Simple Rules for Evanescent Operators in One-Loop Basis Transformations

TL;DR

This paper presents a straightforward method for handling evanescent operators during one-loop basis transformations, crucial for accurate higher-order calculations in quantum field theory.

Contribution

It introduces a simple, systematic procedure for basis changes at 1-loop level that accounts for evanescent operators, improving precision in quantum field theory computations.

Findings

Derived the 1-loop basis transformation from BMU to JMS basis.

Provided a systematic method for including evanescent operators in basis transformations.

Enhanced the accuracy of NLO QCD calculations through this method.

Abstract

The basis transformations of the effective operators often involve Fierz and other relations which are only valid in $D=4$ space-time dimensions. In general, in $D$ space-time dimensions, however, the evanescent operators have to be introduced to preserve such identities. Such operators contribute to one-loop basis transformations as well as to two-loop renormalization group running. In this talk, I discussed a simple procedure for systematically changing of basis at 1-loop level including shifts due to evanescent operators. As an example, we apply this method to derive the 1-loop basis transformation from the BMU basis useful for NLO QCD calculations, to the JMS basis used in the matching to the SMEFT.