of the total energy, again assuming perfect determination of the energy de-posit at shower maximum, is shown in Fig. 3 (right). The labelling of the different curves is analogous to Fig. 2.The systematic uncertainty is very small at about ﬀ	687 9 eV.106 T. Pierog et al./eV)tot(E10log17 17.5 18 18.5 19 19.5 20 20.5)2)  (gr.cmmax/(dE/dXtotE500550600650700750800pFeγQGSJET 01Sibyll 2.1neXus 3.97mean/eV)tot(E10log17 17.5 18 18.5 19 19.5 20 20.5Relative Uncertainty00.020.040.060.080.10.12Tot. Syst. error (quad. sum))γTot. Syst. error (incl. Stat. errorMass Syst. error)γMass Syst. error (incl. model error (Proton)model error (Iron)Figure 3. Left: mean ratio of total shower energy to the energy deposit at shower maximum. The shaded bands show theRMS of the shower-to-shower uctuations. The black lines are the mean conversion factors averaged over the three modelsconsidered here and averaged over proton and iron primaries. Right: relative uncertainty in energy reconstruction impliedby the use of energy deposit at shower maximum and a conversion factor that is averaged over models and primary particletypes.4. Conclusions and outlookDifferences in the extrapolation of the characteristics of had. interactions to ultra-high energy lead to a sig-nificant spread in the predictions of the mean depth of shower maximum. In contrast, the variation of thepredictions on energy estimators such as the calorimetric energy and the energy deposit at shower maximum isrelatively small. The total energy reconstruction uncertainty, assuming a perfect shower measurement, is dom-inated by the unknown primary composition. Using the calorimetric energy one obtains an uncertainty that issmaller than 4% for hadronic primaries in the energy range of relevance to current fluorescence detector exper-iments. The energy deposit at shower maximum can also be applied as independent energy estimator. Thoughbeing characterized by larger statistical fluctuations, it gives an almost model- and composition-independentmeasure of the primary energy at about ﬀ	6 eV.References[1] M. Risse and D. Heck, Astropart. Phys. 20 (2004) 661.[2] M. Alekseeva et al., these proceedings, ger-ostapchenko-S-abs2-he14-poster; T. Pierog et al., astro-ph/0411260.[3] H.J. Drescher, M. Hladik, S. Ostapchenko, T. Pierog, and K. Werner, Phys. Rep. 350 (2001) 93 andhep-ph/0007198.[4] N.N. Kalmykov, S. Ostapchenko, and A.I. Pavlov, Nucl. Phys. B (Proc. Suppl.) 52B (1997) 17 and Phys.At. Nucl. 56 (1993) (3) 346.[5] R. Engel, T. K. Gaisser, P. Lipari, and T. Stanev, Proc. of 26th ICRC (Salt Lake City) vol. 1, p. 415, 1999;R. S. Fletcher, T. K. Gaisser, P. Lipari, and T. Stanev, Phys. Rev. D50 (1994) 5710.[6] H. Fesefeldt, Report PITHA-85/02, RWTH Aachen, 1985.[7] R. Engel and H. Klages, C. R. Physique 5 (2004) 505.[8] H.M.J. Barbosa, F. Catalani, J.A. Chinellato, and C. Dobrigkeit, Astropart. Phys. 22 (2004) 159.

Dependence of the longitudinal shower profile on the characteristics of hadronic multiparticle production

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