Dipole operators in Fierz identities

TL;DR

This paper analyzes how dipole operators affect one-loop Fierz identities, providing shifts in QCD and QED for four-fermion operators, thereby simplifying basis changes and operator elimination in quantum field theory calculations.

Contribution

It introduces a systematic study of dipole operator contributions to one-loop Fierz identities, enhancing the simplification of operator basis transformations.

Findings

Derived QCD and QED shifts for four-fermion operators

Simplified one-loop basis change procedures

Enabled consistent elimination of complex operators

Abstract

We study the contribution from dipole operators to one-loop Fierz identities and provide the resulting QCD and QED shifts to the tree-level relations for all four-fermion operators. The results simplify one-loop basis changes as well as matching computations and allow one to consistently eliminate operators from an operator basis which give rise to complications, e.g. traces involving $\gamma_5$.