A generalized description of the signal size in extensive air shower detectors and its applications

The number as well as the energy and angular distributions of particles in extensive air showers (EAS) depend on the stage of the shower development and the distance to the shower axis. In this work we derive an analytic parameterization of the particle distributions at ground from air shower simulations convolved with the response of a surface detector array. Shower particles are classified into four components according to the shower component they belong to: the muonic component, the electromagnetic component stemming from muon interactions and muon decay, the purely electromagnetic component, and the newly introduced electromagnetic component from low-energy hadrons. Using this scheme, we will show that the total signal at ground level for different surface detectors can be described with minimal fluctuations with parameterizations depending on the primary energy, position of the shower maximum, and the overall number of muons in the shower. The simulation results for different combinations of primaries and hadronic interaction models are reproduced with an accuracy better than 5-10% in the range from 100 m to 2000 m from the shower core. This parameterization is then used as a Lateral Distribution ansatz to reconstruct showers in current EAS experiments. Since this ansatz depends on physical parameters, it opens the possibility to infer them from data.