标题： 三环五点费曼积分的解析计算 显示英文标题

标题： An Analytic Computation of Three-Loop Five-Point Feynman Integrals

摘要： 我们在维度正则化方案中评估了三环五点五边形框框无质量积分族，通过规范微分方程。 我们使用计算代数几何的工具来实现必要的积分约简。 微分方程的边界值在欧几里得区域中被解析确定。 为了表达最终结果，我们引入了一种新的六阶函数表示形式，该形式为权三函数与从微分方程导出的权二核的乘积的一重积分。 我们的工作为三环多腿费曼积分的解析计算铺平了道路。 显示英文摘要

摘要： We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary integral reductions. The boundary values of the differential equation are determined analytically in the Euclidean region. To express the final result, we introduce a new representation of weight six functions in terms of one-fold integrals over the product of weight-three functions with weight-two kernels that are derived from the differential equation. Our work paves the way to the analytic computation of three-loop multi-leg Feynman integrals.