Determination ofαs(1 GeV)from the charmonium fine structure

The strong coupling constant ${\alpha }_s\left(\mu \right)$ is extracted from the fits to charmonium spectrum and fine structure splittings. The relativistic kinematics is taken into account and relativistic corrections are shown to increase the matrix elements defining spin effects up to $40\%.$ The value of ${\alpha }_s\left(\mu \right)$ at the low-energy scale $\mu =1.0\mathrm{}\pm 0.2\hspace{0.5em}\mathrm{GeV}$ was found to be ${\alpha }_s\left(\mu \right)=0.38\mathrm{}\pm 0.03\left(\exp \right)+0.04\left(\mathrm{theor}\right)$ which is about $50\%$ lower than the standard perturbative two-loop approximation and is in good agreement with the freezing ${\alpha }_s$ behavior.