Resolution of Infrared Divergences in Gluon-Gluon Scattering Regulated on a Lightcone Worldsheet Lattice

TL;DR

This paper addresses infrared divergences in gluon-gluon scattering by refining the treatment of soft radiation on a lightcone lattice, achieving better high-energy behavior and confirming agreement with covariant methods.

Contribution

It introduces less restrictive constraints on unobserved radiation in lightcone gauge, improving the understanding of IR divergences and matching covariant calculations.

Findings

High-energy behavior of total probabilities improved from -ln^2s to ln s ln t

Complete agreement found between lightcone and covariant regularization methods

Enhanced analysis of IR divergences in gluon scattering processes

Abstract

We improve and update the discussion, given some years ago by my collaborators and me, of infrared divergences and Bremsstrahlung in one-loop gluon scattering probabilities in lightcone gauge. In that work, we showed that adding soft and collinear gluon radiation, satisfying simple Lorentz invariant constraints, not only cancelled all IR divergences, but resulted in compact expressions for the consequent scattering probabilities. Here we impose less restrictive (albeit noncovariant) constraints on the unobserved radiation, which increases the high energy (s) fixed momentum transfer (t) behavior of the total probabilities from -ln^2s to ln s ln t, a behavior shared by the (IR divergent) elastic probabilities. Using this new treatment we also make a much more detailed comparison of the lightcone results to covariant calculations using dimensional regularization, finding complete agreement between the two styles of calculation.