QCD perturbation theory at low energies

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