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Normalized Fuchsian form on Riemann sphere and differential equations for multiloop integrals

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arxiv 1707.07856 v1 pith:HECOWE7H submitted 2017-07-25 hep-th hep-ph

classification hep-thhep-ph
keywords formdifferentialfuchsiannormalizedconsiderepsilonequationsintegrals
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abstract

We consider the question of reducibility of the differential system to normalized Fuchsian form on the Riemann sphere. The differential equations for the multiloop integrals in $\epsilon$-form constitute a particular example of the normalized Fuchsian form. We formulate the algorithmic criterion of reducibility. We also consider the question of the proper choice of variable in the differential system suitable for its reduction to $\epsilon$-form.

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Cited by 2 Pith papers

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  1. Monodromy of multiloop integrals in $d$ dimensions

    hep-th 2025-06 conditional novelty 7.0 of 10

    For several multiloop Feynman integral systems, the monodromy group has a basis where its generators are matrices over Z[z,1/z] with z = exp(iπd), obtained by a numerical recognition method.

  2. Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics

    hep-ph 2019-08 conditional novelty 7.0 of 10

    The thesis computes three-loop and two-loop QCD corrections to Higgs processes with full quark mass dependence, including a new analytic series-expansion treatment of elliptic two-loop master integrals for Higgs-plus-...

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