Restoration of azimuthal symmetry of muon densities in extended air showers

At ground level, the azimuthal distribution of muons in inclined Extensive Air Showers (EAS) is asymmetric, mainly due to geometric effects. Several EAS observables sensitive to the primary particle mass, are constructed after mapping the density of secondary particles from the ground plane to the shower plane (perpendicular to the shower axis). A simple orthogonal projection of the muon coordinates onto this plane distorts the azimuthal symmetry in the shower plane. Using CORSIKA simulations, we correct for this distortion by projecting each muon onto the normal plane following its incoming direction, taking also into account the attenuation probability. We show that besides restoring the azimuthal symmetry of muons density around the shower axis, the application of this procedure has a significant impact on the reconstruction of the distribution of the muon production depth and of its maximum, $X_{\rm max}^{\mu}$, which is an EAS observable sensitive to the primary particle mass. Our results qualitatively suggest that not including it in the reconstruction process of $X_{\rm max}^{\mu}$ may introduce a bias in the results obtained by analyzing the actual data on the basis of Monte Carlo simulations.
Comment: Accepted for publication in Astroparticle Physics