Renormalization group approach towards the QCD phase diagram
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enormalization Group Approach towards the QCD Phase Diagram¶ B.-J. Schaefera and J. Wambachb, c a
Institut für Physik, Karl-Franzens-Universität, Universitätsplatz 5, A-81 Graz, Austria b Institut für Kernphysik, TU Darmstadt, Schlößgartenstraße 9, D-64289 Darmstadt c Theory Division, GSI mbH, Planckstraße 1, D-64291 Darmstadt, Germany Abstract—The idea of the functional renormalization group and one-loop improved renormalization group flows are reviewed. The associated flow equations and nonperturbative approximations schemes for its solutions are discussed. These techniques are then applied to the strong interaction in the framework of an effective quark meson model, which is introduced in great detail. The renormalization group analysis of the two flavor quark meson model is extended to finite temperature and quark chemical potential which allows for an analysis of the chiral phase diagram beyond the mean field approximation. PACS numbers: 12.38.Mh DOI: 10.1134/S1063779608070083
1. INTRODUCTION Quantum Chromodynamics (QCD) is the quantum field theory of strongly interacting matter. Many of its vacuum features have been tested experimentally over a wide range of momentum scales. At high momenta or small distances, the asymptotic freedom of non-Abelian gauge theories can be used to apply perturbative methods for the computation of physical observables. Due to the running of the strong gauge coupling, the situation becomes significantly more complicated at smaller momentum scales or larger distances. Here perturbation theory breaks down and nonperturbative methods are called for. There are no analytical methods starting from first principles which allow us to treat QCD at larger distances, where the strong gauge coupling becomes large and perturbation theory fails. The main reason for this difficulty is that QCD describes qualitatively different physics at different length or energy scales. The situation is further complicated at finite temperature and/or baryon density. For instance, at very high temperatures perturbative calculations are plagued by serious infrared divergences. Furthermore, it is generally expected that at high enough temperature and densities hadronic matter attains a state in which chiral symmetry is almost restored and its fundamental degrees of freedom, the quarks and gluons, are no longer confined. The system undergoes a phase transition from the ordinary hadronic phase to a chirally restored and deconfined quark gluon plasma (QGP). Furthermore, recent theoretical studies reveal an
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text was submitted by the authors in English.
increasing richness in the structure of the phase diagram of strongly interacting matter. Therefore, nonperturbative methods are indispensable to obtain quantitatively reliable results, because one has to deal with large couplings and a perturbative expansion of physical observables fails. One such nonperturbative method is given by the renormalization group (RG). The RG method represents an efficient way to describe critical phenomena and phase transitions. I
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