Pade Estimate of QCD's Infrared Boundary

Abstract

A mass scale $μ_c$ 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 $μ_c$ of the attractor providing a natural boundary between the infrared and ultraviolet regimes. It is demonstrated that [2|2], [3|1] and [1|3] Pade-approximant versions of the three-flavour 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 $μ_c$.