On the resolution of singularities of multiple Mellin–Barnes integrals

2009/01/04 by Alexander V. Smirnov, A. V. Smirnov, V. A. Smirnov +1 · 176 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Black Holes and Theoretical Physics #Computer science #Dimensional regularization #Electromagnetic Scattering and Analysis #Fourier transform #Gravitational singularity #Laplace transform #Mathematical analysis #Mathematical functions and polynomials #Mathematical physics #Mathematics #Mellin inversion theorem #Mellin transform #Regularization (linguistics) #Renormalization #Resolution (logic) #hep-ph

paper · pdf · doi:10.1140/epjc/s10052-009-1039-6

published in The European Physical Journal C 62(2), 445-449 (Springer Science+Business Media) · LaTeX, 10 pages

arxiv created 2009/01/04 · openalex publication_date 2009/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

One of the two existing strategies of resolving singularities of multifold Mellin–Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The corresponding algorithm is implemented as a Mathematica code MBresolve.m

Citations

• Heavy-to-heavy quark decays at next-to-next-to-leading order
• Two-loop massive operator matrix elements for unpolarized heavy flavor production to O(ϵ)
• Toward a NNLO calculation of the B¯→Xsγ decay rate with a cut on photon energy: I. Two-loop result for the soft function
• Heavy-quark production in massless quark scattering at two loops in QCD
• Automatized analytic continuation of Mellin–Barnes integrals
• Two-Loop Iteration of Five-PointN=4Super-Yang-Mills Amplitudes
• Tops from light quarks: Full mass dependence at two-loops in QCD
• Analytical result for dimensionally regularized massive on-shell planar double box
• Analytical result for dimensionally regularized massless on-shell planar triple box

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