Symbol letters of Feynman integrals from Gram determinants
Xuhang Jiang, Jiahao Liu, Xiaofeng Xu, Li Lin Yang
Abstract
Symbol letters are crucial for analytically calculating Feynman integrals in terms of iterated integrals. We present a novel method to construct the symbol letters for a given integral family without prior knowledge of the canonical differential equations. We provide a program package implementing our algorithm, and demonstrate its effectiveness in solving non-trivial problems with multiple loops and legs. Using our method, we successfully bootstrap the canonical differential equations for a two-loop five-point family with two external masses and for a three-loop four-point family with two external masses, which were previously unknown in the literature. We anticipate that our method can be applied to a wide range of cutting-edge calculations in the future.