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

الأصل · EN

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 σᵣ, σₛ, σₜ, 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.