The Role of M\"obius Constants and Scattering Functions in CHY Scalar Amplitudes
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. M\"obius invariance dictates the final amplitude to be independent of the three M\"obius constants σr, σs, σt, but their choice affects integrations and the intermediate results. The effect of the M\"obius 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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