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

Understand

In this work, we extend the construction of dual color decomposition in Yang-Mills theory to one-loop level, i.e., we show how to write one-loop integrands 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-loop integrands for color scalar theory with proper dual color coefficients.In dual DDM decomposition, The dual color coefficients can be obtained directly from BCJ-form by applying Jacobi-like identities for kinematic factors.
• In dual trace decomposition, the dual trace factors can be obtained by imposing one-loop KK relations, reflection relation and their relation with the kinematic factors in dual DDM-form.