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Scattering amplitudes in Yang-Mills theory are known to exhibit kinematicstructures which hint to an underlying kinematic algebra that is dual to thegauge group color algebra. This color-kinematics duality is still poorlyunderstood in terms of conventional Feynman rules, or from a Lagrangianformalism. In this work, we present explicit Lagrangians whose Feynman rulesgenerate duality-satisfying tree-level BCJ numerators, to any multiplicity inthe next-to-MHV sector of pure Yang Mills theory. Our Lagrangians make use ofat most three pairs of auxiliary fields (2,1,0-forms) -- surprisingly fewcompared to previous attempts of Lagrangians at low multiplicities. To restrictthe Lagrangian freedom it is necessary to make several non-trivial assumptionsregarding field content, kinetic terms, and interactions, which we discuss insome detail. Future progress likely hinges on relaxing these assumptions.

Lagrangians Manifesting Color-Kinematics Duality in the NMHV Sector of Yang-Mills