D-ideal of generic mass banana integrals in dimensional regularization

Abstract: 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.