Asymptotic freedom and quarks confinement treated through Thompson’s approach

Abstract

In this work, we first use Thompson’s renormalization group method to treat QCD–vacuum behavior close to the regime of asymptotic freedom. The QCD–vacuum behaves effectively like a “paramagnetic system” of a classical theory in the sense that virtual color charges (gluons) emerge in it as a spin effect of a paramagnetic material when a magnetic field aligns their microscopic magnetic dipoles. Making a classical analogy with the paramagnetism of Landau’s theory, we are able to introduce a kind of Landau effective action without temperature and phase transition for just representing QCD–vacuum behavior at higher energies as being magnetization of a paramagnetic material in the presence of a magnetic field H. This reasoning allows us to use Thompson’s heuristic approach to obtain an “effective susceptibility” (χ > 0) of the QCD–vacuum. It depends on the logarithm of the energy scale u to investigate hadronic matter. Consequently, we are able to get an “effective magnetic permeability” (μ > 1) of such a “paramagnetic vacuum”. As the QCD–vacuum must obey Lorentz invariance, the attainment of μ > 1 must simply require that the “effective electrical permittivity” is ϵ < 1 in such a way that μϵ = 1 (c2 = 1). This leads to the anti-screening effect, where the asymptotic freedom takes place. On the other hand, quarks confinement, a subject which is not treatable by perturbative calculations, is worked by the present approach. We apply the method to study this issue for obtaining the string constant, which is in agreement with the experiments.