Impact of final state interactions on neutrino-nucleon pion production cross sections extracted from neutrino-deuteron reaction data

The current and near-future neutrino oscillation experiments require significantly improved neutrino-nucleus reaction models. Neutrino-nucleon pion production data play a crucial role to validate corresponding elementary amplitudes that go into such neutrino-nucleus models. Thus the currently available data extracted from charged-current neutrino-deuteron reaction data ($ν_μd\to μ^-πNN$) must be corrected for nuclear effects such as the Fermi motion and final state interactions (FSI). We study $ν_μd\to μ^-πNN$ with a theoretical model including the impulse mechanism supplemented by FSI from $NN$ and $πN$ rescatterings. An analysis of the spectator momentum distributions reveals that the FSI effects significantly reduce the spectra over the quasi-free peak region, and leads to a useful recipe to extract information of elementary $ν_μN\to μ^-πN$ processes using $ν_μd\to μ^-πNN$ data, with the important FSI corrections taken into account. We provide $ν_μN\to μ^-πN$ total cross sections by correcting the deuterium bubble chamber data for the FSI and Fermi motion. The results will bring a significant improvement on neutrino-nucleus reaction models for the near-future neutrino-oscillation experiments.