Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory

TL;DR

This paper demonstrates the color-kinematics duality for the Sudakov form factor in non-supersymmetric Yang-Mills theory up to two loops, providing explicit integrands and exploring implications for higher loops.

Contribution

It constructs explicit two-loop integrands satisfying the color-kinematics duality in non-supersymmetric Yang-Mills theory, including novel topologies and free parameters.

Findings

Integrands satisfy color-kinematics duality up to two loops.

Massless-bubble and tadpole topologies are necessary at two loops.

The duality may extend to higher loops due to free parameters.

Abstract

We study the duality between color and kinematics for the Sudakov form factors of ${\rm tr}(F^2)$ in non-supersymmetric pure Yang-Mills theory. We construct the integrands that manifest the color-kinematics duality up to two loops. The resulting numerators are given in terms of Lorentz products of momenta and polarization vectors, which have the same powers of loop momenta as that from the Feynman rules. The integrands are checked by $d$-dimensional unitarity cuts and are valid in any dimension. We find that massless-bubble and tadpole topologies are needed at two loops to realize the color-kinematics duality. Interestingly, the two-loop solution contains a large number of free parameters suggesting the duality may hold at higher loop orders.