Impact of QCD jets and heavy-quark production in cosmic-ray proton atmospheric showers up to 10$^{20}$ eV

The PYTHIA 6 Monte Carlo (MC) event generator, commonly used in collider physics, is interfaced for the first time with a fast transport simulation of a hydrogen atmosphere, with the same density as air, in order to study the properties of extended atmospheric showers (EAS) produced by cosmic ray protons with energies E$_{CR}\approx 10^{14}$--$10^{20}$ eV. At variance with the hadronic MC generators (EPOS-LHC, QGSJET, and SIBYLL) commonly used in cosmic-rays physics, PYTHIA includes the generation of harder hadronic jets and heavy (charm and bottom) quarks, thereby producing higher transverse momentum final particles, that could explain several anomalies observed in the data. The electromagnetic, hadronic, and muonic properties of EAS generated with various settings of PYTHIA 6, tuned to proton-proton data measured at the LHC, are compared to those from EPOS-LHC, QGSJET 01, QGSJET II, and SIBYLL 2.1. Despite their different underlying parton dynamics, the characteristics of the EAS generated with PYTHIA 6 are in between those predicted by the rest of MC generators. The only exceptions are the muonic components at large transverse distances from the shower axis, where PYTHIA predicts more activity than the rest of the models. Heavy-quark production, as implemented in this study for a hydrogen atmosphere, does not seem to play a key role in the EAS muon properties, pointing to nuclear effects as responsible of the muon anomalies observed in the air-shower data.