A bstractIn this paper, we investigate the expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes. First, we propose two types of recursive expansions of tree level EYM amplitudes with an arbitrary number of gluons, gravitons and traces by those amplitudes with fewer traces or/and gravitons. Then we give many support evidence, including proofs using the Cachazo-He-Yuan (CHY) formula and Britto-Cachazo-Feng-Witten (BCFW) recursive relation. As a byproduct, two types of generalized BCJ relations for multitrace EYM are further proposed, which will be useful in the BCFW proof. After one applies the recursive expansions repeatedly, any multitrace EYM amplitudes can be given in the Kleiss-Kuijf (KK) basis of tree level color ordered Yang-Mills (YM) amplitudes. Thus the Bern-Carrasco-Johansson (BCJ) numerators, as the expansion coefficients, for all multitrace EYM amplitudes are naturally constructed.

中文翻译：

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扩展所有多轨迹树级 EYM 幅度

摘要在本文中，我们研究了树级多道爱因斯坦-杨-米尔斯 (EYM) 振幅的扩展。首先，我们提出了两种类型的树级 EYM 振幅的递归扩展，具有任意数量的胶子、引力子和轨迹，这些振幅具有较少的轨迹或/和引力子。然后我们给出了许多支持证据，包括使用 Cachazo-He-Yuan (CHY) 公式和 Britto-Cachazo-Feng-Witten (BCFW) 递归关系的证明。作为副产品，进一步提出了两种用于多迹 EYM 的广义 BCJ 关系，这将在 BCFW 证明中有用。在重复应用递归展开之后，可以在树级颜色有序杨米尔斯 (YM) 振幅的 Kleiss-Kuijf (KK) 基础中给出任何多迹 EYM 振幅。因此 Bern-Carrasco-Johansson (BCJ) 分子，