Model dependence of the polarization asymmetries in weak pion production off the nucleon

The work presents the study of the polarization observables in the single pion production (SPP) induced by the interaction of the muon neutrino (antineutrino) with nucleons. The SPP cross sections and spin asymmetries are computed within two phenomenological models. One is based on the nonlinear sigma model [E. Hernandez, J. Nieves, and M. Valverde, Phys. Rev. D 76, 033005 (2007)] and the other has origin in the linear sigma model [G. L. Fogli and G. Nardulli, Nucl. Phys. B160, 116 (1979)]. First, we show that the final nucleon polarization and target spin asymmetries are good observables to obtain information about the ${C}_{5}^{A}$ axial form factor. Second, we demonstrate that the nucleon polarization and the target spin asymmetries are sensitive to the relative phase between resonance and nonresonance amplitudes. We conclude that the polarization of the final nucleon and the target spin asymmetry are promising observables for testing SPP models, including studies of the axial content of $\mathrm{\ensuremath{\Delta}}(1232)$ resonance and unitarization procedures.