双圈主围道的唯一性
Uniqueness of two-loop master contours
AI总结：
本文对双箱拓扑积分的最大切割解进行完整分类，将其与黎曼曲面几何联系起来，证明在四无质量外动量情形下主围道具有唯一性，并利用手征积分作为主积分在四维中计算双圈振幅，得到紧凑结果。
摘要：
双圈振幅的广义幺正性计算通过将振幅在一组主积分基上展开，然后取若干广义切割来确定系数。本文给出了具有双箱拓扑的积分最大切割解的完整分类。本文提出的思想预计也适用于所有双圈拓扑。我们发现这些最大切割解自然地与黎曼曲面相关联，其拓扑由双箱图顶点处的状态数决定。在四个无质量外动量的情形下，我们发现一旦正确理解这些黎曼曲面的几何结构，就存在唯一定义的主围道，可在双圈振幅的基分解中产生双箱积分的系数。这与单圈广义幺正性中的情形完全类似。此外，我们指出 Arkani-Hamed 等人最近引入的手征积分可以用作任意规范理论中双圈振幅双箱贡献的主积分。这些积分的红外有限性使得其系数以及积分表达式都可以在严格四维中计算，从而带来显著的技术简化。我们在四点情形下计算了这些积分，并得到了非常紧凑的结果。
英文摘要：
Generalized-unitarity calculations of two-loop amplitudes are performed by expanding the amplitude in a basis of master integrals and then determining the coefficients by taking a number of generalized cuts. In this paper, we present a complete classification of the solutions to the maximal cut of integrals with the double-box topology. The ideas presented here are expected to be relevant for all two-loop topologies as well. We find that these maximal-cut solutions are naturally associated with Riemann surfaces whose topology is determined by the number of states at the vertices of the double-box graph. In the case of four massless external momenta we find that, once the geometry of these Riemann surfaces is properly understood, there are uniquely defined master contours producing the coefficients of the double-box integrals in the basis decomposition of the two-loop amplitude. This is in perfect analogy with the situation in one-loop generalized unitarity. In addition, we point out that the chiral integrals recently introduced by Arkani-Hamed et al. can be used as master integrals for the double-box contributions to the two-loop amplitudes in any gauge theory. The infrared finiteness of these integrals allow for their coefficients as well as their integrated expressions to be evaluated in strictly four dimensions, providing significant technical simplification. We evaluate these integrals at four points and obtain remarkably compact results.
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