PCAC and coherent pion production by low energy neutrinos

Coherent pi^+ and pi^0 production in low energy neutrino reactions is discussed in the framework of the partially conserved axial vector current theory (PCAC). The role of lepton mass effects in suppressing the pi^+ production is emphasized. Instead of using models of pion nucleus scattering, the available data on pion Carbon scattering are implemented for an analysis of the PCAC prediction. Our results agree well with the published upper limits for pi^+ production but are much below the recent MiniBooNE result for pi^0 production.