Optimization of Re+e- and "freezing" of the QCD couplant at low energies.

The new result for the third-order QCD corrections to Re+e− , unlike the old, incorrect result, is nicely compatible with the principle-of-minimal-sensitivity optimization method. Moreover, it leads to infrared fixed-point behaviour: the optimized couplant, αs/π, for Re+e− does not diverge at low energies, but “freezes” to a value 0.26 below about 300 MeV. This provides some direct theoretical evidence, purely from perturbation theory, for the “freezing” of the couplant – an idea that has long been a popular and successful phenomenological hypothesis. We use the “smearing” method of Poggio, Quinn, and Weinberg to compare the resulting theoretical prediction for Re+e− with experimental data down to the lowest energies, and find excellent agreement.