arXiv:1001.3216v1 [hep-ph] 19 Jan 2010 QCD phase diagram at high temperature and density Mei Huang 1 , 2 ∗ $^{1}$Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China 2 Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing, China This article reviews recent progress of QCD phase structure, including color superconductor at high baryon density and strongly interacting quark-gluon plasma (sQGP) at high temperature cre- ated through relativistic heavy ion collision. A brief overview is given on the discovery of sQGP at RHIC. The possibility of locating the critical end point (CEP) from the property of bulk viscosity over entropy density is discussed. For the phase structure at high baryon density, the status of the unconventional color superconducting phase with mismatched pairing is reviewed. The chromomag- netic instability, Sarma instability and Higgs instability in the gapless color superconducting phase are clarified. PACS numbers: Quantum Chromodynamics (QCD) is an asymptoti- cally free theory [1] and regarded as the fundamental theory of quarks and gluons. At very high energies, in- teraction forces become weak, thus perturbation calcu- lations can be used. The perturbative QCD predictions have been extensively confirmed by experiments, while QCD in the non-perturbative regime is still a challenge to theorists. The fundamental quarks and gluons of QCD have not been seen as free particles, but are always con- fined within hadrons. It is still difficult to construct the hadrons in terms of nearly massless quarks and gluons. The observed baryon spectrum indicates that the (ap- proximate) chiral symmetry is spontaneously broken in the vacuum. As a result, the eight pseudoscalar mesons π , K and η are light pseudo-Nambu-Goldstone bosons, and the constituent quark obtains dynamical mass, which contributes to the baryon mass. Besides conventional mesons and baryons, QCD itself does not exclude the ex- istence of the non-conventional states such as glueballs, hybrid mesons and multi-quark states [2]. Since 1970s, people have been interested in QCD at ex- treme conditions. It is expected that the chiral symme- try can be restored, and quarks and gluons will become deconfined at high temperatures and/or densities [3–6]. Fig. 1 is the typical QCD phase diagram, which shows the system is in deconfined quark-gluon plasma phase at high temperature, and in color superconducting phase at high baryon density. Results from lattice show that the quark-gluon plasma (QGP) does exist. For the system with zero net baryon density, the deconfinement and chiral symmetry restora- tion phase transitions happen at the same critical tem- perature [7]. At asymptotically high temperatures, e.g., during the first microseconds of the “Big Bang”, the many-body system composed of quarks and gluons can be regarded as an ideal Fermi and Boson gas. It is believed that the “little Bang” can be produced at RHIC and LHC. Recently, it was shown that the new state of mat- ter produced at RHIC is far away from the asymptotically hot QGP, but in a strongly coupled regime. This state is called strongly coupled quark-gluon plasma (sQGP)[8]. For most recent reviews about QGP, e.g., see Ref. [9–12]. Studying QCD at finite baryon density is the tra- ditional subject of nuclear physics. The behaviour of QCD at finite baryon density and low temperature is central for astrophysics to understand the structure of compact stars, and conditions near the core of collaps- ing stars (supernovae, hypernovae). Cold nuclear mat- ter, such as in the interior of a Pb nucleus, is at T = 0 and µ$_{B}$ ≃ m$_{N}$ = 940MeV. Emerging from this point, there is a first-order nuclear liquid-gas phase transition, which terminates in a critical endpoint at a temperature ∼ 10MeV [13]. If one squeezes matter further and fur- ther, nuleons will overlap. Quarks and gluons in one nucleon can feel quarks and gluons in other nucleons. Eventually, deconfinement phase transition will happen. Unfortunately, at the moment, lattice QCD is facing the “sign problem” at nonzero net baryon densities. Our understanding at finite baryon densities has to rely on effective QCD models. Phenomenological models indi- cated that, at nonzero baryon density, the QGP phase and the hadron gas are separated by a critical line of I. INTRODUCTION FIG. 1: QCD phase diagram at finite temperature and baryon density. ∗ huangm@ihep.ac.cn