U_A(1) Anomaly in Hot and Dense QCD and the Critical Surface

Abstract

We discuss the chiral phase transition in hot and dense QCD with three light flavors. Inspired by the well known fact that the U_A(1) anomaly could induce first order phase transitions, we study the effect of the possible restoration of the U_A(1) symmetry at finite density. In particular, we explore the link between the U_A(1) restoration and the recent lattice QCD results of de Forcrand and Philipsen, in which the first order phase transition region near zero chemical potential (mu) shrinks in the quark mass and mu space when mu is increased. Starting from the Ginzburg-Landau theory for general discussions, we then use the Nambu--Jona-Lasinio model for quantitative studies. With the partial U_A(1) restoration modeled by the density dependent 't Hooft interaction, we fit the shrinking of the critical surface found in de Forcrand and Philipsen's lattice calculation at low mu. At higher mu, the critical surface might shrink or expand, depending on the scenarios. This raises the possibility that despite the shrinking of the critical surface at lower mu, the QCD critical end point might still exist due to the expansion at higher mu. In this case, very high precision lattice data will be needed to detect the back-bending of the critical surface with the currently available analytic continuation or Taylor expansion approaches. Lattice computations could, however, test whether the U_A(1) restoration is responsible for the shrinking of the critical surface by computing eta' mass or the topological susceptibility at small mu.

8 pages, 5 figures

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• The phase diagram of dense QCD
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• Introductory lectures on lattice QCD at nonzero baryon number
• Role of Vector Interaction and Axial Anomaly in the PNJL Modeling of the QCD Phase Diagram
• Existence of the critical endpoint in the vector meson extended linear sigma model
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• Singular values of the Dirac operator in dense QCD-like theories
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• The Myriad Uses of Instantons
• Electric conductivity with the magnetic field and the chiral anomaly in a holographic QCD model
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• $X$ Meson aka ${\eta }^{\prime }$ and Kobayashi-Maskawa-'t Hooft Six-quark Vertex -- $U(1{)}_A$ Anomaly and Generalized Nambu-Jona-Lasinio Model --
• The sign problem across the QCD phase transition
• New Insight about the Effective Restoration of U_A(1) Symmetry
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• Model analysis on thermal UV-cutoff effects on the critical boundary in hot QCD
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• Model analysis of thermal UV-cutoff effects on the chiral critical surface at finite temperature and chemical potential
• A chiral random matrix model with 2+1 flavors at finite temperature and density