A bstractIn this work we extend two dual color decompositions of Yang-Mills amplitude to one-loop level. Starting from double-copy expression we translate the Yang-Mills integrand into the dual Del Duca-Dixon-Maltoni formulation and subsequently to the dual color-ordered formula. The dual trace factors are obtained after simultaneously solving the one-loop Kleiss-Kuijf relations, the reflection relation, and the relation that expresses the kinematic factors in the dual Del Duca-Dixon-Maltoni form.

中文翻译：

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Yang-Mills 理论中单循环水平的双色分解

摘要在这项工作中，我们将 Yang-Mills 幅度的两种双色分解扩展到一个循环级别。从双拷贝表达式开始，我们将 Yang-Mills 被积函数转化为双 Del Duca-Dixon-Maltoni 公式，然后转化为双色序公式。对偶轨迹因子是在同时求解单环 Kleiss-Kuijf 关系、反射关系和表达双 Del Duca-Dixon-Maltoni 形式的运动学因子​​的关系后得到的。