Single pion production in CC νμN scattering within a consistent effective Born approximation

The one pion production in charged current νμN scattering is analyzed within an extended version of a model used previously to include the Δ(1232) contribution in elastic and radiative pion-nucleon scattering, and in pion photoproduction. Because the resonant amplitude needs to be invariant under contact transformations, we identify the correct forms of the Δ propagator and the W-NΔ vertex that are consistent with this requirement. The only free parameter of the model, the axial form factor at zero momentum transfer, is fixed from data on the differential cross section for νμp→μ-pπ+ scattering. A reasonable agreement with the experimental data of all the νN→μN'π total cross sections is obtained. We show that the use of the complete Δ propagator instead of the Rarita-Schwinger one improves the theoretical results, leading to differences ranging from 10 to 30%, depending on the specific process