One-loop flavor changing electromagnetic transitions

TL;DR

This paper analyzes one-loop flavor-changing electromagnetic transitions in heavy fermions, emphasizing the impact of external fermion masses and a key sign difference in charge factors between up and down type transitions.

Contribution

It provides formulas for the effective vertex in various approximations and the exact results for specific transitions, highlighting an often overlooked sign difference.

Findings

Sign difference in charge factors between $s\to d\gamma$ and $c\to u\gamma$ transitions.

Formulas for $F\to f\gamma$ effective vertex in multiple approximations.

Exact formulas for $t\to c\gamma$ and $\tau\to \mu\gamma$ transitions.

Abstract

We discuss the effect of the external fermion masses in the flavor-changing radiative transitions of a heavy fermion (quark or lepton) to a lighter fermion at the one-loop level, and point out an often overlooked crucial difference in the sign of a charge factor between transitions of the down type $s\to d\gamma$ and the up type $c\to u\gamma$. We give formulas for the $F\to f\gamma$ effective vertex in various approximations and the exact formula for $t\to c\gamma$ and $\tau \to \mu \gamma$.