Single photon production ${\nu }_{l}N\to {\nu }_{l}N\gamma$ in neutrino-nucleon scattering

The quasielastic charged current (CCQE) ${\nu }_{e}n\to e^{-}p$ scattering is the dominant mechanism to detect appearance of a ${\nu }_e$ in an almost ${\nu }_{\mu }$ flux at the 1 GeV scale. Actual experiments show a precision below 1% and between less known background contributions, but necessary to constraint the event excess, we have the radiative corrections. A consistent model recently developed for the simultaneous description of elastic and radiative $\pi N$ scattering, pion-photoproduction and single pion production processes, both for charged and neutral current neutrino-nucleon scattering, is extended for the evaluation of the radiative $\nu_l N\rightarrow \nu_l N \gamma$ cross section. Our results are similar to a previous (but inconsistent) theoretical evaluation in the low energy region, and show an increment in the upper region where the $\mathrm{\Delta }$ resonance becomes relevant.