A new analytic approach to physical observables in QCD

Abstract

An analytic ghost-free model for the QCD running coupling a(Q(^2)) is proposed. It is constructed from a more general approach we developed particularly for investigating physical observables of the type F(Q(^2)) in regions that are inaccessible to perturbative methods of quantum field theory This approach directly links the infrared (IR) and the ultraviolet (UV) regions together under the causal analyticity requirement in the complex Q(_2) plane. Due to the inclusion of crucial non-perturbative effects, the running coupling in our model not only excludes unphysical singularities but also freezes to a finite value at the IR limit Q(_2) = 0. This makes it consistent with a popular phenomenological hypothesis, namely the IR freezing phenomenon. Applying this model to compute the Gluon condensate, we obtain a result that is in good agreement with the most recent phenomeno logical estimate. Having calculated the β - function corresponding to our QCD coupling constant, we find that it behaves qualitatively like its perturbative counterpart, when calculated beyond the leading order and with a number of quark flavours allowing for the occurrence of IR fixed points. A further application of our analytic approach in the area of wave functionals has been included. We have proven the existence of a local expansion for the logarithm of the Schrӧdinger vacuum functional in any scalar field theory with a non-zero mass gap. This expansion is expected to converge for source fields χ(π) whose Fourier transforms χ(^~)(k) have sufficiently small supports. We have demonstrated how to reconstruct the vacuum functional for an arbitrary source χ(π) from the local expansion of its logarithm by exploiting analyticity in a complex scale parameter.