Resonance Contributions to Radiative Corrections in Charged-Current Elastic (Anti)Neutrino-Nucleon Scattering at GeV Energies

We present the first evaluation of virtual resonance contributions to the charged-current (anti)neutrino-nucleon elastic scattering at GeV energies, focusing on the dominant $\mathrm{\Delta }(1232)$ resonance. We approximate the vector part of the $N\to \mathrm{\Delta }$ transition by the leading magnetic dipole term. Our results for the cross-section corrections at fixed neutrino energy indicate the permille-level contribution of resonance intermediate states to the elastic and radiative scattering cross sections. This calculation exhibits the expected infrared behavior of the invariant amplitudes and unpolarized cross sections. Our findings provide important insights into inelastic excitations in the charged-current (anti)neutrino-nucleon elastic scattering at GeV energies.