A Parametrization of Cosmic Ray Shower Profiles Based on Shower Width

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).