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

TL;DR

This paper revisits the CHY construction of one-loop scattering amplitudes, proposing a new approach to obtain quadratic propagators by redefining Parke-Taylor factors, and conjectures a new amplitude for massless Bi-adjoint  theory.

Contribution

It introduces a novel redefinition of Parke-Taylor factors in the CHY framework to produce quadratic propagators at one-loop and conjectures a new amplitude for the Bi-adjoint  theory.

Findings

Reclassification of one-loop CHY integrands.

A new prescription reproducing quadratic propagators.

Conjecture of a new one-loop amplitude for Bi-adjoint  theory.

Abstract

In this paper we reconsider the Cachazo-He-Yuan construction (CHY) of the so called scattering amplitudes at one-loop, in order to obtain quadratic propagators. In theories with colour ordering the key ingredient is the redefinition of the Parke-Taylor factors. After classifying all the possible one-loop CHY-integrands we conjecture a new one-loop amplitude for the massless Bi-adjoint $\Phi^3$ theory. The prescription directly reproduces the quadratic propagators from of the traditional Feynman approach.