Comparison of the moments of the distribution predicted by different cosmic ray shower simulation models

In this paper we study the depth at which a cosmic ray shower reaches its maximum ( X max ) as predicted by Monte Carlo simulation. The use of X max in the determination of the primary particle mass can only be done by comparing the measured values with simulation predictions. For this reason it is important to study the differences between the available simulation models. We have done a study of the first and second moments of the X max distribution using the Corsika and Conex programs. The study was done with high statistics in the energy range from 10 17 to 10 20.4 eV. We focus our analysis in the different implementations of the hadronic interaction models Sibyll2.1 and QGSJetII in Corsika and Conex. We show that the predictions of the 〈 X max 〉 and RMS ( X max ) depend slightly on the combination of simulation program and hadronic interaction model. Although these differences are small, they are not negligible in some cases (up to 5 g/cm2 for the worse case) and they should be considered as a systematic uncertainty of the model predictions for 〈 X max 〉 and RMS ( X max ) . We have included a table with the suggested systematic uncertainties for the model predictions. Finally, we present a parametrization of the X max distribution as a function of mass and energy according to the models Sibyll2.1 and QGSJetII, and showed an example of its application to obtain the predicted X max distributions from cosmic ray propagation models.