Lepton mass effects in single pion production by neutrinos

We reconsider the Feynman-Kislinger-Ravndal model applied to neutrino-excitation of baryon resonances. The effects of lepton mass are included, using the formalism of Kuzmin, Lyubushkin, and Naumov. In addition we take account of the pion-pole contribution to the hadronic axial vector current. Application of this new formalism to the reaction ${\nu }_{\mu }+p\to {\mu }^{-}+{\Delta }^{++}$ at $E_{\nu }\sim 1\mathrm{GeV}$ gives a suppressed cross section at small angles, in agreement with the screening correction in Adler’s forward-scattering theorem. Application to the process ${\nu }_{\tau }+p\to {\tau }^{-}+{\Delta }^{++}$ at $E_{\nu }\sim 7\mathrm{GeV}$ leads to the prediction of right-handed ${\tau }^{-}$ polarization for forward-going leptons, in line with a calculation based on an isobar model. Our formalism represents an improved version of the Rein-Sehgal model, incorporating lepton mass effects in a manner consistent with partially conserved axial-vector current.