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 TMF, 2003, Volume 134, Number 3, Pages 416–429 (Mi tmf168)

Perturbation Theory and the Analytic Approach in the Context of the Inclusive $\tau$-Lepton Decay

O. P. Solovtsova

Joint Institute for Nuclear Research

Abstract: We perform a comparative analysis of different forms of pertubative expansions in spacelike and timelike regions. In the context of the inclusive -lepton decay, we compare the results obtained using the standard perturbation theory and the Shirkov–Solovtsov analytic approach, which modifies the perturbative expansions such that the new approximations reflect basic principles of the theory, such as renormalization invariance, spectrality, and causality. We show the advantages and self-consistency of the analytic approach in describing the $\tau$-lepton decay.

Keywords: quantum chromodynamics, renormalization group, perturbation theory, $\tau$-lepton

DOI: https://doi.org/10.4213/tmf168

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English version:
Theoretical and Mathematical Physics, 2003, 134:3, 365–376

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Revised: 17.06.2002

Citation: O. P. Solovtsova, “Perturbation Theory and the Analytic Approach in the Context of the Inclusive $\tau$-Lepton Decay”, TMF, 134:3 (2003), 416–429; Theoret. and Math. Phys., 134:3 (2003), 365–376

Citation in format AMSBIB
\Bibitem{Sol03} \by O.~P.~Solovtsova \paper Perturbation Theory and the Analytic Approach in the Context of the Inclusive $\tau$-Lepton Decay \jour TMF \yr 2003 \vol 134 \issue 3 \pages 416--429 \mathnet{http://mi.mathnet.ru/tmf168} \crossref{https://doi.org/10.4213/tmf168} \transl \jour Theoret. and Math. Phys. \yr 2003 \vol 134 \issue 3 \pages 365--376 \crossref{https://doi.org/10.1023/A:1022601522327} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000182047100007} 

• http://mi.mathnet.ru/eng/tmf168
• https://doi.org/10.4213/tmf168
• http://mi.mathnet.ru/eng/tmf/v134/i3/p416

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This publication is cited in the following articles:
1. Prosperi, GM, “On the running coupling constant in QCD”, Progress in Particle and Nuclear Physics, 58:2 (2006), 387
2. Shirkov D.V., “Analytic perturbation theory model for QCD and upsilon decay”, Nuclear Phys B Proc Suppl, 162 (2006), 33–38
3. D. V. Shirkov, I. L. Solovtsov, “Ten years of the analytic perturbation theory in QCD”, Theoret. and Math. Phys., 150:1 (2007), 132–152
4. Wu X.-G. Brodsky S.J. Mojaza M., “The Renormalization Scale-Setting Problem in QCD”, Prog. Part. Nucl. Phys., 72 (2013), 44–98
5. JETP Letters, 104:9 (2016), 601–608
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