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Accelerated convergence of perturbative QCD by optimal conformal mapping of the Borel plane

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arxiv hep-ph/9811367 v1 pith:34GRB7AT submitted 1998-11-17 hep-ph

classification hep-ph
keywords borelconvergenceconformalmappingoptimalperturbativeaccelerateaccelerated
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The technique of conformal mappings is applied to enlarge the convergence of the Borel series and to accelerate the convergence of Borel-summed Green functions in perturbative QCD. We use the optimal mapping, which takes into account the location of all the singularities of the Borel transform as well as the present knowledge about its behaviour near the first branch points. The determination of \alpha_{s}(m_{\tau}) from the hadronic decay rate of the \tau-lepton is discussed as an illustration of the method.

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  1. Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings

    hep-ph 2019-08 conditional novelty 5.0 of 10

    The paper predicts the six-, seven-, and eight-loop Adler function coefficients in MS QCD as c5,1=287±40, c6,1=2948±208, c7,1=(1.89±0.75)×10^4 by reexpanding conformal-mapping accelerated Borel series.

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