Fixed and unfixed points: Infrared limits in optimized QCD perturbation theory

Perturbative QCD, when optimized by the principle of minimal sensitivity at fourth order, yields finite results for image down to image. For two massless flavors (image) this occurs because the couplant “freezes” at a fixed-point of the optimized β function. However, for larger imageʼs, between 6.7 and 15.2, the infrared limit arises by a novel mechanism in which the evolution of the optimized β function with energy Q is crucial. The evolving β function develops a minimum that, as image, just touches the axis at image (the “pinch point”), while the infrared limit of the optimized couplant is at a larger value, image (the “unfixed point”). This phenomenon results in image approaching its infrared limit not as a power law, but as image. Implications for the phase structure of QCD as a function of image are briefly considered.