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In order to obtain the analytic expression of an amplitude from a genericCHY-integrand, a new algorithm based on the so-called cross-ratio identitieshas been proposed recently. In this paper, we apply this new approach to avariety of theories including: non-linear sigma model, special Galileon theory,pure Yang-Mills theory, pure gravity, Born-Infeld theory, Dirac-Born-Infeldtheory and its extension, Yang-Mills-scalar theory, Einstein-Maxwell theory aswell as Einstein-Yang-Mills theory. CHY-integrands of these theories whichcontain higher-order poles can be calculated conveniently by using thecross-ratio identity method, and all results above have been verifiednumerically.

Analytic expressions of amplitudes by the cross-ratio identity method