Pade-Summation Approach to QCD -Function Infrared Properties

We address whether Pad\'e-summations of the $\bar{MS}$ QCD $\beta$-functionfor a given number of flavours exhibit an infrared-stable fixed point, oralternatively, an infrared attractor of a double valued couplant as noted byKogan and Shifman for the case of supersymmetric gluodynamics. Below anapproximant-dependent flavour threshold $(6 \leq n_f \leq 8)$, we find thatPad\'e-summation $\beta$-functions incorporating $[2|1], [1|2], [2|2], [1|3]$,and $[3|1]$ approximants always exhibit a positive pole prior to the occurrenceof their first positive zero, precluding any identification of this firstpositive zero as an infrared-stable fixed point of the $\beta$- function. Thisresult is shown to be true regardless of the magnitude of the presently-unknownfive-loop $\beta$-function contribution. Moreover, the pole in questionsuggests the occurrence of dynamics in which both a strong and anasymptotically-free phase share a common infrared attractor. We briefly discussthe possible relevance of infrared-attractor dynamics to the success of recentcalculations of the glueball mass spectra in QCD with $N_c \to \infty$ viasupergravity. As $n_f$ increases above an approximant-dependent flavourthreshold, Pad\'e-summation $\beta$-functions incorporating $[2|2], [1|3]$, and$[3|1]$ approximants exhibit dynamics controlled by an infrared-stable fixedpoint over a widening domain of the five-loop $\bar{MS}$ $\beta$-functionparameter $(\beta_4/\beta_0)$. Above this threshold, all approximantsconsidered exhibit infrared-stable fixed points that decrease in magnitude withincreasing flavour number.Comment: 20 postscript figures now embedded in latex2e. Minor changes to tex