A pr 2 01 5 Energy reconstruction of hadron-initiated showers of ultra-high energy cosmic rays

The current methods to determine the primary energy of ultra -high energy cosmic rays (UHECRs) are di fferent when dealing with hadron or photon primaries. The current experiments co mbine two di fferent techniques, an array of surface detectors and fluorescence telescopes. The latter allow an almost calorim etric measurement of the primary energy. Thus, hadron-init iated showers detected by both type of detectors are used to calibrate the e nergy estimator from the surface array (usually the interpo lated signal at a certain distance from the shower core S(r0)) with the primary energy. On the other hand, this calibrati on is not feasible when searching for photon primaries since no high energy photon h as been unambiguously detected so far. Therefore, pure Mont e Carlo parametrizations are used instead. In this work, we present a new method to determine the primary energy of hadron-induced showers in a hybrid experiment bas ed on a technique previously developed for photon primaries. I t consists on a set of calibration curves that relate the surf ace energy estimator,S(r0), and the depth of maximum development of the shower, Xmax, obtained from the fluorescence telescopes. Then, the primary energy can be determined from pure surface infor mation sinceS(r0) and the zenith angle of the incoming shower are only needed. Considering a mixed sample of ultra-high energ y proton and iron primaries and taking into account the recon struction uncertainties and shower to shower fluctuations, we demonst rate that the primary energy may be determined with a systema tic uncertainty below 1% and resolution around 16% in the energy range from 1018.5 to 1019.6 eV. Several array geometries, the shape of the energy error distributions and the uncertainties due to the unknown composition of the primary flux have been analy zed as well.