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

TL;DR

This work investigates heavy quark production in ultra-high-energy cosmic ray interactions with the atmosphere within the Color Glass Condensate and dipole framework. By modeling both photon- and hadron-induced processes, it shows that the saturation scale becomes larger than the charm semihard scale at $E>10^{18}$ eV, leading to substantial suppression of charm production and, consequently, the prompt lepton flux. The study provides CGC-based cross sections, geometric scaling relations, and nuclear shadowing treatments, and delivers practical $x_F$-distribution parameterizations for cosmic ray shower simulations. It further finds that bottom production is less sensitive to saturation, yet its relative importance grows at the highest energies, reinforcing the overall conclusion that saturation effects curtail the expected prompt lepton background in neutrino searches.

Abstract

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 μ_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 τ_c = (Q^2+μ_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.