Derivation of Feynman rules for higher order poles using cross-ratio identities in CHY construction

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 duplexdouble pole. The equivalence between the present formulas and the previously conjectured ones is discussed for the first two situations.

One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations

“…There have been developed several methods to evaluate the integrals, from different perspectives. Some approaches study the solutions to the scattering equations for particular kinematics and/or dimensions [4,[13][14][15][16][17][18][19], others work with a polynomial form [20][21][22][23][24][25][26][27][28][29], or formulating sets of integration rules [30][31][32][33][34]. A different approach was proposed in [35], taking the double covered version of the sphere, the so called Λ-algorithm, which we will employ in this work.…”

UV consistency conditions for Cachazo-He-Yuan integrands

“…where J is some Jacobian factor resulting from solving the delta functions. In practice, the scattering equations are nontrivial to solve (see [43][44][45][46] for developments), but they do not enter into our discussion.…”

UV consistency conditions for CHY integrands

“…where J is some Jacobian factor resulting from solving the delta functions. In practice the scattering equations are non-trivial to solve (see [43][44][45][46] for developments), but they do not enter into our discussion.…”