The effective neutrino charge radius in the presence of fermion masses

Abstract

We show how the crucial gauge cancellations leading to a physical definition of an effective neutrino charge radius persist in the presence of non-vanishing fermion masses. An explicit one-loop calculation demonstrates that, as happens in the massless case, the pinch technique rearrangement of the Feynman amplitudes, together with the judicious exploitation of the fundamental current relation J α ( 3 ) = 2 ( J Z + sin θ w 2 J γ ) α , leads to a completely gauge independent definition of the effective neutrino charge radius. Using the formalism of the Nielsen identities it is further proved that the same cancellation mechanism operates unaltered to all orders in perturbation theory.