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arXiv · 1905.05101

Off-Shell Yang-Mills Amplitude in the CHY Formalism

C. S. Lam
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Abstract

Möbius invariance is used to construct gluon tree amplitudes in the Cachazo, He, and Yuan (CHY) formalism. If it is equally effective in steering the construction of off-shell tree amplitudes, then the S-matrix CHY theory can be used to replace the Lagrangian Yang-Mills theory. In the process of investigating this possibility, we find that the CHY formula can indeed be modified to obtain a Möbius invariant off-shell amplitude, but unfortunately this modified amplitude $M_P$ is not the Yang-Mills amplitude because it lacks gauge invariance. A complementary amplitude $M_Q$ must be added to restore gauge invariance, but its construction relies on the Lagrangian and not Möbius invariance. Although neither $M_P$ nor $M_Q$ is fully gauge invariant, both are partially gauge invariant in a sense to be explained. This partial gauge invariance turns out to be very useful for checking calculations. A Feynman amplitude so split into the sum of $M_P$ and $M_Q$ also contains fewer terms.

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C. S. Lam. 2019-05-13. Off-Shell Yang-Mills Amplitude in the CHY Formalism. https://doi.org/10.1103/physrevd.100.045009

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