A Parametrization of Cosmic Ray Shower Profiles Based on Shower Width

TL;DR

This paper introduces a new parametrization of cosmic ray shower profiles using width and asymmetry, reducing correlations and improving reconstruction accuracy across different profile functions.

Contribution

It proposes a unified shower profile parametrization based on full width at half maximum and asymmetry, enhancing consistency and reducing parameter correlations.

Findings

Reduced parameter correlations in shower profile reconstructions.

Unified parametrization applicable to multiple profile functions.

Improved constraints on uncorrelated parameters during reconstruction.

Abstract

Cosmic ray (CR) air showers, detected via the air fluorescence technique, are reconstructed in part using functions that parameterize the longitudinal profile of each shower. The profile parameterization yields the position of shower maximum, X_max, which is sensitive to the incident CR particle type: e.g. p, C/N/O, Fe or photons. The integral of the profile is directly related to the shower energy. The Pierre Auger fluorescence reconstruction uses the Gaisser-Hillas 4-parameter form. The HiRes group has used both the Gaisser-Hillas form and a 3-parameter Gaussian in Age form. Historically analytic shower theory suggested yet other forms; the best known is a 3-parameter form popularized by Greisen. Our work now uses the shower full width half-maximum, "fwhm", and shower asymmetry parameter, "f", to unify the parameterization of all three profile functions. Furthermore shower profiles expressed in terms of the new parameters: (fwhm, f) have correlations greatly reduced over Gaisser-Hillas parameters (X_0, lambda). This allows shower profile reconstructions to add constraints (if needed) on the mostly uncorrelated parameters (fwhm, f).