All-loop planar integrands in Yang-Mills theory from recursion
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912284042854400 |
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| author | Cao, Qu Zhu, Fan |
| author_facet | Cao, Qu Zhu, Fan |
| contents | In this letter, we generalize the recursion methods based on cut equations arXiv:2412.21027, originally developed for scalar theories, to gluons in pure Yang-Mills theory. In gauge theories, planar loop integrands are subtle to defined and obtained due to the existence of scaleless integrals. A critical challenge arises when constructing higher-loop integrands via recursion methods: integrands with or without all scaleless terms both are incompatible with the reconstruction formalism in arXiv:2412.21027. To address this, we introduce a $\textit{refined}$ integrand by systematically removing specific scaleless contributions, and develop an algorithmic implementation of the recursion to all-loop level. We explicitly demonstrate the framework by three steps and obtain the recursion formula in pure Yang-Mills theory. In the ancillary files, we provide the results up to the two-loop five-point integrand and the simplified result in the large-$D$ limit for the three-loop four-point case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_15860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | All-loop planar integrands in Yang-Mills theory from recursion Cao, Qu Zhu, Fan High Energy Physics - Theory In this letter, we generalize the recursion methods based on cut equations arXiv:2412.21027, originally developed for scalar theories, to gluons in pure Yang-Mills theory. In gauge theories, planar loop integrands are subtle to defined and obtained due to the existence of scaleless integrals. A critical challenge arises when constructing higher-loop integrands via recursion methods: integrands with or without all scaleless terms both are incompatible with the reconstruction formalism in arXiv:2412.21027. To address this, we introduce a $\textit{refined}$ integrand by systematically removing specific scaleless contributions, and develop an algorithmic implementation of the recursion to all-loop level. We explicitly demonstrate the framework by three steps and obtain the recursion formula in pure Yang-Mills theory. In the ancillary files, we provide the results up to the two-loop five-point integrand and the simplified result in the large-$D$ limit for the three-loop four-point case. |
| title | All-loop planar integrands in Yang-Mills theory from recursion |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.15860 |