The Space-Cone Gauge, Lorentz Invariance and On-Shell Recursion for One-Loop Yang-Mills amplitudes

TL;DR

This paper develops recursion relations for specific one-loop Yang-Mills amplitudes using the space-cone gauge, leveraging helicity symmetry and gauge Lorentz invariance to determine soft factors.

Contribution

It introduces a novel approach to derive recursion relations for one-loop amplitudes in QCD using the space-cone gauge and symmetry principles.

Findings

Recursion relations for (++... +) and (-++... +) amplitudes are obtained.

Helicity symmetry guides the choice of reference twistors and momentum shifts.

Gauge Lorentz invariance determines the soft factors in the amplitudes.

Abstract

Recursion relations are succinctly obtained for $(++... +)$ and $(-++... +)$ amplitudes in the context of the space-cone gauge in QCD. We rely on the helicity symmetry of the problems to dictate our choices of reference twistors and the momentum shifts to complexify the amplitudes. Of great importance is the power of gauge Lorentz invariance, which is enough to determine the soft factors in the latter cases.