Behaviour of quantum chromodynamics near an infrared fixed point.

In perturbation theory, the QCD running coupling depends on the renormalization scheme or is parameterised by a physical process. The problem is that artefacts of this ambiguity may upset physical conclusions outside the asymptotically free region, in particular near an infrared fixed point. Thus, a non-perturbative definition for the QCD running coupling is required that should be a monotonic and analytic function of the space-like energy scale Q². The most physical coupling is Grunberg's definition for the running coupling as an effective charge αɢ(Q²). However, we find that it works only for sufficiently high energy scales. At some finite values of the energy scale, near the top of the resonance region, the β-function associated with αɢ(Q²) has a false zero below which αɢ(Q²) decreases. We test this conclusion further by applying chiral perturbation theory to the running coupling based on the method of effective charges. We consider the Drell-Yan ratio R(q²) and Adlerfunction D(Q²) in the time-like and space-like domains, respectively. These quantities tend to a finite value in the both infrared and ultraviolet limits: R(0) = D(0) = 0:5 for π±; K± and R(∞) = D(∞) = 2 for the light quarks. This means that the running coupling becomes negative in the infrared limit. Therefore, neither the time-like nor the space-like effective charges is a monotonic function over the whole energy scale. We also try to cancel the space-like pole of the proposed exact β-function, using the property of renormalization scheme dependence. Our modified exact β-function is non-singular for all finite values of the running coupling α and has an infrared fixed point even for a small number of quark flavours.Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 201