Expansion of All Multitrace Tree Level EYM Amplitudes

TL;DR

This paper develops recursive expansion methods for multitrace Einstein-Yang-Mills amplitudes, providing proofs and relations that enable expressing these amplitudes in a color-ordered basis, facilitating the construction of BCJ numerators.

Contribution

It introduces new recursive expansions and generalized BCJ relations for multitrace EYM amplitudes, expanding the computational framework and theoretical understanding.

Findings

Recursive expansions for multitrace EYM amplitudes are established.

Proofs using CHY formula and BCFW recursion validate the expansions.

BCJ numerators for all multitrace EYM amplitudes are constructed.

Abstract

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. 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.