Saturation Physics in Ultra High Energy Cosmic Rays: Heavy Quark Production

In this work we estimate the heavy quark production in the interaction of ultra high energy cosmic rays in the atmosphere, considering that the primary cosmic ray is a proton or a photon. At these energies the saturation momentum Q_{sat}^2 stays above the hard scale \mu_c^2=4m_c^2, implying charm production probing the saturation regime. In particular, we show that the ep HERA data presents a scaling on \tau_c = (Q^2+\mu_c^2)/Q_{sat}^2. We derive our results considering the dipole picture and the Color Glass Condensate formalism, which one shows to be able to describe the heavy quark production in photon-proton and proton-proton collisions. Nuclear effects are considered in computation of cross sections for scattering on air nuclei. Implications on the flux of prompt leptons at the earth are analyzed and a large suppression is predicted.Comment: 18 pages, 10 figures, 2 tables. Version to be published in JHE