Expansion of Einstein-Yang-Mills theory by Differential Operators

The factorization form of the integrands in the Cachazo-He-Yuan (CHY) formalism makes the generalized Kawai-Lewellen-Tye (KLT) relations manifest, thus amplitudes of one theory can be expanded in terms of the amplitudes of another theory. Although this claim seems a rather natural consequence of the above structure, finding the exact expansion coefficients to express an amplitude in terms of another amplitudes is, nonetheless, a nontrivial task despite many efforts devoted to it in the literature. In this paper, we propose a new strategy based in using the differential operators introduced by Cheung, Shen and Wen, and taking advantage of the fact these operators already relate the amplitudes of different theories. Using this new method, expansion coefficients can be found effectively.