Weak $\eta$ production off the nucleon

The weak $\eta$-meson production off the nucleon induced by (anti)neutrinos is studied at low and intermediate energies, the range of interest for several ongoing and future neutrino experiments. We consider Born diagrams and the excitation of $N^\ast (1535)S_{11}$ and $N^\ast(1650)S_{11}$ resonances. The vector part of the N-$S_{11}$ transition form factors has been obtained from the MAID helicity amplitudes while the poorly known axial part is constrained with the help of the partial conservation of the axial current (PCAC) and assuming the pion-pole dominance of the pseudoscalar form factor.