From $D_{s}^{\pm}$ production asymmetry at the LHC to prompt $ν_τ$ at IceCube

Abstract: The description of the heavy meson production at large energies and forward rapidities at the LHC is fundamental to derive realistic predictions of the prompt atmospheric neutrino flux at the IceCube Observatory. In particular, the prompt tau neutrino flux is determined by the decay of $D_s$ mesons produced in cosmic ray - air interactions at high energies and large values of the Feynman - $x_F$ variable. Recent data from the LHCb Collaboration indicate a production asymmetry for $D_s^+$ and $D_s^-$ mesons, which cannot be explained in terms of the standard modelling of the hadronization process. In this paper we demonstrate that this asymmetry can be described assuming an asymmetric strange sea ($s(x) \ne \bar s(x)$) in the proton wave function and taking into account of the charm and strange fragmentation into $D_s$ mesons. Moreover, we show that the strange quark fragmentation contribution is dominant at large - $x_F$ ($\ge 0.3$). The prompt $\nu_{\tau}$ flux is calculated and the enhancement associated to the strange quark fragmentation contribution, disregarded in previous calculations, is estimated.