Dynamical coupled-channels model for neutrino-induced meson productions in resonance region

A dynamical coupled-channels (DCC) model for neutrino-nucleon reactions in the resonance region is developed. Starting from the DCC model that we have previously developed through an analysis of $\pi N, \gamma N\to \pi N, \eta N, K\Lambda, K\Sigma$ reaction data for $W\le 2.1$ GeV, we extend the model of the vector current to $Q^2\le$ 3.0 (GeV/$c$)$^2$ by analyzing electron-induced reaction data for both proton and neutron targets. We derive axial-current matrix elements that are related to the $\pi N$ interactions of the DCC model through the Partially Conserved Axial Current (PCAC) relation. Consequently, the interference pattern between resonant and non-resonant amplitudes is uniquely determined. We calculate cross sections for neutrino-induced meson productions, and compare them with available data. Our result for the single-pion production reasonably agrees with the data. We also make a comparison with the double-pion production data. Our model is the first DCC model that can give the double-pion production cross sections in the resonance region. We also make comparison of our result with other existing models to reveal an importance of testing the models in the light of PCAC and electron reaction data. The DCC model developed here will be a useful input for constructing a neutrino-nucleus reaction model and a neutrino event generator for analyses of neutrino experiments.