One-loop CHY-Integrand of Bi-adjoint Scalar Theory

TL;DR

This paper develops a refined method for constructing one-loop CHY integrands in bi-adjoint scalar theory by explicitly removing tadpole and bubble contributions using a pole-isolation technique.

Contribution

It introduces a novel approach to eliminate singular contributions in one-loop integrands by exploiting the idea of 'picking poles' with a special cross ratio factor.

Findings

Successfully removes tadpole and bubble contributions at one-loop level.

Provides a new technique for isolating specific pole structures in integrands.

Enhances the accuracy of amplitude calculations in bi-adjoint scalar theory.

Abstract

In this paper, the one-loop CHY-integrands of bi-adjoint scalar theory has been reinvestigated. Differing from previous constructions, we have explicitly removed contributions from tadpole and massless bubbles when taking the forward limit of corresponding tree-level amplitudes. The way to remove those singular contributions is to exploit the idea of 'picking poles', which is to multiply a special cross ratio factor with the role of isolating terms having a particular pole structure.