Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism

Fei Teng; Yi-Jian Du; Yong-Shi Wu

Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism

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arxiv 1608.00883 v2 pith:MXHBMLKM submitted 2016-08-02 hep-th

Yi-Jian Du , Fei Teng , Yong-Shi Wu This is my paper · ORCID

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keywords theorydirectevaluationpointamplitudeseinstein-yang-millsformalismformula

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abstract

In this paper we extend our techniques, developed in a previous paper (Du, etc, JHEP 05(2016)086) for direct evaluation of arbitrary $n$-point tree-level MHV amplitudes in 4d Yang-Mills and gravity theory using the Cachazo-He-Yuan (CHY) formalism, to the 4d Einstein-Yang-Mills (EYM) theory. Any single-trace color-ordered $n$-point tree-level MHV amplitude in EYM theory, obtained by a direct evaluation of the CHY formula, is of an elegant factorized form of a Parke-Taylor factor and a Hodges determinant, much simpler and more compact than the existing formulas in the literature. We prove that our new expression is equivalent to the conjectured Selivanov-Bern-De Freitas-Wong (SBDW) formula, with the help of a new theorem showing that the SBDW generating function has a graph theory interpretation. Together with Ref. (Du, etc, JHEP 05(2016)086), we provide strong analytic evidence for hidden simplicity in quantum field theory.

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Note on single-trace EYM amplitudes with MHV configuration
hep-th 2025-01 conditional novelty 5.0 of 10

Tree-level single-trace MHV Einstein-Yang-Mills amplitudes with any number of gravitons are re-expressed as sums of pure gluon Parke-Taylor amplitudes, with each graviton represented by a collinear gluon pair.

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