External leg corrections in the unitarity method

TL;DR

This paper introduces an off-shell continuation method to evaluate divergent unitarity cuts involving massive external fermions, enabling finite bubble coefficient calculations in quantum field theory.

Contribution

It proposes a novel off-shell continuation technique to handle divergences in unitarity cuts for massive external fermions, improving the calculation accuracy.

Findings

Finite bubble coefficients obtained using the new continuation method.

Explicit inclusion of external leg counterterm contributions.

Method applicable to divergent unitarity cut evaluations.

Abstract

Unitarity cuts diverge in the channel of a single massive external fermion. We propose an off-shell continuation of the momentum that allows a finite evaluation of the unitarity cuts. If the cut is taken with complete amplitudes on each side, our continuation and expansion around the on-shell configuration produces the finite contribution to the bubble coefficient. Finite parts in the expansion of the external leg counterterms must be included explicitly as well.