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

## TL;DR

This paper presents a novel on-shell method for computing one-loop amplitudes involving massive fermions, utilizing six-dimensional spinor-helicity formalism and unitarity cuts, avoiding divergences and fixing ambiguities through infrared and ultraviolet pole matching.

## Contribution

It introduces a unitarity-compatible approach that leverages six-dimensional formalism to efficiently compute massive fermion amplitudes at one loop, avoiding wavefunction divergences.

## Key findings

- Successfully computes one-loop amplitudes with massive fermions using on-shell methods.
- Avoids divergences in wavefunction cuts by matching infrared and ultraviolet poles.
- Constructs an effective six-dimensional Lagrangian to simplify amplitude calculations.

## 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 $4-2\epsilon$ dimensions and ultraviolet poles in $6-2\epsilon$ 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.