# Quadratic Feynman Loop Integrands From Massless Scattering Equations

## TL;DR

This paper introduces a new method to derive Feynman-like quadratic propagators from the CHY approach for loop integrands, with a geometric interpretation involving higher genus Riemann surfaces.

## Contribution

A novel technique that produces quadratic Feynman propagators directly from the CHY scattering equations, extending the approach to loop level.

## Key findings

- Produces quadratic propagators matching Feynman's
- Applicable to $$ theory, with potential extensions
- Provides a geometric interpretation involving higher genus surfaces

## Abstract

Recently the Cachazo-He-Yuan (CHY) approach has been extended to loop level, but the resulting loop integrand has propagators that are linear in the loop momentum unlike Feynman's. In this note we present a new technique that directly produces quadratic propagators identical to Feynman's from the CHY approach. This paper focuses on $\Phi^3$ theory but extensions to others theories are briefly discussed. In addition, our proposal has an interesting geometric meaning, we can interpret this new formula as a unitary cut on a higher genus Riemann surface.