Neutrino-induced single-pion production off the nucleon in covariant chiral perturbation theory with explicit delta degrees of freedom

We present a calculation of neutrino-induced pion production off the nucleon up to one-loop order in covariant SU(2) chiral effective field theory with explicit inclusion of the Δ(1232) resonance. The calculation is carried out by employing the extended-on-mass-shell scheme to handle terms that violate power-counting, and the complex mass scheme to account for the complex pole position of intermediate deltas. Of the 25 next-to-leading and next-to-next-to-leading low-energy constants entering the amplitude, 17 are already determined in non-weak processes, while four are estimated by fitting the axial nucleon-to-delta transition form factors to the Adler parametrization. The remaining four low-energy constants are set to zero. Results for the total and differential cross sections are presented and compared to experimental data from ANL and BNL, and to results from models and event generators.