# One-loop MHV Rules and Pure Yang-Mills

## TL;DR

This paper addresses the incompleteness of the standard MHV diagram approach in pure Yang-Mills theory by introducing Lorentz violating counterterms that generate missing rational terms in one-loop amplitudes, aligning with known results.

## Contribution

It proposes that Lorentz violating counterterms in a specific regularization scheme produce the missing rational terms in one-loop pure Yang-Mills amplitudes, enhancing the MHV framework.

## Key findings

- Counterterms generate missing rational terms in one-loop amplitudes.
- A simple counterterm reproduces all-plus helicity amplitudes.
- Results agree with known expressions for one-loop amplitudes.

## Abstract

It has been known for some time that the standard MHV diagram formulation of perturbative Yang-Mills theory is incomplete, as it misses rational terms in one-loop scattering amplitudes of pure Yang-Mills. We propose that certain Lorentz violating counterterms, when expressed in the field variables which give rise to standard MHV vertices, produce precisely these missing terms. These counterterms appear when Yang-Mills is treated with a regulator, introduced by Thorn and collaborators, which arises in worldsheet formulations of Yang-Mills theory in the lightcone gauge. As an illustration of our proposal, we show that a simple one-loop, two-point counterterm is the generating function for the infinite sequence of one-loop, all-plus helicity amplitudes in pure Yang-Mills, in complete agreement with known expressions.