Feynman Rules of Higher-order Poles in CHY Construction

TL;DR

This paper extends the Feynman rules within the CHY framework to include higher-order poles, providing new rules and validating them through complex examples.

Contribution

It introduces generalized Feynman rules for higher-order poles in CHY integrands, derived from known analytic results, and demonstrates their validity with non-trivial examples.

Findings

New Feynman rules for double and triple poles in CHY integrands

Validation of rules through complex non-trivial examples

Enhanced understanding of higher-order pole contributions in scattering amplitudes

Abstract

In this paper, we generalize the integration rules for scattering equations to situations where higher-order poles are present. We describe the strategy to deduce the Feynman rules of higher-order poles from known analytic results of simple CHY-integrands, and propose the Feynman rules for single double pole and triple pole as well as duplex-double pole and triplex-double pole structures. We demonstrate the validation and strength of these rules by ample non-trivial examples.