Final state radiation from high and ultrahigh energy neutrino interactions

Charged leptons produced by high-energy and ultrahigh-energy neutrinos have a substantial probability of emitting prompt internal bremsstrahlung $\nu_\ell + N \rightarrow \ell + X + \gamma$. This can have important consequences for neutrino detection. We discuss observable consequences at high- and ultrahigh-energy neutrino telescopes and the Large Hadron Collider's Forward Physics Facility. Logarithmic enhancements can be substantial (e.g., $\sim 20\%$) when either the charged lepton's energy or the rest of the cascade is measured. We comment on final state radiation's impacts on measuring the inelasticity distribution, $\nu/\bar{\nu}$ flux ratio, throughgoing muons, and double-bang signatures for high-energy neutrino observation. Furthermore, for ultrahigh-energy neutrino observation, we find that final state radiation increases the overall detectable energy by as much as 20\%, affects flavor measurements, and decreases the energy of both Earth-emergent tau leptons and regenerated tau neutrinos. Many of these have significant impacts on measuring neutrino fluxes and spectra. Finally, for the Large Hadron Collider's Forward Physics Facility, we find that final state radiation will impact future extractions of strange quark parton distribution functions. Final state radiation should be included in future analyses at neutrino telescopes and the Forward Physics Facility.