Gauge Independence of Magnetic Moment and Vanishing Charge of Dirac Neutrinos: an Exact One-loop Demonstration

TL;DR

This paper explicitly demonstrates that the magnetic moment and zero charge of Dirac neutrinos are gauge-independent at one-loop level in the extended standard model, ensuring their physical observability.

Contribution

It provides an exact one-loop proof of gauge independence for neutrino magnetic moment and charge in both R_xi and unitary gauges, using direct integrand manipulation.

Findings

Magnetic moment and charge are gauge-independent at one loop.

The proof applies for any particle masses and neutrino mixing.

The method involves algebraic manipulation of loop integrands.

Abstract

The magnetic moment and vanishing charge of a Dirac neutrino are physically observable quantities and must not depend on the choice of gauge in a consistent quantum field theory. We verify this statement explicitly at the one loop level in both R_xi and unitary gauges of the minimally extended standard model. We accomplish this by manipulating directly the integrands of loop integrals and employing simple algebraic identities and integral relations. Our result generally applies for any masses of the relevant particles and unitary neutrino mixing.