Abstract:
Various aspects of the current status of ultrarelativistic heavy ion collisions are reviewed. Perspectives of heavy ion physics in the future are given as well.

Abstract:
In this article, we outline the modeling of a realistic dynamical model for comprehensive description of high energy heavy ion collisions. Comparing theoretical calculations and experimental data at RHIC, we give detailed discussions on the key ingredients for the construction of a multi-module model: initial condition, hydrodynamical expansion, hadronization, and freezeout processes.

Abstract:
We explore the relation between proton and nucleon number fluctuations in the final state in relativistic heavy ion collisions. It is shown that the correlations between the isospins of nucleons in the final state are almost negligible over a wide range of collision energy. This leads to a factorization of the distribution function of the proton, neutron, and their antiparticles in the final state with binomial distribution functions. Using the factorization, we derive formulas to determine nucleon number cumulants, which are not direct experimental observables, from proton number fluctuations, which are experimentally observable in event-by-event analyses. With a simple treatment for strange baryons, the nucleon number cumulants are further promoted to the baryon number ones. Experimental determination of the baryon number cumulants makes it possible to compare various theoretical studies on them directly with experiments. Effects of nonzero isospin density on this formula are addressed quantitatively. It is shown that the effects are well suppressed over a wide energy range.

Abstract:
Hydrodynamical calculations have been successful in describing global observables in ultrarelativistic heavy ion collisions, which aim to observe the production of the quark-gluon plasma. On the other hand, recently, a lot of evidence that there exists a critical end point (CEP) in the QCD phase diagram has been accumulating. Nevertheless, so far, no equation of state with the CEP has been employed in hydrodynamical calculations. In this paper, we construct the equation of state with the CEP on the basis of the universality hypothesis and show that the CEP acts as an attractor of isentropic trajectories. We also consider the time evolution in the case with the CEP and discuss how the CEP affects the final state observables, such as the correlation length, fluctuation, chemical freezeout, kinetic freezeout, and so on. Finally, we argue that the anomalously low kinetic freezeout temperature at the BNL Relativistic Heavy Ion Collider suggests the possibility of the existence of the CEP.

Abstract:
Baryon number cumulants are invaluable tools to diagnose the primordial stage of heavy ion collisions if they can be measured. In experiments, however, proton number cumulants have been measured as substitutes. In fact, proton number fluctuations are further modified in the hadron phase and different from those of baryon number. We show that the isospin distribution of nucleons at kinetic freezeout is binomial and factorized. This leads to formulas that express the baryon number cumulants sorely in terms of proron number fluctuations, which are experimentally observable.

Abstract:
Bulk fluctuations of conserved charges measured by event-by-event analysis in relativistic heavy ion collisions are observables which are believed to carry significant information on the primordial thermodynamics of the hot medium created by the collisions. Active studies have been done recently experimentally, theoretically, and on the lattice. In particular, non-Gaussianity of the fluctuations aquires much attention recently. In this review, we give a pedagogical introduction to these physics, and overview recent developments in this field of research. Starting from the definition of cumulants, basic concepts in fluctuation physics, such as thermal fluctuations in statistical mechanics and time evolution of fluctuations in diffusive systems, are described. Physics which are expected to occur in the QCD phase diagram and their measurement by event-by-event analyses are also elucidated.

Abstract:
We point out that the third moments of conserved charges, the baryon and electric charge numbers, and energy, as well as their mixed moments, change their signs around the QCD phase boundary in the temperature and baryon chemical potential plane. These signs can be measured in relativistic heavy ion collisions, and will give clear information on the phase structure of QCD and the state of the system in the early stage of relativistic heavy ion collisions. The behaviors of these moments on the temperature axis and at small quark chemical potential can be analyzed in lattice QCD simulations. We emphasize that the third moments obtained on the lattice, together with the experimental results, will provide a deep understanding about the QCD phase diagram and the location of the state created in heavy ion collisions.

Abstract:
The third moments of conserved charges, the baryon and electric charge numbers, and energy, as well as their mixed moments, carry more information on the state around the QCD phase boundary than previously proposed fluctuation observables and higher order moments. In particular, their signs give plenty of information on the location of the state created in relativistic heavy ion collisions in the temperature and baryon chemical potential plane. We demonstrate this with an effective model.

Abstract:
We discuss various mechanisms for the creation of an asymmetric charge fluctuation with respect to the reaction plane among hadrons emitted in relativistic heavy-ion collisions. We show that such mechanisms exist in both, the hadronic gas and the partonic phases of QCD. The mechanisms considered here all require the presence of a strong magnetic field (the ``chiral magnetic effect''), but they do not involve parity or charge-parity violations. We analyze how a transient local electric current fluctuation generated by the chiral magnetic effect can dynamically evolve into an asymmetric charge distribution among the final-state hadrons in momentum space. We estimate the magnitude of the event-by-event fluctuations of the final-state charge asymmetry due to the partonic and hadronic mechanisms.

Abstract:
The size of the average fluctuations of net baryon number and electric charge in a finite volume of hadronic matter differs widely between the confined and deconfined phases. These differences may be exploited as indicators of the formation of a quark-gluon plasma in relativistic heavy-ion collisions, because fluctuations created in the initial state survive until freeze-out due to the rapid expansion of the hot fireball.