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

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 $Φ^3$ theory. The prescription directly reproduces the quadratic propagators from of the traditional Feynman approach.

43 pages, new appendix added, few typos corrected. Accepted for publication in JHEP