Energy reconstruction of hadron-initiated showers of ultra-high energy cosmic rays

• A new method to determine the primary energy of ultra-high energy cosmic rays in hybrid experiments is presented.
• The energy could be determined without bias and resolution around 16%.
• Several array geometries have been considered.
• The energy error distributions are nearly Gaussian.
• The maximum uncertainty of the method due to the unknown composition of the primary flux is 10%.

The current methods to determine the primary energy of ultra-high energy cosmic rays (UHECRs) are different when dealing with hadron or photon primaries. The current experiments combine two different techniques, an array of surface detectors and fluorescence telescopes. The latter allow an almost calorimetric measurement of the primary energy. Thus, hadron-initiated showers detected by both type of detectors are used to calibrate the energy estimator from the surface array (usually the interpolated signal at a certain distance from the shower core S(r0))S(r0)) with the primary energy. On the other hand, this calibration is not feasible when searching for photon primaries since no high energy photon has been unambiguously detected so far. Therefore, pure Monte 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 based on a technique previously developed for photon primaries. It consists on a set of calibration curves that relate the surface energy estimator, S(r0)S(r0), and the depth of maximum development of the shower, XmaxXmax, obtained from the fluorescence telescopes. Then, the primary energy can be determined from pure surface information since S(r0)S(r0) and the zenith angle of the incoming shower are only needed. Considering a mixed sample of ultra-high energy proton and iron primaries and taking into account the reconstruction uncertainties and shower to shower fluctuations, we demonstrate that the primary energy may be determined with a systematic 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 analyzed as well.