Padé-Summation Approach to QCD β-Function Infrared Properties

In view of the successful asymptotic Padé-approximant predictions for higher-loop terms within QCD and massive scalar field theory, we address whether Padé-summations of the MS QCD β-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 ≤ nf ≤ 8), we find that Padé-summation β-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 β-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 βfunction. This result is shown to be true regardless of the magnitude of the presently-unknown five-loop β-function contribution explicitly appearing within Padé-summation β-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 Nc → ∞ via supergravity. As nf increases above an approximant-dependent flavour threshold, Padé-summation β-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 β-function parameter (β4/β0). Subsequent to the above-mentioned flavour threshold, all approximants considered exhibit infrared-stable fixed points that decrease in magnitude with increasing flavour number.