The Construction of Dual-trace Factor in Yang-Mills Theory

Recently, it has been proposed that tree-level Yang-Mills amplitudes can be written in dual-trace form, where the dual-trace factors satisfy cyclic symmetry and KK-relation. In this paper, we present a systematic construction of dual-trace factors based on the proposed relations between them and kinematic numerators of BCJ form in DDM chain. We show that solutions from our algorithm satisfy the relabeling property. We have also shown that using the relabeling property, solutions can be obtained independently.