The Fermionic Universal One-Loop Effective Action

TL;DR

This paper derives a universal one-loop effective action for fermions, enabling simplified calculations of effective operators from heavy fermion loops using path integral and covariant derivative expansion techniques.

Contribution

It introduces the fermionic universal one-loop effective action (UOLEA), expanding the universal structure to include heavy fermions with various couplings, and clarifies its relation to previous results.

Findings

Derived the fermionic UOLEA for heavy fermions with multiple couplings.

Provided analytical expressions for effective operators from heavy fermion loops.

Clarified the relation of new terms to existing literature.

Abstract

Recent development of path integral matching techniques based on the covariant derivative expansion has made manifest a universal structure of one-loop effective Lagrangians. The universal terms can be computed once and for all to serve as a reference for one-loop matching calculations and to ease their automation. Here we present the fermionic universal one-loop effective action (UOLEA), resulting from integrating out heavy fermions with scalar, pseudo-scalar, vector and axial-vector couplings. We also clarify the relation of the new terms computed here to terms previously computed in the literature and those that remain to complete the UOLEA. Our results can be readily used to efficiently obtain analytical expressions for effective operators arising from heavy fermion loops.