Forward neutrino production and event rates at the Future Circular Collider for hadron collisions

A proposed future ultra high energy collider such as the Future Circular Collider is expected to produce intense and collimated neutrino beams from weak hadron decays. In this study, we estimate the production yields of such neutrinos from proton-proton collisions at a center-of-mass energy of 100~TeV and an integrated luminosity of 1~ab$^{-1}$. Based on a hypothetical detector positioned either 0.5~km or 2~km downstream from the interaction point along the beamline, we derive the expected rates of charged current neutrino scattering events and their extension to neutrino energies of up to 50~TeV. We, for the first time, also evaluate the feasibility of observing the experimentally unverified direct production of $W^{\pm}$ bosons from neutrino-nucleus interactions.