Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 127, Number 1, Pages 3–20
DOI: https://doi.org/10.4213/tmf445
(Mi tmf445)
 

This article is cited in 82 scientific papers (total in 82 papers)

Analytic Perturbation Theory for QCD Observables

D. V. Shirkov

Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
References:
Abstract: We investigate the connection between ghost-free formulations of the RG-invariant QCD perturbation theory in the spacelike and timelike regions. Our basic tool is the “double spectral representation”, similar to the representation for the Adler function, which stems from the first principles of local QFT and relates real functions in the Euclidean and Minkowskian (i.e., timelike) regions. On this base, we establish a simple relation between the approach (known from the early 1980s) of resumming the $\pi^2$ terms for the invariant coupling function $\tilde\alpha(s)$ and QCD observables in the timelike region and the invariant analytic approach (devised a few years ago) leading to the “analyticized” coupling function $\alpha_{\text{an}}(Q^2)$ and nonpower expansion for observables in the spacelike domain. The function $\alpha_{\text{an}}(Q^2)$ and the expansion are free of unphysical singularities. The formulated self-consistent scheme, analytic perturbation theory (APT), relates renorm-invariant, effective coupling functions $\alpha_{\text{an}}(Q^2)$ and $\tilde\alpha(s)$, as well as nonpower perturbation expansions for observables in the Euclidean and Minkowskian domains, free of extra singularities and with better convergence in the infrared region. We present a global generalization of the new APT scheme in the case of real QCD, including the domain with various numbers of active quarks. Preliminary estimates indicate that calculations in the framework of the global scheme can produce results quite different from the usual ones for $\bar\alpha_{s}$ , even in the five-quark region. Numerical examples are given.
Received: 22.11.2000
English version:
Theoretical and Mathematical Physics, 2001, Volume 127, Issue 1, Pages 409–423
DOI: https://doi.org/10.1023/A:1010302206227
Bibliographic databases:
Language: Russian
Citation: D. V. Shirkov, “Analytic Perturbation Theory for QCD Observables”, TMF, 127:1 (2001), 3–20; Theoret. and Math. Phys., 127:1 (2001), 409–423
Citation in format AMSBIB
\Bibitem{Shi01}
\by D.~V.~Shirkov
\paper Analytic Perturbation Theory for QCD Observables
\jour TMF
\yr 2001
\vol 127
\issue 1
\pages 3--20
\mathnet{http://mi.mathnet.ru/tmf445}
\crossref{https://doi.org/10.4213/tmf445}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1863116}
\zmath{https://zbmath.org/?q=an:0993.81054}
\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 127
\issue 1
\pages 409--423
\crossref{https://doi.org/10.1023/A:1010302206227}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000170446000001}
Linking options:
  • https://www.mathnet.ru/eng/tmf445
  • https://doi.org/10.4213/tmf445
  • https://www.mathnet.ru/eng/tmf/v127/i1/p3
  • This publication is cited in the following 82 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024