Morales Roger, Spiering Anne, Wilhelm Matthias, Yang Qinglin, Zhang Chi
Niels Bohr International Academy, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Phys Rev Lett. 2023 Jul 28;131(4):041601. doi: 10.1103/PhysRevLett.131.041601.
The symbol bootstrap has proven to be a powerful tool for calculating polylogarithmic Feynman integrals and scattering amplitudes. In this Letter, we initiate the symbol bootstrap for elliptic Feynman integrals. Concretely, we bootstrap the symbol of the twelve-point two-loop double-box integral in four dimensions, which depends on nine dual-conformal cross ratios. We obtain the symbol alphabet, which contains 100 logarithms as well as nine simple elliptic integrals, via a Schubert-type analysis, which we equally generalize to the elliptic case. In particular, we find a compact, one-line formula for the (2,2) coproduct of the result.
符号引导法已被证明是计算多重对数费曼积分和散射振幅的有力工具。在本论文中，我们开启了椭圆费曼积分的符号引导法。具体而言，我们对四维中十二点双圈双盒积分的符号进行引导，该积分依赖于九个对偶共形交叉比。通过舒伯特型分析，我们得到了符号字母表，其中包含100个对数以及九个简单椭圆积分，我们同样将此分析推广到椭圆情形。特别地，我们找到了结果的(2,2)余积的一个紧凑的单行公式。
