Using the Auger mass-composition analysis of ultra high energy cosmic rays, based on the shape-fitting of Xmax distributions [1], we demonstrate that mass composition and energy spectra measured by Auger, Telescope Array and HiRes can be brought into good agreement. The shape-fitting analysis of Xmax distributions shows that the measured sum of proton and Helium fractions, for some hadronic-interaction models, can saturate the total flux. Such p+He model, with small admixture of other light nuclei, naturally follows from cosmology with recombination and reheating phases. The most radical assumption of the presented model is the assumed unreliability of the experimental separation of Helium and protons, which allows to consider He/p ratio as a free parameter. The results presented here show that the models with dominant p+He composition explain well the energy spectrum of the dip in the latest (2015 -2017) data of Auger and Telescope Array, but have some tension at the highest energies with the expected Greisen-Zatsepin-Kuzmin cutoff. The Auger-Prime upgrade experiment has a great potential to reject or confirm this model.
ЖЭТФprocess on the Extragalactic Background Light (EBL) and on CMB. This process naturally produces secondary lighter nuclei, mixing thus with the primary composition. As was first predicted by Gerasimova and Rozental [9] in 1961, i.e. before the discovery of CMB, nuclei photo-disintegration on EBL results in a suppression of the UHECR energy spectrum (GR steepening). In fact, as was realised later, see e.g. [10], a more sharp cutoff occurs at higher energies where the nucleus photo-disintegration time on CMB becomes equal to that on EBL. This cutoff arises at Lorenz-factor Γ ∼ (3 − 5) × 10 9 for all nuclei. The energy of the cutoff E cut ∝ AΓ is different for primary nuclei with different A. This fact together with the unavoidable mixed composition, due to the production of secondary nuclei makes unclear any composition signature in the observed spectrum.At present the best method to measure the mass composition is given by the observation of fluorescent light produced by the e-m component of EAS in the atmosphere. All three aforementioned detectors use this method. However, for better accuracy the fluorescent-light method needs additional information, which in the case of HiRes is given by the stereo observation of fluorescent light, and in the case of Auger (and recently of TA) this additional information is obtained from the data of on-ground detectors (water-Cherenkov detectors in Auger and scintillation detectors in TA).The basic observable parameter related to mass composition is X max (E), the atmospheric depth where the number N (E) of particles in the cascade, with total energy E, reaches its maximum X max , is sensitive to the number of nucleons in the primary nucleus. Heavy nuclei interact higher in the atmosphere and have smaller fluctuations. In practice the actual quantity which allows to find the mass composition is the distribution N (X max ) of the showers with total energy E.I...