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In this work, we extend the construction of dual color decomposition inYang-Mills theory to one-loop level, i.e., we show how to write one-loopintegrands in Yang-Mills theory to the dual DDM-form and the dual trace-form.In dual forms, integrands are decomposed in terms of color-ordered one-loopintegrands for color scalar theory with proper dual color coefficients.In dualDDM decomposition, The dual color coefficients can be obtained directly fromBCJ-form by applying Jacobi-like identities for kinematic factors. In dualtrace decomposition, the dual trace factors can be obtained by imposingone-loop KK relations, reflection relation and their relation with thekinematic factors in dual DDM-form.

Dual-color decompositions at one-loop level in Yang-Mills theory