A bstractIn this paper we extend our techniques, developed in a previous paper [1] 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. [1], we provide strong analytic evidence for hidden simplicity in quantum field theory.

中文翻译：

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使用 CHY 形式主义直接评估 4d Einstein-Yang-Mills 理论中的 n 点单迹 MHV 振幅

摘要在本文中，我们扩展了我们在之前的论文 [1] 中开发的技术，用于使用 Cachazo-He-Yuan (CHY) 形式主义直接评估 4d Yang-Mills 和重力理论中的任意 n 点树级 MHV 振幅， 4d 爱因斯坦-杨-米尔斯 (EYM) 理论。EYM 理论中的任何单迹颜色排序的 n 点树级 MHV 幅度，通过对 CHY 公式的直接评估获得，是 Parke-Taylor 因子和 Hodges 行列式的优雅分解形式，更简单，更多比文献中现有的公式更紧凑。我们证明了我们的新表达式等价于推测的 Selivanov-Bern-De Freitas-Wong (SBDW) 公式，借助新定理表明 SBDW 生成函数具有图论解释。与参考一起。[1],