Ghost-Free APT Analysis of Perturbative QCD Observables

  • Dmitry V. Shirkov
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 616)


The review of the essence and of application of recently devised ghost-free Analytic Perturbation Theory (APT) is presented. First, we discuss the main intrinsic problem of perturbative QCD — ghost singularities and with the resume of its resolving within the APT. By examples for diverse energy and momentum transfer values we show the property of better convergence for the APT modified QCD expansion.

It is shown that in the APT analysis the three-loop contribution (~ α 3 s) is numerically inessential. This gives raise a hope for practical solution of the well-known problem of non-satisfactory convergence of QFT perturbation series due to its asymptotic nature. Our next result is that a usual perturbative analysis of time-like events is not adequate at s ≤ 2 GeV2. In particular, this relates to τ decay.

Then, for the “high” (f = 5) region it is shown that the common NLO, NLLA perturbation approximation widely used there (at 10 GeV≲√s≲170 GeV) yields a systematic theoretic negative error of a couple per cent level for the ά (2) s values. This results in a conclusion that the ά s(M 2 Z) value averaged over the f = 5 data appreciably differs 〈ά s(M 2 Z)〉f=5 ≃ 0.124 from the currently popular “world average” (= 0.118 ).


Power Expansion Analytic Perturbation Theory Loop Case Lambert Function Adler Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Dmitry V. Shirkov
    • 1
  1. 1.Bogoliubov LaboratoryJINRDubnaRussia

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