# Derivation of Feynman Rules for Higher Order Poles Using Cross-ratio Identities in CHY Construction

## TL;DR

This paper develops a method using cross-ratio identities to derive Feynman rules for higher order poles in CHY integrals, confirming conjectured rules for specific cases and enhancing the theoretical framework.

## Contribution

It introduces a systematic approach to derive Feynman rules for higher order poles in CHY integrals using cross-ratio identities, validating previous conjectures for certain cases.

## Key findings

- Derived Feynman rules for double and triple poles using cross-ratio identities.
- Confirmed the equivalence of new formulas with previous conjectures for specific pole cases.
- Enhanced understanding of higher order pole integration in CHY formalism.

## Abstract

In order to generalize the integration rules to general CHY integrands which include higher order poles, algorithms are proposed in two directions. One is to conjecture new rules, and the other is to use the cross-ratio identity method. In this paper,we use the cross-ratio identity approach to re-derive the conjectured integration rules involving higher order poles for several special cases: the single double pole, single triple pole and duplex-double pole. The equivalence between the present formulas and the previously conjectured ones is discussed for the first two situations.