Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions

TL;DR

This paper develops a systematic method to compute complete form factors of gauge-invariant operators in pure Yang-Mills theory at loop level using six-dimensional spinor-helicity formalism, unitarity, and dimensional reconstruction, with new results for operators of the form Tr F^n.

Contribution

It introduces an extension of dimensional reconstruction to form factors in six dimensions and provides a systematic prescription for scalar operators, along with new one-loop form factor results.

Findings

Derived new one-loop minimal and non-minimal form factors for Tr F^n with n>2.

Developed a Mathematica package for six-dimensional spinor-helicity calculations.

Extended dimensional reconstruction to multiple loops for amplitudes and form factors.

Abstract

We present a systematic procedure to compute complete, analytic form factors of gauge-invariant operators at loop level in pure Yang-Mills. We consider applications to operators of the form $\mathrm{Tr}\, F^n$ where $F$ is the gluon field strength. Our approach is based on an extension to form factors of the dimensional reconstruction technique, in conjunction with the six-dimensional spinor-helicity formalism and generalised unitarity. For form factors this technique requires the introduction of additional scalar operators, for which we provide a systematic prescription. We also discuss a generalisation of dimensional reconstruction to any number of loops, both for amplitudes and form factors. Several novel results for one-loop minimal and non-minimal form factors of $\mathrm{Tr}\, F^n$ with $n>2$ are presented. Finally, we describe the \texttt{Mathematica} package \texttt{SpinorHelicity6D}, which is tailored to handle six-dimensional quantities written in the spinor-helicity formalism.