Pade-summation approach to QCD β-function infrared properties

In view of the successful asymptotic Pade-approximant predictions for higher-loop terms within QCD and massive scalar field theory, we address whether Pade-summations of the <(MS)over bar> QCD beta-function for a given number of flavours exhibit an infrared-stable fixed point, or alternatively, an infrared attractor of a double valued couplant as noted by Kogan and Shifman for the case of supersymmetric gluodynamics. Below an approximant-dependent flavour threshold (6 less than or equal to n(f) less than or equal to 8), we find that Pade-summation beta-functions incorporating [2/1], [1/2], [2/2], [1/3], and [3/1] approximants whose Maclaurin expansions match known higher-than-one-loop contributions to the beta-function series always exhibit a positive pole prior to the occurrence of their first positive zero, precluding any identification of this first positive zero as an infrared-stable fixed point of the beta-function. This result is shown to be true regardless of the magnitude of the presently-unknown five-loop beta-function contribution explicitly appearing within Pade-summation beta-functions incorporating [2/2], [1/3] and [3/1] approximants. Moreover, the pole in question suggests the occurrence of dynamics in which both a strong and an asymptotically-free phase share a common infrared attractor. We briefly discuss the possible relevance of infrared-attractor dynamics to the success of recent calculations of the glueball mass spectra in QCD with N-c --> infinity via supergravity. As n(f) increases above an approximant-dependent flavour threshold, Pade-summation beta-functions incorporating [2/2], [1/3] and [3/1] approximants exhibit dynamics controlled by an infrared-stable fixed point over a widening domain of the five-loop <(MS)over bar> beta-function parameter (beta(4)/beta(0)) Subsequent to the above-mentioned flavour threshold, all approximants considered exhibit infrared-stable fixed points that decrease in magnitude with increasing flavour number.