# Analytic expressions of amplitudes by the cross-ratio identity method

## TL;DR

This paper applies a new cross-ratio identity method to derive analytic amplitude expressions for various theories within the CHY formalism, enabling efficient calculation of complex integrands with higher-order poles.

## Contribution

It extends the cross-ratio identity approach to a wide range of theories, providing a systematic and verified way to compute their CHY-integrands with higher-order poles.

## Key findings

- Successfully derived analytic amplitudes for multiple theories
- Verified results numerically for accuracy
- Enhanced computational efficiency for complex integrands

## Abstract

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: 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, Einstein-Maxwell theory as well as 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.