Amplitudes in Pure Yang-Mills and MHV Diagrams

TL;DR

This paper develops a method to compute one-loop gluon scattering amplitudes in non-supersymmetric Yang-Mills theory using MHV diagrams, revealing new insights into amplitude contributions and variable transformations.

Contribution

It introduces a novel approach combining MHV diagrams with lightcone Yang-Mills variables to calculate all-negative helicity amplitudes at one loop.

Findings

Calculated all-negative helicity one-loop amplitudes.

Identified Jacobian contributions from variable changes.

Connected amplitude contributions to violations of the equivalence theorem.

Abstract

We show how to calculate the one-loop scattering amplitude with all gluons of negative helicity in non-supersymmetric Yang-Mills theory using MHV diagrams. We argue that the amplitude with all positive helicity gluons arises from a Jacobian which occurs when one performs a Backlund-type holomorphic change of variables in the lightcone Yang-Mills Lagrangian. This also results in contributions to scattering amplitudes from violations of the equivalence theorem. Furthermore, we discuss how the one-loop amplitudes with a single positive or negative helicity gluon arise in this formalism. Perturbation theory in the new variables leads to a hybrid of MHV diagrams and lightcone Yang-Mills theory.