Non-Supersymmetric Loop Amplitudes and MHV Vertices

TL;DR

This paper extends the MHV diagram approach to non-supersymmetric Yang-Mills theories, deriving compact formulas for one-loop multi-gluon amplitudes and connecting them to known results and twistor space interpretations.

Contribution

It provides the first compact expression for the cut-constructible part of one-loop MHV amplitudes in pure Yang-Mills theory, broadening the applicability of MHV methods.

Findings

Derived a compact formula for one-loop MHV amplitudes in pure Yang-Mills.

Showed reduction to known amplitudes in special cases.

Discussed twistor space interpretation of the results.

Abstract

We show how the MHV diagram description of Yang-Mills theories can be used to study non-supersymmetric loop amplitudes. In particular, we derive a compact expression for the cut-constructible part of the general one-loop MHV multi-gluon scattering amplitude in pure Yang-Mills theory. We show that in special cases this expression reduces to known amplitudes - the amplitude with adjacent negative-helicity gluons, and the five gluon non-adjacent amplitude. Finally, we briefly discuss the twistor space interpretation of our result.