Thompson's Renormalization Group Method Applied to QCD at High Energy Scale
Cl?udio Nassif
We use a renormalization group method to treat QCD-vacuum behavior specially closer to the regime of asymptotic freedom. QCD-vacuum behaves effectively like a ?paramagnetic system? of a classical theory in the sense that virtual color charges (gluons) emerges in it as a spin effect of a paramagnetic material when a magnetic field aligns their microscopic magnetic dipoles. Due to that strong classical analogy with the paramagnetism of Landau's theory,we will be able to use a certain 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 will allow us to apply Thompson's approach to such an action in order to extract an ?effective susceptibility? (χ > 0) of QCD-vacuum. It depends on logarithmic of energy scale u to investigate hadronic matter. Consequently we are able to get an ?effective magnetic permeability? (μ > 1) of such a ?paramagnetic vacuum?. Actually,as QCD-vacuum must obey Lorentz invariance,the attainment of μ > 1 must simply require that the ?effective electrical permissivity? is ǫ < 1 in such a way that μǫ = 1 (c2 = 1). This leads to the anti-screening effect where the asymptotic freedom takes place. We will also be able to extend our investigation to include both the diamagnetic fermionic properties of QED-vacuum (screening) and the paramagnetic bosonic properties of QCD-vacuum (anti-screening) into the same formalism by obtaining a β-function at 1 loop,where both the bosonic and fermionic contributions are considered.
