Radiative corrections to anti-neutrino proton scattering at low energies

Abstract

For the low-energy anti-neutrino reaction, $\bar{\nu}_e + p \to e^+ + n$, which is of great current interest in connection with on-going high-precision neutrino-oscillation experiments, we calculate the differential cross section in a model-independent effective field theory (EFT), taking into account radiative corrections of order $\alpha$. In EFT, the short-distance radiative corrections are subsumed into well-defined low-energy constants the values of which can in principle be determined from the available neutron beta-decay data. In our low-energy EFT, the order-$\alpha$ radiative corrections are considered to be of the same order as the nucleon recoil corrections, which include the "weak magnetism" contribution. These recoil corrections have been evaluated as well. We emphasize that EFT allows for a systematic evaluation of higher order corrections, providing estimates of theoretical uncertainties in our results.