On the nature of the finite-temperature transition in QCD
Abstract
We discuss the nature of the finite-temperature transition in QCD with Nf massless flavors. Universality arguments show that a continuous (second-order) transition must be related to a 3-D universality class characterized by a complex Nf X Nf matrix order parameter and by the symmetry-breaking pattern [SU(Nf)L X SU(Nf)R]/Z(Nf)V -> SU(Nf)V/Z(Nf)V, or [U(Nf)L X U(Nf)R]/U(1)V -> U(Nf)V/U(1)V if the U(1)A symmetry is effectively restored at Tc. The existence of any of these universality classes requires the presence of a stable fixed point in the corresponding 3-D Phi4 theory with the expected symmetry-breaking pattern. Otherwise, the transition is of first order. In order to search for stable fixed points in these Phi4 theories, we exploit a 3-D perturbative approach in which physical quantities are expanded in powers of appropriate renormalized quartic couplings. We compute the corresponding Callan-Symanzik beta-functions to six loops. We also determine the large-order behavior to further constrain the analysis. No stable fixed point is found, except for Nf=2, corresponding to the symmetry-breaking pattern [SU(2)L X SU(2)R]/Z(2)V -> SU(2)V/Z(2)V equivalent to O(4) -> O(3). Our results confirm and put on a firmer ground earlier analyses performed close to four dimensions, based on first-order calculations in the framework of the epsilon=4-d expansion. These results indicate that the finite-temperature phase transition in QCD is of first order for Nf>2. A continuous transition is allowed only for Nf=2. But, since the theory with symmetry-breaking pattern [U(2)L X U(2)R]/U(1)V -> U(2)V/U(1)V does not have stable fixed points, the transition can be continuous only if the effective breaking of the U(1)A symmetry is sufficiently large.
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