Kinematic Hopf algebra and BCJ numerators at finite $\alpha'$

Gang Chen; Laurentiu Rodina; Congkao Wen

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arXiv · 2403.04614

Kinematic Hopf algebra and BCJ numerators at finite $\alpha'$

Gang Chen·Laurentiu Rodina·Congkao Wen

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Abstract

In this letter, starting from a kinematic Hopf algebra, we first construct a closed-form formula for all Bern-Carrasco-Johansson (BCJ) numerators in Yang-Mills (YM) theory with infinite orders of $\alpha'$ corrections, known as $\rm DF^2+YM$ theory, when coupled to two heavy particles which can be removed through a simple factorization limit. The full $\alpha'$ dependence appears simply in massive physical propagator factors, with factorization strongly constraining the construction. The intricate structure induced by the massive poles also naturally leads us to find a novel closed-form and local expression for BCJ numerators in usual pure YM theory, based directly on the kinematic Hopf algebra.

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Gang Chen, Laurentiu Rodina, Congkao Wen. 2024-03-07. Kinematic Hopf algebra and BCJ numerators at finite $\alpha'$. https://arxiv.org/abs/2403.04614

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