Expansion of All Multitrace Tree Level EYM Amplitudes

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In 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.