Colour-Kinematics Duality for One-Loop Rational Amplitudes

TL;DR

This paper investigates the extension of colour-kinematics duality from tree level to one-loop amplitudes in gauge theory, demonstrating its existence in specific classes of pure Yang-Mills amplitudes and exploring implications for gravity via the double copy.

Contribution

It provides the first evidence of colour-kinematics duality at one loop in pure Yang-Mills theory for certain amplitude classes using the self-dual sector.

Findings

Duality exists for all-plus helicity amplitudes at one loop.

Explicit examples of the duality are constructed.

Relations among partial amplitudes are derived.

Abstract

Colour-kinematics duality is the conjecture of a group theory-like structure for the kinematic dependence of scattering amplitudes in gauge theory and gravity. This structure has been verified at tree level in various ways, but similar progress has been lacking at loop level, where the power of the duality would be most significant. Here we explore colour-kinematics duality at one loop using the self-dual sector as a starting point. The duality is shown to exist in pure Yang-Mills theory for two infinite classes of amplitudes: amplitudes with any number of particles either all of the same helicity or with one particle helicity opposite the rest. We provide a simple Lagrangian-based argument in favour of the double copy relation between gauge theory and gravity amplitudes in these classes, and provide some explicit examples. We further discuss aspects of the duality which persist after integration, leading to relations among partial amplitudes. Finally, we describe form factors in the self-dual theory at tree level which also satisfy the duality.