Built on

Y.-X. Chen, Y.-J. Du, and B. Feng, On tree amplitudes with gluons coupled to gravitons
Original
1953
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1986
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Z. Bern, A. De Freitas, and H. L. Wong, On the coupling of gravitons to matter
2000
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2005
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R. Britto, F. Cachazo, B. Feng, and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory
2005
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Z. Bern, J. J. M. Carrasco, and H. Johansson, New Relations for Gauge-Theory Amplitudes
Original
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N. E. J. Bjerrum-Bohr, P. H. Damgaard, and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes
Original
2009
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Y.-X. Chen, Y.-J. Du, and Q. Ma, Relations Between Closed String Amplitudes at Higher-order Tree Level and Open String Amplitudes
Original
2010
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Y.-X. Chen, Y.-J. Du, and Q. Ma, Disk relations for tree amplitudes in minimal coupling theory of gauge field and gravity
Original
2010
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Original
2010
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Original
2010
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N. E. J. Bjerrum-Bohr, P. H. Damgaard, B. Feng, and T. Sondergaard, Proof of Gravity and Yang-Mills Amplitude Relations
Original
2010
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B. Feng, R. Huang, and Y. Jia, Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
Original
2011
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Y.-X. Chen, Y.-J. Du, and B. Feng, A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
Original
2011
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P. Benincasa and E. Conde, On the Tree-Level Structure of Scattering Amplitudes of Massless Particles
Original
2011
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C. R. Mafra, O. Schlotterer, and S. Stieberger, Explicit BCJ Numerators from Pure Spinors
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2017

Expansion of Einstein-Yang-Mills Amplitude

Fu, Chih-Hao, Du, Yi-Jian, Huang, Rijun et al.

Understand

In this paper, we provide a thorough study on the expansion of single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered Yang-Mills amplitudes, from various different perspectives.

Using the gauge invariance principle, we propose a recursive construction, where EYM amplitude with any number of gravitons could be expanded into EYM amplitudes with less number of gravitons.
Through this construction, we can write down the complete expansion of EYM amplitude in the basis of color-ordered Yang-Mills amplitudes.
As a byproduct, we are able to write down the polynomial form of BCJ numerator, i.e., numerators satisfying the color-kinematic duality, for Yang-Mills amplitude.