标题： 通用质量香蕉积分的D-理想在维数正则化中 显示英文标题

标题： D-ideal of generic mass banana integrals in dimensional regularization

摘要： 我们提出了一组$\ell + 3$个简单的微分算子，并证明它们在维数正则化中消去一个$\ell$圈通用质量香蕉积分。 我们研究了由这些算子生成的理想奇异点集，并表明它包含在第一类和第二类兰道奇异点集中。 通过麦考利矩阵方法，我们计算了相应的同源秩至$\ell = 8$，得到$2^{\ell +1}-1$，这与通用质量香蕉积分的主积分数量一致。 基于这些发现，我们猜想所提出的算子在维数正则化中生成通用质量香蕉积分的消去理想。 显示英文摘要

摘要： We present a set of $\ell + 3$ simple differential operators and prove that they annihilate an $\ell$-loop generic mass banana integral in dimensional regularization. We study the singular locus of the ideal generated by these operators and show that it is contained in the set of Landau singularities of the first and second type. Through the Macaulay matrix method, we calculate the corresponding holonomic rank up to $\ell = 8$, obtaining $2^{\ell +1}-1$, which agrees with the number of master integrals for the generic mass banana integrals. Based on these findings, we conjecture that the proposed operators generate the annihilating ideal for the generic mass banana integrals in dimensional regularization.