Neutral current neutrino–nucleon scattering within a consistent isobar model and the Δ(1232) resonance-background interference

One-pion production in neutrino scattering off nucleons and nuclei plays and important role as a source of relevant data on hadronic structure and in the analysis of neutrino oscillation experiments. Here we develop a consistent model to describe these processes in the case of neutral currents, which treats the resonant and background contributions to the cross sections in a coherent way. Previously we have used this model to describe the elastic and radiative pion–nucleon scattering, pion-photoproduction reactions and the single-pion production in charged current neutrino–nucleon scattering. In this paper we have extended the model to describe the single-pion production in neutral current neutrino–nucleon scattering for πN invariant-mass distributions up to 2 GeV. For that purpose we include the effects of finite size of hadrons by introducing an appropriate form factor. Good agreement is found between our results and available experimental data for the total cross sections and the invariant-mass distributions of the πN system, as well as with simulations in the case of scattering on free nucleons.