Perturbative QCD fitting of KEDR and BESIII $e^{+}{e}^{-}$ data for R(s) and ${\alpha }_s$ determination

Abstract

The experimental data collected by KEDR and BESIII collaborations at the energies below charm quark thresholds are compared with the massless QCD expressions for the $e^{+}{e}^{-}$ annihilation R-ratio truncated at different orders of perturbation theory. The fits demonstrate the dependence of the extracted ${\alpha }_s(M_Z)$ values on the orders of truncation of the corresponding approximations. The next-to-leading order, next-to-next-to-leading order and next-to-next-to-next-to-leading order fits of the combined KEDR data and BESIII data , truncated at the scale of mass of $J/\Psi$ meson, give the following results ${\alpha }_s(M_Z)=0.1151_{-0.0069}^{+0.0052}$, ${\alpha }_s(M_Z)=0.1190_{-0.0081}^{+0.0064}$and ${\alpha }_s(M_Z)=0.1283_{-0.0075}^{+0.0028}$. The increasing tendency of fitted ${\alpha }_s(M_Z)$ value is associated with the effects of not totally controlled within asymptotic perturbation theory expansions kinematical ${\pi }^2$ contributions to R-ratio coefficients due to analytical continuation from the space-like to time-like energy regions. The applications of the fixed orders of perturbation theory expansions and careful treatment of the analytical continuation effects are commented.

Final version; Change in Eqs.(12)-(14) and expression added after it;

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