Thompson's renormalization group method applied to QCD at high energy scale

Abstract

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 $ε<1$ in such a way that $με=1$ ($c^2=1$). 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.