Forward production of prompt neutrinos in the atmosphere and at the LHC

The atmospheric neutrino flux at very high energies is dominated by prompt neutrinos, mostly contributed by the decays of charmed hadrons produced in the forward direction by cosmic ray interactions with air nuclei. Theoretical predictions of the prompt atmospheric neutrino flux have large uncertainties mainly related with charm hadron production. Two ongoing forward experiments and the proposed Forward Physics Facility at the LHC can detect prompt neutrinos from the charm hadrons produced in the forward direction. We will present the kinematic regions relevant to the prompt atmospheric neutrino flux in terms of collider kinematic variables, the collision energy sqrt{s} and the charm hadron's center-of-mass rapidity y, and discuss implications of the forward experiments at the LHC on the theoretical predictions of the prompt atmospheric neutrino flux.