All available theoretical estimates of neutrino-induced coherent pion production rely on the local approximation for the Delta propagator. The validity of this approximation is scrutinized. It is found that the local approximation overestimates the n
eutrino-induced coherent pion production on nuclei significantly, by up to 100%.
It is pointed out that so far all theoretical estimates of coherent pion production off nuclei induced by neutrinos rely on the local approximation well known in photonuclear physics. The effects of dropping this approximation are discussed. It is fo
und that in a plane wave approximation for the pion the local approximation overestimates the coherent neutrino-induced pion production on nuclei.
