论文标题
椭圆形多重载体和符号元素的符号学
Symbology for elliptic multiple polylogarithms and the symbol prime
论文作者
论文摘要
Feynman积分，尤其是散射幅度中发生的椭圆形多重聚类。它们可以以其符号为特征，符号是所谓的符号字母中的张量产品。与非椭圆形的情况相反，椭圆字母本身满足了高度非平凡的身份，我们在本文中讨论了这一点。此外，我们介绍了符号素数，这是椭圆符号字母的符号的类似物，这使这些身份体现出来。我们以两循环顺序证明了它在两个具体示例中的使用：在二维中的不等质量日出积分和四个维度的十分双盒积分。最后，我们还报告了九点双盒积分的二点双盒积分的结果，这是十点积分的软限制。
Elliptic multiple polylogarithms occur in Feynman integrals and in particular in scattering amplitudes. They can be characterized by their symbol, a tensor product in the so-called symbol letters. In contrast to the non-elliptic case, the elliptic letters themselves satisfy highly non-trivial identities, which we discuss in this paper. Moreover, we introduce the symbol prime, an analog of the symbol for elliptic symbol letters, which makes these identities manifest. We demonstrate its use in two concrete examples at two-loop order: the unequal-mass sunrise integral in two dimensions and the ten-point double-box integral in four dimensions. Finally, we also report the result of the polylogarithmic nine-point double-box integral, which arises as the soft limit of the ten-point integral.
