Charge and Magnetic Moment of the Neutrino in the Background Field Method and in the Linear R_xi^L Gauge

TL;DR

This paper calculates the neutrino's charge and magnetic moment using the Background Field Method and linear R_xi^L gauge, confirming the neutrino's electric charge cancels and the magnetic moment is gauge-independent.

Contribution

It introduces a formal Ward-Takahashi identity in the Background Field Method that ensures the neutrino's electric charge cancels and demonstrates the gauge invariance of the magnetic moment calculation.

Findings

Neutrino electric charge cancels due to Ward-Takahashi identity.

Magnetic moment calculation is gauge parameter independent.

Verification of identities in arbitrary gauges.

Abstract

We present a computation of the charge and the magnetic moment of the neutrino in the recently developed electro-weak Background Field Method and in the linear $R_{\xi}^L$ gauge. First, we deduce a formal Ward-Takahashi identity which implies the immediate cancellation of the neutrino electric charge. This Ward-Takahashi identity is as simple as that for QED. The computation of the (proper and improper) one loop vertex diagrams contributing to the neutrino electric charge is also presented in an arbitrary gauge, checking in this way the Ward-Takahashi identity previously obtained. Finally, the calculation of the magnetic moment of the neutrino, in the minimal extension of the Standard Model with massive Dirac neutrinos, is presented, showing its gauge parameter and gauge structure independence explicitly.