Applying color-kinematics duality in pure Yang-Mills at three loops

A bstract We present the first application of color-kinematics (CK) duality at the three-loop level in non-supersymmetric pure Yang-Mills (YM) theory. Building on the minimal deformation approach introduced in [1], we extend its use to the three-loop Sudakov form factor. Although three classes of unitarity cuts fail under the globally off-shell CK-dual ansatz, a compact and elegant solution is achieved by deforming a single master numerator. The final numerators exhibit Lorentz invariance in d dimensions and take a local form. This method harnesses CK duality’s full potential by enforcing a subset of off-shell dual Jacobi identities for the deformation, offering a promising path toward constructing three-loop amplitudes in non-supersymmetric YM theory and gravity through CK duality and double copy.