One-loop Fierz Transformations

Fierz transformations for four-fermion operators are generalized to the one-loop level. A general renormalization scheme is used to compute QCD and QED corrections to the tree-level relations, which result from Fierz-evanescent operators. The results can be used to perform general one-loop basis transformations involving four-fermi and evanescent operators. We illustrate the usefulness of our results by discussing two examples from a matching calculation and a one-loop basis change.