Simple rules for evanescent operators in one-loop basis transformations

Abstract

Basis transformations often involve Fierz and other relations that are only valid in $D=4$ dimensions. In general $D$ spacetime dimensions, however, evanescent operators have to be introduced in order to preserve such identities. Such evanescent operators contribute to one-loop basis transformations as well as to two-loop renormalization group running. We present a simple procedure on how to systematically change basis at the one-loop level by obtaining shifts due to evanescent operators. As an example we apply this method to derive the one-loop basis transformation from the Buras, Misiak and Urban basis useful for next-to-leading order QCD calculations, to the Jenkins, Manohar and Stoffer basis used in the matching to the standard model effective theory.