Analytic expressions of amplitudes by the cross-ratio identity method

In order to obtain the analytic expression of an amplitude from a generic CHY-integrand, a new algorithm based on the so-called cross-ratio identities has been proposed recently. In this paper, we apply this new approach to a variety of theories including the non-linear sigma model, special Galileon theory, pure Yang–Mills theory, pure gravity, Born–Infeld theory, Dirac–Born–Infeld theory and its extension, Yang–Mills-scalar theory, and Einstein–Maxwell and Einstein–Yang–Mills theory. CHY-integrands of these theories which contain higher-order poles can be calculated conveniently by using the cross-ratio identity method, and all results above have been verified numerically.