Scattering of Glue by Glue on the Light-cone Worldsheet I: Helicity Non-conserving Amplitudes

TL;DR

This paper calculates one-loop gluon scattering amplitudes that violate helicity conservation using light-cone gauge, introducing novel regulators and analyzing the physics of helicity non-conserving processes.

Contribution

It presents a new light-cone gauge calculation method with innovative infrared and ultraviolet regulators for helicity non-conserving gluon amplitudes.

Findings

Regulators reproduce known one-loop amplitudes without infrared issues.

Collinear divergences are absent in helicity non-conserving amplitudes.

Loop integrand for maximal helicity violating process is identically zero.

Abstract

We give the light-cone gauge calculation of the one-loop on-shell scattering amplitudes for gluon-gluon scattering which violate helicity conservation. We regulate infrared divergences by discretizing the p^+ integrations, omitting the terms with p^+=0. Collinear divergences are absent diagram by diagram for the helicity non-conserving amplitudes. We also employ a novel ultraviolet regulator that is natural for the light-cone worldsheet description of planar Feynman diagrams. We show that these regulators give the known answers for the helicity non-conserving one-loop amplitudes, which don't suffer from the usual infrared vagaries of massless particle scattering. For the maximal helicity violating process we elucidate the physics of the remarkable fact that the loop momentum integrand for the on-shell Green function associated with this process, with a suitable momentum routing of the different contributing topologies, is identically zero. We enumerate the counterterms that must be included to give Lorentz covariant results to this order, and we show that they can be described locally in the light-cone worldsheet formulation of the sum of planar diagrams.