Precise predictions for multi-${\rm TeV}$ and ${\rm PeV}$ energy neutrino scattering rates

The scattering rate of multi-${\rm TeV}$ and ${\rm PeV}$ energy neutrinos is fast becoming an interesting topic in (astro)particle-physics. This is due to experimental progress at Neutrino Telescopes such as IceCube which have begun to gain sensitivity to the flux of neutrinos in this energy range. In view of this, a precise calculation of the scattering rate of neutrinos upon atoms is presented. The two main components of the calculation are the differential cross-section predictions for neutrino scattering upon an atomic nucleus (such as that which make up water), as well as upon atomic electrons. In the first case, the predictions for neutrino-nucleon cross-sections in charged- and neutral-current scattering are refined by including resonant contributions generated within the photon field of the nucleus, which alter the considered distributions by up to $\approx 4\%$. In the latter case, radiative corrections are provided for all $2\to2$ scattering processes of the form $\bar{\nu}_e e^-\to f\bar{f}^{\prime}$. For antineutrino energies of $E_{\bar{\nu}_e}\approx6{\rm~PeV}$, where these processes become resonantly enhanced (the Glashow resonance) and dominate the total cross-section, these corrections amount to $\approx-10\%$.