Single pion production in CC νμN scatteringwithin a consistent effective Born approximation

摘要

The one pion production in charged current νμN scattering is analyzed within an extended versionof a model used previously to include the Δ(1232) contribution in elastic and radiative pion–nucleonscattering, and in pion photoproduction. Because the resonant amplitude needs to be invariant undercontact transformations, we identify the correct forms of the Δ propagator and the WNΔ vertex thatare consistent with this requirement. The only free parameter of the model, the axial form factor at zeromomentum transfer, is fixed from data on the differential cross section for νμp →μpπ+ scattering.A reasonable agreement with the experimental data of all the νN → μNπ total cross sections isobtained. We show that the use of the complete Δ propagator instead of the Rarita–Schwinger oneimproves the theoretical results, leading to differences ranging from 10 to 30, depending on the specificprocess.