CVC and PCAC in neutrino-lepton interactions

Abstract

We propose a formalism for the approximate calculation of inelastic neutrino interactions of the form ν + A → ν + B, when the states A and B consist of leptons and/or photons only. Using the conservation properties of the leptonic vector and axial vector currents, the cross section is related to that of photon- and axion-induced reactions ( γ, a 0) + A → B. The procedure is applied to coherent photon emission from atoms ( ν + Atom → ν + Atom + γ), radiative neutrino-electron scattering ( ν + e − → ν + e − + γ), and coherent pair production in the Coulomb field of a nucleus (ν + “γ” → ν + ℓ − + ℓ +) .