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

TL;DR

This paper extends techniques for evaluating n-point MHV amplitudes to 4d Einstein-Yang-Mills theory, resulting in a simpler, factorized formula that confirms a conjectured expression and reveals hidden simplicity in quantum field theory.

Contribution

It introduces a new, compact formula for single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY formalism, proving its equivalence to a conjectured formula.

Findings

Derived a factorized, compact formula for EYM MHV amplitudes

Proved equivalence to the SBDW conjectured formula

Revealed hidden simplicity in quantum field theory

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.