A unitarity compatible approach to one-loop amplitudes with massive fermions

Abstract

We explain how one-loop amplitudes with massive fermions can be computed using only on-shell information. We first use the spinor-helicity formalism in six dimensions to perform generalised unitarity cuts in $d$ dimensions. We then show that divergent wavefunction cuts can be avoided, and the remaining ambiguities in the renormalised amplitudes can be fixed, by matching to universal infrared poles in $4-2ϵ$ dimensions and ultraviolet poles in $6-2ϵ$ dimensions. In the latter case we construct an effective Lagrangian in six dimensions and reduce the additional constraint to an on-shell tree-level computation.

Comments: 33 pages, 7 figures, 1 table (v2 updated acknowledgments)