Supplementary data for "Three-loop banana integrals with four unequal masses" (doi:10.60507/FK2/J4OPZY)

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Supplementary data for "Three-loop banana integrals with four unequal masses"

doi:10.60507/FK2/J4OPZY

bonndata

2025-08-01

1

Maggio, Sara, 2025, "Supplementary data for "Three-loop banana integrals with four unequal masses"", https://doi.org/10.60507/FK2/J4OPZY, bonndata, V1

Supplementary data for "Three-loop banana integrals with four unequal masses"

doi:10.60507/FK2/J4OPZY

Maggio, Sara (University of Bonn)

bonndata

Maggio, Sara

Maggio, Sara

2025-07-24

https://doi.org/10.60507/FK2/J4OPZY

Physics

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.

<a href="http://creativecommons.org/licenses/by/4.0">CC BY 4.0</a>

Duhr, C., Maggio, S., Porkert, F., Semper, C. and Stawinski, S.F. (2025). Three-loop banana integrals with four unequal masses.

arXiv:2507.23061

Duhr, C., Maggio, S., Porkert, F., Semper, C. and Stawinski, S.F. (2025). Three-loop banana integrals with four unequal masses.

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Am12.m

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Canonical differential equation with respect to m_1^2 in terms of the entries of the cohomology intersection matrix, Z, Jacobians

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Am22.m

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Canonical differential equation with respect to m_2^2 in terms of the entries of the cohomology intersection matrix, Z, Jacobians

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Am32.m

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Canonical differential equation with respect to m_3^2 in terms of the entries of the cohomology intersection matrix, Z, Jacobians

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Am42.m

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Canonical differential equation with respect to m_4^2 in terms of the entries of the cohomology intersection matrix, Z, Jacobians

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CBanana4M.mx

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Cohomology intersection matrix

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Diffeqm1.m

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initial differential equation matrix with respect to m_1^2

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Diffeqm2.m

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initial differential equation matrix with respect to m_2^2

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Diffeqm3.m

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initial differential equation matrix with respect to m_3^2

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Diffeqm4.m

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initial differential equation matrix with respect to m_4^2

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Maggio_Readme.txt

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r0new.m

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r_0

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r10new.m

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r_{10}

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r11new.m

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r_{11}

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r12new.m

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r_{12}

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r1new.m

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r_1

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r2new.m

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r_2

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r3new.m

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r_3

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r4new.m

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r_4

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r5new.m

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r_5

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r6new.m

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r_6

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r7new.m

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r_7

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r8new.m

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r_8

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r9new.m

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r_9

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Relations_BonnData.nb

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complete set of relations among the \epsilon-functions

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subJ.nb

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substitutions for products of Jacobians that appear in the canonical differential equation

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ZCYInverse.m

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Inverse of Z

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