• DOI:10.1088/1475-7516/2013/07/050
• Corpus ID: 9497212

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

@article{Domenico2013ReinterpretingTD,
  title={Reinterpreting the development of extensive air showers initiated by nuclei and photons},
  author={Manlio De Domenico and Mariangela Settimo and Simone Riggi and Eric Bertin},
  journal={arXiv: High Energy Physics - Phenomenology},
  year={2013}
}

• M. D. Domenico, M. Settimo, +1 author E. Bertin
• Published 10 May 2013
• Physics
• arXiv: High Energy Physics - Phenomenology

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.