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

Understand

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.