All-loop planar integrands in Yang-Mills theory from recursion

Fuente: arXiv
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Main Authors: Cao, Qu, Zhu, Fan
Format: Preprint
Published: 2025
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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
id 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