# Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality

## TL;DR

This paper introduces new two-loop scattering amplitude formulas in Yang-Mills and gravity theories, utilizing double-forward limits and scattering equations, revealing a loop-level colour-kinematics duality from tree-level structures.

## Contribution

It presents novel two-loop integrand formulas expressed as double-forward limits of tree diagrams, connecting non-supersymmetric and supersymmetric theories through ambitwistor string insights.

## Key findings

- Loop integrands are expressed with linear propagators.
- The formulas exhibit a loop-level colour-kinematics duality.
- Connection established between non-supersymmetric and supersymmetric theories.

## Abstract

We propose new formulae for the two-loop n-point D-dimensional integrands of scattering amplitudes in Yang-Mills theory and gravity. The loop integrands are written as a double-forward limit of tree-level trivalent diagrams, and are inferred from the formalism of the two-loop scattering equations. We discuss the relationship between the formulae for non-supersymmetric theories and the Neveu-Schwarz sector of the formulae for maximally supersymmetric theories, which can be derived from ambitwistor strings. An important property of the loop integrands is that they are expressed in a representation that includes linear-type propagators. This representation exhibits a loop-level version of the colour-kinematics duality, which follows directly from tree level via the double-forward limit.