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Pade-approximant treatments of the known terms of the QCD $\beta$-functionare seen to develop possible infrared fixed point structure only if the numberof fermion flavours is sufficiently large. This flavour threshold is seen to bebetween six and nine flavours, depending upon both the specific choice ofapproximant as well as on the presently-unknown five-loop $\beta$-functioncontribution. Below this flavour threshold, Pade approximants based upon theQCD $\beta$-function manifest the same infrared attractor structure as thatwhich characterizes the exact NSVZ $\beta$-function of supersymmetricgluodynamics. Such infrared attractor structure is also seen to characterizePade-approximant treatments of vector SU(N) gauge theory in the large $N$limit, suggesting common infrared dynamics for the strong and weak phases ofthis theory.

Probing the Infrared Structure of Gauge Theories: A Padé-Approximant Approach