标题： 运动学霍普夫代数和有限的$α'$的 BCJ 数值 显示英文标题

标题： Kinematic Hopf algebra and BCJ numerators at finite $α'$

摘要： 在本文中，从一个运动学霍普夫代数出发，我们首先为Yang-Mills (YM)理论中无限阶的$\alpha'$修正，即耦合到两个重粒子的$\rm DF^2+YM$理论，构建了一个所有Bern-Carrasco-Johansson (BCJ)数子的显式公式，这些重粒子可以通过一个简单的因子化极限去除。 完整的$\alpha'$依赖性仅以质量物理传播子因子的形式出现，因子化强烈限制了构造过程。 由质量极点引起的复杂结构也自然引导我们基于运动学霍普夫代数直接找到通常纯YM理论中BCJ数子的新显式和局部表达式。 显示英文摘要

摘要： In this letter, starting from a kinematic Hopf algebra, we first construct a closed-form formula for all Bern-Carrasco-Johansson (BCJ) numerators in Yang-Mills (YM) theory with infinite orders of $\alpha'$ corrections, known as $\rm DF^2+YM$ theory, when coupled to two heavy particles which can be removed through a simple factorization limit. The full $\alpha'$ dependence appears simply in massive physical propagator factors, with factorization strongly constraining the construction. The intricate structure induced by the massive poles also naturally leads us to find a novel closed-form and local expression for BCJ numerators in usual pure YM theory, based directly on the kinematic Hopf algebra.