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The $l$-loop Banana Amplitude from GKZ Systems and relative Calabi-Yau Periods

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arxiv 1912.06201 v2 pith:ADN6NLRA submitted 2019-12-12 hep-th math-phmath.MP

Albrecht Klemm , Christoph Nega , Reza Safari This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords bananamassperiodsamplitudescalabi-yaulooprelativeresults
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We use the GKZ description of periods and certain classes of relative periods on families of Barth-Nieto Calabi-Yau $(l-1)$-folds in order to solve the $l$-loop banana amplitudes with their general mass dependence. As examples we compute the mass dependencies of the banana amplitudes up to the three-loop case and check the results against the known results for special mass values.

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Cited by 4 Pith papers

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    Multiloop sunset integrals in D=2 are expressed as convergent sums of symmetric polynomials in logarithms of mass ratios, with a dimension-raising operator that propagates the result to D=4-2ε.

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    The conservative black-hole scattering angle at fifth post-Minkowskian and second self-force order is computed in terms of K3 periods, but contains a coefficient fixed only by an ad hoc 'γ-3' prescription.

  3. Analytic result of a three-loop integral family in the Higgs decay to four massive bottom quarks

    hep-ph 2026-07 accept novelty 6.5 of 10

    Analytic master-integral results through O(ε²) are obtained for a three-loop family containing elliptic and K3 geometries by building and solving a mixed-sector ε-factorized differential equation.

  4. Differential Space of Feynman Integrals: Annihilators and $\mathcal{D}$-module

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    A Griffiths-Dwork based algorithm builds annihilators and D-modules for Feynman-like integrals, and in all tested cases the holonomic rank matches the twisted de Rham cohomology dimension.

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