On-shell recursion for massive fermion currents

TL;DR

This paper investigates the applicability of BCFW recursion relations to off-shell currents involving massive quarks and gluons, identifying conditions to avoid unphysical poles and establishing valid recursion schemes.

Contribution

It provides conditions for valid BCFW shifts in off-shell currents with massive quarks, and derives an explicit formula for same-helicity gluon configurations.

Findings

Valid recursion relations are established for certain off-shell currents.

A gauge choice is identified that avoids unphysical poles.

An explicit formula for same-helicity gluon currents is derived.

Abstract

We analyze the validity of BCFW recursion relations for currents of n - 2 gluons and two massive quarks, where one of the quarks is off shell and the remaining particles are on shell. These currents are gauge-dependent and can be used as ingredients in the unitarity-based approach to computing one-loop amplitudes. The validity of BCFW recursion relations is well known to depend on the so-called boundary behavior of the currents as the momentum shift parameter goes to infinity. With off-shell currents, a new potential problem arises, namely unphysical poles that depend on the choice of gauge. We identify conditions under which boundary terms are absent and unphysical poles are avoided, so that there is a natural recursion relation. In particular, we are able to choose a gauge in which we construct a valid shift for currents with at least n - 3 gluons of the same helicity. We derive an analytic formula in the case where all gluons have the same helicity. As by-products, we prove the vanishing boundary behavior of general off-shell objects in Feynman gauge, and we find a compact generalization of Berends-Giele gluon currents with a generic reference spinor.