Approaches to QCD phase diagram; effective models, strong-coupling lattice QCD, and compact stars

The outline of the two lectures given in "Dense Matter School 2015" is presented. After an overview on the relevance of the phase diagram to heavy-ion collisions and compact star phenomena, I show some basic formulae to discuss the QCD phase diagram in the mean field treatment of the Nambu-Jona-Lasinio model. Next, I introduce the strong-coupling lattice QCD, which is one of the promising methods to access the QCD phase diagram including the first order phase boundary. In the last part, I discuss the QCD phase diagram in asymmetric matter, which should be formed in compact star phenomena.Comment: Lecture given at Helmholtz International Summer School "Dense Matter 2015", 29 June-11 July 2015 and the 15th International Conference on Strageness in Quark Matter (SQM 2015), 6-11 July 2015, Dubna, Russia. 12 pages, 10 figures. Some typos are corrected in v

Topological feature and phase structure of QCD at complex chemical potential

The pseudo-critical temperature of the confinement-deconfinement transition and the phase transition surface are investigated by using the complex chemical potential. We can interpret the imaginary chemical potential as the Aharonov-Bohm phase, then the analogy of the topological order suggests that the Roberge-Weiss endpoint would define the pseudo-critical temperature. The behavior of the Roberge-Weiss endpoint at small real quark chemical potential is investigated with the perturbative expansion. The expected QCD phase diagram at complex chemical potential is presented.Comment: 6 pages, 2 figure

A chiral symmetric relativistic mean field model with logarithmic sigma potential

We develop a chiral symmetric relativistic mean field model with logarithmic sigma potential derived in the strong coupling limit of the lattice QCD. We find that both of the nuclear matter and finite nuclei are well described in the present model. The normal vacuum is found to have global stability at zero and finite baryon densities, and an equation of state with moderate stiffness (K ~ 280 MeV) is obtained. The binding energies and charge radii of Z closed even-even nuclei are well reproduced in a wide mass range from C to Pb isotopes, except for the underestimates of binding energies in several jj closed nuclei.Comment: 19 pages, 6 figure

Probing neutron-proton dynamics by pions

In order to investigate the nuclear symmetry energy at high density, we study the pion production in central collisions of neutron-rich nuclei ${}^{132}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ at 300 MeV/nucleon using a new approach by combining the antisymmetrized molecular dynamics (AMD) and a hadronic cascade model (JAM). The dynamics of neutrons and protons is solved by AMD, and then pions and $\Delta$ resonances in the reaction process are handled by JAM. We see the mechanism how the $\Delta$ resonance and pions are produced reflecting the dynamics of neutrons and protons. We also investigate the impacts of cluster correlations as well as of the high-density symmetry energy on the nucleon dynamics and consequently on the pion ratio. We find that the $\Delta^-/\Delta^{++}$ production ratio agrees very well with the neutron-proton squared ratio $(N/Z)^2$ in the high-density and high-momentum region. We show quantitatively that $\Delta$ production ratio, and therefore $(N/Z)^2$, are directly reflected in the $\pi^-/\pi^+$ ratio, with modification in the final stage of the reaction.Comment: 14 pages, 10 figures; Figures 3-8 are updated with corrected numerical results. No change in the main conclusion