Coherent Pion Production by Neutrinos

In this talk I review the main features of the coherent/diffractive pion production by neutrinos on nuclei. The method is based on PCAC and relates the reaction $$\mathbf{\text{boson}}$ + $\mathbf{\text{nucleus}}$ \to $\mathbf{\text{pion}}$ + $\mathbf{\text{nucleus}}$$ to elastic pion-nucleus scattering. Estimates for the expected rates and distributions in neutrino reactions are presented with the help of hadronic data. The absolute rates are significantly smaller than the older estimates which brings theory in agreement with the neutral current measurements and the bounds in charged current reactions.