Charmed hadron production in the QGSJET-III model: relevance to calculations of the prompt atmospheric neutrino background

The treatment of charmed hadron production in the framework of the QGSJET-III Monte Carlo generator is developed, including both perturbative and nonperturbative contributions. For the former, a leading order (LO) perturbative formalism is employed. The so-called K-factor designed to take effectively into account higher order corrections, which controls the magnitude of the LO perturbative contribution, is fixed based on a comparison with experimental data on D meson production at the Large Hadron Collider. For the nonperturbative intrinsic charm, a phenomenological Regge-based treatment is developed, with the corresponding normalization being chosen based on measurements of the spectra of Λc baryons at large values of Feynman x. The model is applied for a calculation of the prompt atmospheric muon neutrino flux in the $10-100$ TeV and $1-10$ PeV energy intervals.