Reinterpreting the development of extensive air showers initiated by nuclei and photons

TL;DR

This paper introduces an empirical model using the generalized Gumbel distribution to describe the $ ext{X}_{ ext{max}}$ distribution in extensive air showers caused by nuclei and photons at ultra-high energies, aiding cosmic ray composition analysis.

Contribution

The paper presents a novel analytical model for $ ext{X}_{ ext{max}}$ distribution in EAS, incorporating the impact of hadronic interaction models and extending to ultra-high energies.

Findings

The model accurately describes $ ext{X}_{ ext{max}}$ distributions across a wide energy range.

It highlights the influence of hadronic interaction models on $ ext{X}_{ ext{max}}$ predictions.

Application to experimental data demonstrates the model's utility in cosmic ray studies.

Abstract

Ultra-high energy cosmic rays (UHECRs) interacting with the atmosphere generate extensive air showers (EAS) of secondary particles. The depth corresponding to the maximum development of the shower, $\Xmax$, is a well-known observable for determining the nature of the primary cosmic ray which initiated the cascade process. In this paper, we present an empirical model to describe the distribution of $\Xmax$ for EAS initiated by nuclei, in the energy range from $10^{17}$ eV up to $10^{21}$ eV, and by photons, in the energy range from $10^{17}$ eV up to $10^{19.6}$ eV. Our model adopts the generalized Gumbel distribution motivated by the relationship between the generalized Gumbel statistics and the distribution of the sum of non-identically distributed variables in dissipative stochastic systems. We provide an analytical expression for describing the $\Xmax$ distribution for photons and for nuclei, and for their first two statistical moments, namely $\langle \Xmax\rangle$ and $\sigma^{2}(\Xmax)$. The impact of the hadronic interaction model is investigated in detail, even in the case of the most up-to-date models accounting for LHC observations. We also briefly discuss the differences with a more classical approach and an application to the experimental data based on information theory.