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

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.

arXiv comment26 pages, 1 figure; v2: some typo corrected, more references added, published version

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Cited by in corpus (10)

• Aspects of Scattering Amplitudes and Moduli Space Localization
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Unraveling conformal gravity amplitudes
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• A graphic approach to gauge invariance induced identity
• Constructing EYM amplitudes by inverse soft limit
• Evaluating EYM amplitudes in four dimensions by refined graphic expansion
• A note on multi-trace EYM amplitudes in four dimensions