Expansion of Einstein-Yang-Mills theory by Differential Operators

Abstract

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.

arXiv comment63 pages

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• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Spinor-Helicity Formalism for Massless Fields in AdS${}_4$ II: Potentials
• Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory
• Analytic Tadpole Coefficients of One-loop Integrals
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• Expansion of tree amplitudes for EM and other theories
• Evaluating EYM amplitudes in four dimensions by refined graphic expansion
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Transmuting off-shell CHY integrals in the double-cover framework
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• Factorizations for tree amplitudes in the double-cover framework: from gravity to other theories
• CHY Theory for Several Fields
• The off-shell expansion relation of the Yang-Mills scalar theory