Lepton mass effects in single pion production by neutrinos

Abstract

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 ${\ensuremath{\nu}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+{\ensuremath{\Delta}}^{++}$ at ${E}_{\ensuremath{\nu}}\ensuremath{\sim}1\text{ }\text{ }\mathrm{GeV}$ gives a suppressed cross section at small angles, in agreement with the screening correction in Adler's forward-scattering theorem. Application to the process ${\ensuremath{\nu}}_{\ensuremath{\tau}}+p\ensuremath{\rightarrow}{\ensuremath{\tau}}^{\ensuremath{-}}+{\ensuremath{\Delta}}^{++}$ at ${E}_{\ensuremath{\nu}}\ensuremath{\sim}7\text{ }\text{ }\mathrm{GeV}$ leads to the prediction of right-handed ${\ensuremath{\tau}}^{\ensuremath{-}}$ 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.