The Concepts of "Age" and "Universality" in Cosmic Ray Showers

TL;DR

This paper explores the concept of 'age' in cosmic ray showers, demonstrating its applicability to various primary particles and detailing how properties like electron size, spectra, and distributions depend on this parameter.

Contribution

It extends the use of the 'age' parameter to individual showers from different primaries and provides analytical methods to determine associated spectral and distribution shapes.

Findings

Showers with the same age share similar properties.

Electron and photon spectra are determined by the age parameter.

Analytical calculations of spectral shapes are possible.

Abstract

The concept of "age" as a parameter for the description of the state of development of high energy showers in the atmosphere has been in use in cosmic ray studies for several decades. In this work we briefly discuss how this concept, originally introduced to describe the average behavior of electromagnetic cascades, can be fruitfully applied to describe individual showers generated by primary particles of different nature, including protons, nuclei and neutrinos. Showers with the same age share three different important properties: (i) their electron size has the same fractional rate of change with increasing depth, (ii) the bulk of the electrons and photons in the shower (excluding high energy particles) have energy spectra with shapes and relative normalization uniquely determined by the age parameter, (iii) the electrons and photons in the shower have also the same angular and lateral distributions sufficiently far from the shower axis. In this work we discuss how the properties associated with the shower age can be understood with simple arguments, and how the shapes of the electron and photon spectra and the relative normalization that correspond to a certain age can be calculated analytically.