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arXiv · 1512.05387

The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes

C. S. Lam·York-Peng Yao
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Abstract

The integrations leading to the Cachazo-He-Yuan (CHY) double-color $n$-point massless scalar amplitude are carried out one integral at a time. Möbius invariance dictates the final amplitude to be independent of the three Möbius constants $σ_r, σ_s, σ_t$, but their choice affects integrations and the intermediate results. The effect of the Möbius constants, the two colors, and the scattering functions on each integration is investigated. A systematic way to carry out the $n-3$ integrations is explained, each exposing one of the $n-3$ propagators of the Feynman diagrams. Two detailed examples are shown to illustrate the procedure, one a five-point amplitude, and the other a nine-point amplitude.

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C. S. Lam, York-Peng Yao. 2016-04-25. The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes. https://doi.org/10.1103/physrevd.93.105004

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