One-loop Scattering Equations and Amplitudes from Forward Limit

TL;DR

This paper demonstrates that the forward limit of tree-level scattering equations with two massive particles produces the covariant form of one-loop scattering equations, providing new insights and formulas for one-loop massless amplitudes.

Contribution

It establishes a connection between forward limits of tree-level equations and one-loop scattering equations, introducing a new formula for one-loop massless amplitudes in bi-adjoint scalar theory.

Findings

Forward limit yields covariant one-loop scattering equations.

Clarifies properties of one-loop scattering equations.

Provides a new formula for one-loop massless amplitudes.

Abstract

We show that the forward limit of tree-level scattering equations with two massive particles yields the SL(2,C)-covariant form of the one-loop scattering equations recently proposed by Geyer et al. We clarify several properties about these equations and the formulas at one loop. We then argue that in the bi-adjoint scalar theory, such forward limit yields the correct one-loop massless amplitudes, which leads to a new formula for the latter.