Supplementary data for "Three-loop banana integrals with four unequal masses"
Ancillary files that accompany the paper "Three-loop banana integrals with four unequal masses". This dataset accompanies the paper "Three-loop banana integrals with four unequal masses". It contains the canonical differential equations satisfied by the three-loop banana integrals with four distinct non-zero masses in $D = 2-2\eps$ dimensions. Together with the initial condition in the small-mass limit, this provides all the ingredients to find analytic results for three-loop banana integrals in terms of iterated integrals to any desired order in the dimensional regulator. It also contains: the cohomology intersection matrix, the starting differential equation matrix, the canonical differential equation matrix, the inverse of Z (the \epsilon^0 part of the cohomology intersection matrix without the entries related to the ISPs integrals), the rational functions that appear in the differential equation for G_0, the full set of relations among the \epsilon-functions and some compact substitutions for some entries in the canonical differential equation matrix.
Duhr, C., Maggio, S., Porkert, F., Semper, C. and Stawinski, S.F. (2025). Three-loop banana integrals with four unequal masses.
Canonical differential equation with respect to m_1^2 in terms of the entries of the cohomology intersection matrix, Z, Jacobians
Canonical differential equation with respect to m_2^2 in terms of the entries of the cohomology intersection matrix, Z, Jacobians
Canonical differential equation with respect to m_3^2 in terms of the entries of the cohomology intersection matrix, Z, Jacobians
Canonical differential equation with respect to m_4^2 in terms of the entries of the cohomology intersection matrix, Z, Jacobians
initial differential equation matrix with respect to m_1^2
initial differential equation matrix with respect to m_2^2
initial differential equation matrix with respect to m_3^2
initial differential equation matrix with respect to m_4^2
complete set of relations among the \epsilon-functions
substitutions for products of Jacobians that appear in the canonical differential equation