Coherent pion production by neutrino scattering off nuclei

The main part of coherent pion production by neutrinos on nuclei is essentially determined by partial conservation of the axial current (PCAC), provided that the leptonic momentum transferred square $Q^2$ remains sufficiently small. We give the formulas for the charged and neutral current cross sections, including also the small non-PCAC transverse current contributions and taking into account the effect of the ${\mu }^{-}$-mass. Our results are compared with the experimental ones and other theoretical treatments.