Analytic Perturbation Theory for Practitioners and Upsilon Decay

Abstract

Within the ghost-free Analytic Perturbation Theory (APT), devised in the last decade for low energy QCD, simple approximations are proposed for 3-loop analytic couplings and their effective powers, in both the space-like (Euclidean) and time-like (Minkowskian) regions, accurate enough in the large range (1--100 GeV) of current physical interest.\par Effectiveness of the new Model is illustrated by the example of ${\rm Y}(1\mathrm{S})$ decay where the standard analysis gives ${\alpha }_s(M_{{\rm Y}})=0.170\pm 0.004$ value that is inconsistent with the bulk of data for ${\alpha }_s$. Instead, we obtain ${\alpha }_s^{Mod}(M_{{\rm Y}})=0.185\pm 0.005$ that corresponds to ${\alpha }_s^{Mod}(M_Z)=0.120\pm 0.002$ that is close to the world average.\par The issue of scale uncertainty for ${\rm Y}$ decay is also discussed.

12 pages, 0 figures. Model slightly modified to increase its accuracy. Numerical results upgraded, references added. The issue of scale uncertainty is discussed

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Cited by in corpus (14)

• On the running coupling constant in QCD
• Ten years of the Analytic Perturbation Theory in QCD
• Bound state approach to the QCD coupling at low energy scales
• QCD coupling below 1 GeV from quarkonium spectrum
• Bjorken Sum Rule and pQCD frontier on the move
• Global Fractional Analytic Perturbation Theory in QCD with Selected Applications
• Nucleon spin structure and pQCD frontier on the move
• FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory
• QCDMAPT: program package for Analytic approach to QCD
• Nucleon spin structure at low momentum transfers
• "Massive" Perturbative QCD, regular in the IR limit
• Extracting infrared QCD coupling from meson spectrum
• On applications of Mathematica Package "FAPT" in QCD
• Novel Sets of Coupling Expansion Parameters for low-energy pQCD