Radiative corrections to low-energy neutrino reactions

We show that the radiative corrections to charged current (CC) nuclear reactions with an electron (positron) in the final state are described by a universal function. The consistency of our treatment of the radiative corrections with the procedure used to extract the value of the axial coupling constant $g_A$ is discussed. To illustrate we apply our results to (anti) neutrino deuterium disintegration and to $\mathrm{pp}$ fusion in the sun. The limit of vanishing electron mass is considered, and a simple formula sufficiently accurate for $E_{\mathrm{obs}}\gtrsim 1\mathrm{MeV}$ is obtained. The size of the nuclear structure-dependent effects is also discussed. Finally, we consider CC transitions with an electron (positron) in the initial state and discuss some applications to electron capture reactions.