On one-loop amplitudes in gauge theories
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913627694432256 |
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| author | Cao, Qu Dong, Jin He, Song Zhu, Fan |
| author_facet | Cao, Qu Dong, Jin He, Song Zhu, Fan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_19629 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On one-loop amplitudes in gauge theories Cao, Qu Dong, Jin He, Song Zhu, Fan High Energy Physics - Theory 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. |
| title | On one-loop amplitudes in gauge theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.19629 |