One-loop contributions to decays $e_b\to e_a \gamma$ and $(g-2)_{e_a}$ anomalies, and Ward identity

TL;DR

This paper derives analytic formulas for one-loop contributions to lepton flavor violating decays and anomalous magnetic moments, highlighting gauge consistency and Ward identity validation in quantum field theory calculations.

Contribution

It provides explicit formulas in the unitary gauge for lepton decay processes and magnetic moments, ensuring gauge invariance and Ward identity compliance.

Findings

Formulas expressed in Passarino-Veltman notation

Results consistent across different gauges and mass limits

Ward identity validation ensures correct photon couplings

Abstract

In this paper, we will present analytic formulas to express one-loop contributions to lepton flavor violating decays $e_b\to e_a \gamma$, which are also relevant to the anomalous dipole magnetic moments of charged leptons $e_a$. These formulas were computed in the unitary gauge, using the well-known Passarino-Veltman notations. We also show that our results are consistent with those calculated previously in the 't Hooft-Veltman gauge, or in the limit of zero lepton masses. At the one-loop level, we show that the appearance of fermion-scalar-vector type diagrams in the unitary gauge will violate the Ward Identity relating to an external photon. As a result, the validation of the Ward Identity guarantees that the photon always couples with two identical particles in an arbitrary triple coupling vertex containing a photon.