A Method to Estimate the Primary Mass of Ultrahigh-energy Cosmic Rays from Measurements of the Depth of the Shower Maximum and the Muon Content

Abstract

The origin and mass composition of ultrahigh-energy cosmic rays is one of the big open questions of modern physics. Estimating the mass of ultrahigh-energy cosmic rays always involves the comparison of data with simulations using hadronic interaction models. The state-of-the-art hadronic interaction models, however, fail to agree with each other on the expected depths of the shower maxima, and on the average number of muons produced in air showers initiated by the same primary particles. Thus the interpretation of data in terms of the primary masses of cosmic rays differs depending on which hadronic interaction model is considered as a reference. Good agreement, however, can be found in the implications from hadronic interaction models in the prediction of the change of the average depth of the shower maximum and in the relative change in the number of produced muons as a function of the nuclear mass of the primary cosmic ray. Considering these, a model-independent estimation of the primary mass of ultrahigh-energy cosmic rays can be given in relative terms. In this work we propose a method to estimate the primary mass of ultrahigh-energy cosmic rays from the depth of the shower maximum and the number of muons produced in the shower, utilizing the similarities of modern hadronic interaction models. We discuss a geometric approach that combines the depth of the shower maximum and the number of muons produced in a shower to estimate the mass of the primary particle.