S-matrix equivalence restored

TL;DR

This paper establishes a direct correspondence between the canonical transformation coefficients and light-cone diagrams in Yang-Mills theory, demonstrating S-matrix equivalence at one-loop level with certain helicity configurations.

Contribution

It derives a new recursion relation linking canonical transformation coefficients to light-cone diagrams, clarifying S-matrix equivalence in light-cone Yang-Mills theory.

Findings

S-matrix equivalence holds up to one-loop with regularized MHV vertices.

The difference involves omission of all-positive helicity one-loop amplitudes.

A new recursion relation for transformation coefficients was established.

Abstract

The canonical transformation that maps light-cone Yang-Mills theory to a Lagrangian description of the MHV rules is non-local, consequently the two sets of fields do not necessarily generate the same S-matrix. By deriving a new recursion relation for the canonical transformation expansion coefficients, we find a direct map between these coefficients and tree level light-cone diagrams. We use this to show that, at least up to one-loop with dimensionally regularised MHV vertices, the only difference is the omission of the one-loop amplitudes in which all gluons have positive helicity.