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We have studied neutral and charged current (anti)neutrino induced $\eta$production off the free nucleon target at MicroBooNE energies, in the light ofrecent results reported by the MicroBooNE collaboration for the total $\eta$production cross section. This study has been made using a theoretical model inwhich the weak hadronic current receives contribution from the nonresonant Bornterms as well as from the resonance excitations. The Born terms are obtainedusing the SU(3) symmetric chiral model, used earlier in the study of $K-$mesonproduction. The contribution from the resonance terms is considered from theexcitation of five nucleon resonances viz. $S_{11}(1535)$, $S_{11}(1650)$,$P_{11}(1710)$, $P_{11}(1880)$, and $S_{11}(1895)$. To fix the parameters ofthe vector current interaction, this model is first used to study theelectromagnetic production of $\eta$ mesons induced by real and virtualphotons, and the theoretical results have been compared with the data from theMAINZ and JLab experiments. The partially conserved axial-vector currenthypothesis and generalized Goldberger-Treiman relation are used to fix theparameters of the axial-vector current interaction. The results are presentedfor the total cross section for the neutral and charged current induced $\eta$production, ratio of the cross sections for the charged current to neutralcurrent, MicroBooNE flux averaged cross section $\langle \sigma \rangle$,$\left \langle \frac{d\sigma}{dQ^2} \right\rangle$ and $\left\langle\frac{d\sigma}{dp_\eta} \right\rangle$, which may be useful in the futureanalysis of MicroBooNE as well as other accelerator and atmospheric neutrinoexperiments being performed in the ${\cal O}$(1)~GeV energy region.

Weak production of $\eta$ mesons induced by $\nu_{\mu}(\bar{\nu}_\mu)$ at MicroBooNE energies