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

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

2007-08-16

arxiv.org/abs/0708.2167v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, no figures and 28 references

Scientific paper

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" ($\chi>0$) 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" ($\mu>1$) of such a "paramagnetic vacuum". Actually,as QCD-vacuum must obey Lorentz invariance,the attainment of $\mu>1$ must simply require that the "effective electrical permissivity" is $\epsilon<1$ in such a way that $\mu\epsilon=1$ ($c^2=1$). 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 $\beta$-function at 1 loop,where both the bosonic and fermionic contributions are considered.

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