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Computer Physics Communications
Article . 2006 . Peer-reviewed
License: Elsevier TDM
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Article . 2006
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https://dx.doi.org/10.48550/ar...
Article . 2005
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Article . 2006
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Automatized analytic continuation of Mellin–Barnes integrals

Automatized analytic continuation of Mellin-Barnes integrals
Authors: Michal Czakon;

Automatized analytic continuation of Mellin–Barnes integrals

Abstract

I describe a package written in MATHEMATICA that automatizes typical operations performed during evaluation of Feynman graphs with Mellin-Barnes (MB) techniques. The main procedure allows to analytically continue a MB integral in a given parameter without any intervention from the user and thus to resolve the singularity structure in this parameter. The package can also perform numerical integrations at specified kinematic points, as long as the integrands have satisfactory convergence properties. I demonstrate that, at least in the case of massive graphs in the physical region, the convergence may turn out to be poor, making naive numerical integration of MB integrals unusable. I present possible solutions to this problem, but argue that full automatization in such cases may not be achievable.

23 pages, 11 figures, numerical evaluation functionality added

Keywords

High Energy Physics - Theory, analytic continuation, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), numerical evaluation, Feynman integrals and graphs; applications of algebraic topology and algebraic geometry, Feynman integrals, FOS: Physical sciences, Mellin-Barnes integrals, Computational methods for problems pertaining to quantum theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
312
Top 1%
Top 1%
Top 1%
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bronze