Charged current (anti)neutrino induced eta production off the nucleon

The charged current (anti)neutrino induced eta production from the nucleons is studied in a model based on the effective Lagrangians to evaluate the contribution from the nonresonant and resonant diagrams. The contribution from the nonresonant background terms has been obtained using a microscopic model based on the SU(3) chiral Lagrangians. The contribution from the resonant diagrams due to the low lying $S_{11}(1535)$, $S_{11} (1650)$, and $P_{11} (1710)$ resonances has been evaluated using an effective phenomenological Lagrangian with its parameters determined from the experimental values of their branching ratios and decay widths to the $N\eta$ channel. The model is first used to reproduce satisfactorily the experimental data from the MAINZ and JLab on the total cross sections for the photo- and electro- production of $\eta$ mesons, which fixes the model parameters in the vector current interaction. The PCAC hypothesis and generalized Goldberger-Treiman relation are used to fix the parameters of the axial vector interaction. The model is then applied to study the weak production of eta mesons induced by the neutrinos and antineutrinos, and predicts the numerical values for the $Q^2$-distribution, $\eta$-momentum distribution, and the total cross section for the reactions $\nu_{\mu} + n \longrightarrow \mu^{-} + p + \eta$ and $\bar{\nu}_{\mu} + p \longrightarrow \mu^+ + n + \eta$ in the energy region up to 2 GeV. It is found that the photo, electro, and (anti)neutrino production of eta mesons is dominated by the contribution from the $S_{11}(1535)$ resonance. The results discussed in this work are relevant for the present and future accelerator experiments like MicroBooNE, T2K, NOvA, MINERvA, T2-HyperK and DUNE as well as for the atmospheric neutrino experiments.