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

Abstract

In this paper we study the depth at which a cosmic ray shower reaches its maximum (\Xmax) as predicted by Monte Carlo simulation. The use of \Xmax 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 \Xmax distribution using the \Corsika and \Conex programs. The study was done with high statistics in the energy range from $10^{17}$ to \energy{20.4}. We focus our analysis in the different implementations of the hadronic interaction models \Sibyll and \Qgsjet in \Corsika and \Conex. We show that the predictions of the \meanXmax and \sigmaXmax 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/cm$^2$ for the worse case) and they should be considered as a systematic uncertainty of the model predictions for \meanXmax and \sigmaXmax. We have included a table with the suggested systematic uncertainties for the model predictions. Finally, we present a parametrization of the \Xmax distribution as a function of mass and energy according to the models \Sibyll and \Qgsjet, and showed an example of its application to obtain the predicted \Xmax distributions from cosmic ray propagation models.