High Density EOS — Heavy-Ion Collisions, Compact Stars and Strangeness —

The baryon density in the cores of massive neutron stars may reach (4 − 10)ρ0, which is the largest density in stable matter in our universe. Because of the large chemical potential, various forms of matter are expected to appear in neutron star cores, such as strange hadrons, meson condensate, quark matter, and color superconductor, in addition to nucleons and leptons. It is also possible to probe various phases of nuclear matter by using heavy-ion collisions. At collider energies (RHIC and LHC), the quark gluon plasma (QGP) is formed with almost zero baryon chemical potential, while we can probe baryon-rich region by using lower-energy heavy-ion collisions. Compared with compact stars, the isospin asymmetry (δ = (N − Z)/A) is small in heavy-ion collisions. At high temperatures, T > 100 MeV, pions are produced abundantly and reduce the anisotropy of baryonic part. Isospin chemical potential (δμ = μn−μp) is evaluated to be 10 MeV or less in high-energy heavyion collisions, while it can reach 100 − 200 MeV in neutron star matter. In order to understand the whole phase-diagram structure in (T, ρB, δ) space schematically shown in Fig. 1, we need to combine knowledge from compact stars and heavy-ion collisions. One of the most interesting questions in dense nuclear matter physics is the existence of the firstorder phase-transition boundary at high baryon densities. If the QCD phase transition in cold nuclear matter is of the first order, we must have at least one QCD critical point (CP) in the QCD phase diagram: The transition at zero baryon chemical potential is crossover, then the first-order phase boundary needs to terminate at CP. The existence of CP or the first-order phase transition boundary would be accessible in heavy-ion collisions. On the one hand, large fluctuations of conserved charges are expected around CP. Because of the second-order phase transition nature at CP, the susceptibilities and higher-order cumulants diverge at CP owing to the divergent correlation length, and thus one expects anomalously large fluctuations would be observed if the system passes around CP. Recent data show non-monotonic behavior of the fourth order cumulant (κσ2) of net proton numbers as a function of the colliding energy [1], and the interpretation of the data is under active debate. On the other hand, the softening of equation of state (EOS) is expected with the first-order phase transition, and causes reduction of the directed flow. The transverse collective flows, such as the directed flow v1 = 〈cos φ〉 and the elliptic flow v2 = 〈cos 2φ〉, have been utilized to explore the properties of hot and dense matter EOS in the early stages of heavy-ion collisions. Particles are generally kicked in the