标题： 二环五点两质量平面积分和威尔逊环中的双重拉格朗日插入 显示英文标题

标题： Two-Loop Five-Point Two-Mass Planar Integrals and Double Lagrangian Insertions in a Wilson Loop

摘要： 我们考虑具有两个非定域外部腿的平面二环五点费曼积分的完整集合。 这些积分对于计算强相互作用量子色动力学在强子对撞机上产生两个重矢量玻色子与喷注或光子的二阶修正具有重要意义。 我们为这些积分构建了纯基，并通过有限域上的数值采样重建了其规范形式的解析微分方程。 新识别的符号字母集是迄今为止最复杂的之一，为自举方法提供了有价值的数据。 然后我们将结果应用于平面最大超对称杨-米尔斯理论中四尖点威尔逊环的双重拉格朗日插入研究，通过两环计算它。 我们观察到它在四维空间中是有限的、共形不变的且具有统一的超越性。 此外，我们通过两环计算提供了其在幅度多面体区域内的正性的数值证据。 显示英文摘要

摘要： We consider the complete set of planar two-loop five-point Feynman integrals with two off-shell external legs. These integrals are relevant, for instance, for the calculation of the second-order QCD corrections to the production of two heavy vector bosons in association with a jet or a photon at a hadron collider. We construct pure bases for these integrals and reconstruct their analytic differential equations in canonical form through numerical sampling over finite fields. The newly identified symbol alphabet, one of the most complex to date, provides valuable data for bootstrap methods. We then apply our results to initiate the study of double Lagrangian insertions in a four-cusp Wilson loop in planar maximally supersymmetric Yang-Mills theory, computing it through two loops. We observe that it is finite, conformally invariant in four dimensions, and of uniform transcendentality. Furthermore, we provide numerical evidence for its positivity within the amplituhedron region through two loops.