Pade estimate of QCD's infrared boundary

A mass scale mu (c) representing the boundary between effective theories of strong interactions and perturbative QCD (infrared and ultraviolet regimes) exists when the beta -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 mu (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 (n(f) = 3) QCD beta -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 mu (c). (C) 2001 Published by Elsevier Science B.V.