Padé estimate of QCDʹs infrared boundary

A mass scale μc representing the boundary between effective theories of strong interactions and perturbative QCD (infrared and ultraviolet regimes) exists when the β-function is characterized by a simple pole. This behaviour, which is known to occur in N=1 supersymmetric Yang–Mills theories, leads to an infrared attractor in the evolution of the coupling constant, with the mass scale μc of the attractor providing a natural boundary between the infrared and ultraviolet regimes. It is demonstrated that [2|2], [3|1] and [1|3] Padé-approximant versions of the three-flavour (nf=3) QCD β-function each contain a simple pole corresponding to such an infrared attractor. All three approximants, separately considered, are seen to lead to nearly equivalent estimates for the mass scale μc.