Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators

TL;DR

This paper extends the CHY approach to include non-planar one-loop Parke-Taylor factors, enabling the description of non-planar amplitudes with quadratic propagators and introducing new non-planar CHY-graphs.

Contribution

It introduces non-planar one-loop Parke-Taylor factors in the CHY formalism and identifies new non-planar CHY-graphs for subleading order amplitudes.

Findings

Identified non-planar one-loop Parke-Taylor factors.

Applied these factors to bi-adjoint Φ^3 theory.

Discovered non-planar CHY-graphs with no Feynman equivalent.

Abstract

In this work we have studied the Kleiss-Kuijf relations for the recently introduced Parke-Taylor factors at one-loop in the CHY approach, that reproduce quadratic Feynman propagators. By doing this, we were able to identify the non-planar one-loop Parke-Taylor factors. In order to check that, in fact, these new factors can describe non-planar amplitudes, we applied them to the bi-adjoint $\Phi^3$ theory. As a byproduct, we found a new type of graphs that we called the non-planar CHY-graphs. These graphs encode all the information for the subleading order at one-loop, and there is not an equivalent of these in the Feynman formalism.