Perturbative QCD fitting of the $e^+e^-$ to hadrons KEDR and BESIII data for R(s) and $α_s$ determination

The experimental data collected by KEDR and BESIII collaborations at the energies below charming quark thresholds are compared with the coordinally truncated at different orders of perturbation theory QCD expressions for the $e^+e^-$ annihilation R-ratio and the renormalization group $β$-function. The fits demonstrate the dependence of the extracted $α_s(M_Z)$ values from orders of the truncation of the corresponding approximations. The next-to-leading order and next-to-next-to-leading order fits of the combined KEDR data and BESIII data , truncated at the mass scale of $J/Ψ$ meson, give the following results $α_s(M_Z)= 0.1179^{+0.0051}_{-0.0069}$ and $α_s(M_Z)=0.1221^{+0.0063}_{-0.0723}$. The subjects related to the applications of the fixed orders of perturbation theory expansions and careful treatment of the analytical continuation effects are commented.