On the influence of statistics on the determination of the mean value of the depth of shower maximum for ultra high energy cosmic ray showers

TL;DR

This paper investigates whether statistical biases in the analysis of Xmax distributions could explain discrepancies in cosmic ray composition data, concluding that such biases are insufficient to account for the observed deviations.

Contribution

The study provides a more accurate modeling of Xmax distributions, demonstrating that statistical biases are minimal and unlikely to explain the differences between Auger and HiRes data.

Findings

Bias in Xmax measurement is significantly smaller with improved distribution modeling.

Statistical bias cannot fully explain the deviation of Auger data from proton expectations.

Results support the interpretation of a composition transition at high energies.

Abstract

The chemical composition of ultra high energy cosmic rays is still uncertain. The latest results obtained by the Pierre Auger Observatory and the HiRes Collaboration, concerning the measurement of the mean value and the fluctuations of the atmospheric depth at which the showers reach the maximum development, Xmax, are inconsistent. From comparison with air shower simulations it can be seen that, while the Auger data may be interpreted as a gradual transition to heavy nuclei for energies larger than ~ 2-3x10^18 eV, the HiRes data are consistent with a composition dominated by protons. In Ref. [1] it is suggested that a possible explanation of the observed deviation of the mean value of Xmax from the proton expectation, observed by Auger, could originate in a statistical bias arising from the approximated exponential shape of the Xmax distribution, combined with the decrease of the number of events as a function of primary energy. In this paper we consider a better description of the Xmax distribution and show that the possible bias in the Auger data is at least one order of magnitude smaller than the one obtained when assuming an exponential distribution. Therefore, we conclude that the deviation of the Auger data from the proton expectation is unlikely explained by such statistical effect.