Infrared Dynamics in Vector-Like Gauge Theories: QCD and Beyond

Pade-approximant methods are used to extract information about leading positive zeros or poles of QCD and SQCD beta-functions from the known terms of their perturbative series. For QCD, such methods are seen to corroborate the flavour-threshold behaviour obtained via lattice approaches for the occurrence of infrared-stable fixed points.All possible Pade-approximant versions of the known (one- to four-loop) terms of the QCD MS-bar beta-function series are consistent with this threshold occurring at or above n_f = 6. This conclusion continues to be true even if higher-degree Pade-approximants are introduced to accommodate an arbitrary five-loop contribution to the QCD beta-function for a given number of flavours.