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arXiv · 2412.19629

On one-loop amplitudes in gauge theories

Qu Cao·Jin Dong·Song He·Fan Zhu
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Abstract

We propose a new ``universal expansion" for one-loop amplitudes with arbitrary number of gluons in $D$ dimensions, which holds for general gauge theories with gluons/fermions/scalars in the loop, including pure and supersymmetric Yang-Mills theories. It expresses the $n$-gluon amplitudes as a linear combination of universal scalar-loop amplitudes with $n{-}m$ gluons and $m$ scalars, multiplied by gauge-invariant building blocks (defined for general gauge theories); the integrands of these scalar-loop amplitudes are given in terms of tree-level objects attached to the scalar loop, or by differential operators acting on the most important part which is proportional to $D$ (with $m=0$). We present closed-formula for these one-loop integrands and prove them by showing that the single cuts are correctly reproduced by the gluing of an additional pair of gluons (fermions/scalars) in the forward limit, plus $n$ gluons in a tree amplitude.

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Qu Cao, Jin Dong, Song He, Fan Zhu. 2024-12-27. On one-loop amplitudes in gauge theories. https://arxiv.org/abs/2412.19629

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