QCD perturbation theory at low energies

We apply the optimization procedure based on the principle of minimal sesitivity to the third-order calculation of ${\mathit{R}}_{\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$. The effective couplant remains finite, freezing to a value ${\mathrm{\alpha }}_{\mathit{s}}$/π=0.26 at low energies. Using Poggio-Quinn-Weinberg smearing we find good agreement between theory and experiment right down to zero energy.