$Xmaxμ$ vs. $Nμ$ from extensive air showers as estimator for the mass of primary UHECR's. Application for the Pierre Auger Observatory

We study the possibility of primary mass estimation for Ultra High Energy Cosmic Rays (UHECR's) using the $Xmaxμ$ (the height where the number of muons produced on the core of Extensive Air Showers (EAS) is maximum) and the number $Nμ$ of muons detected on ground. We use the 2D distribution - $Xmaxμ$ against $Nμ$ in order to find its sensitivity to the mass of the primary particle. For that, we construct a 2D Probability Function Prob(p,Fe | $Xmaxμ$⁠, $Nμ$⁠) which estimates the probability that a certain point from the plane (⁠$Xmaxμ$⁠, $Nμ$⁠) corresponds to a shower induced by a proton, respectively an iron nucleus. To test the procedure, we analyze a set of simulated EAS induced by protons and iron nuclei at energies of 10¹⁹eV and 20° zenith angle with CORSIKA. Using the Bayesian approach and taking into account the geometry of the infill detectors from the Pierre Auger Observatory, we observe an improvement in the accuracy of the primary mass reconstruction in comparison with the results obtained using only the $Xmaxμ$ distributions.