Energy determination of cosmic ray showers in surface arrays using signal inference at a single distance from the core

In most high energy cosmic ray surface arrays, the primary energy is currently determined from the value of the lateral distribution function at a fixed distance from the shower core, r0. The value of r0 is mainly related to the geometry of the array and is, therefore, considered as fixed independently of the shower energy or direction. We argue, however, that the dependence of r0 on energy and zenith angle is not negligible. Therefore, in the present work we propose a new characteristic distance, which we call ropt, specifically determined for each individual shower, with the objective of optimizing the energy reconstruction. This parameter may not only improve the energy determination, but also allow a more reliable reconstruction of the shape and position of rapidly varying spectral features. We show that the use of a specific ropt determined on a shower-to-shower basis, instead of using a fixed characteristic value, is of particular benefit in dealing with the energy reconstruction of events with saturated detectors, which are in general a large fraction of all the events detected by an array as energy increases. Furthermore, the ropt approach has the additional advantage of applying the same unified treatment for all detected events, regardless of whether they have saturated detectors or not.