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 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 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 PCAC.