QCD critical point and event-by-event fluctuations in heavy ion collisions

A summary of work done in collaboration with K. Rajagopal and E. Shuryak. We show how heavy ion collision experiments, in particular, event-by-event fluctuation measurements, can lead to the discovery of the critical point on the phase diagram of QCD.Comment: 4 pages. Summary of work done in collaboration with K. Rajagopal and E. Shuryak (hep-ph/9903292). To be published in the proceedings of Quark Matter 99, Torino, Italy, May 10-14, 199

Dirac operator as a random matrix and the quenched limit of QCD with chemical potential

The behavior of quenched QCD at nonzero chemical potential $\mu$ has been a long-standing puzzle. An explicit solution is found using the random matrix approach to chiral symmetry breaking. At nonzero $\mu$ the quenched QCD is not a simple $n\to0$ limit of a theory with $n$ quarks: a naive `replica trick' fails. A limit that leads to the quenched QCD is that of a theory with $2n$ quarks: $n$ quarks with original action and $n$ quarks with conjugate action.Comment: 3 pages, espcrc, 2 figures. Talk presented at LATTICE96(finite temperature

The Phase Diagram of QCD

We show that current experimental knowledge of QCD together with general model independent arguments such as continuity, universality and thermodynamic relations, as well as the information gained from various models can be used to constrain the phase diagram of QCD as a function of temperature and baryon chemical potential.Comment: 6 pages; to appear in Proceedings of the Intl Workshop on QCD at Finite Baryon Density, Bielefeld, Germany, April 199

Non-Gaussian fluctuations near the QCD critical point

We study the effect of the QCD critical point on non-Gaussian moments (cumulants) of fluctuations of experimental observables in heavy-ion collisions. We find that these moments are very sensitive to the proximity of the critical point, as measured by the magnitude of the correlation length xi. For example, the cubic central moment of multiplicity ~ xi^4.5 and the quartic cumulant ~ xi^7. We estimate the magnitude of critical point contributions to non-Gaussian fluctuations of pion and proton multiplicities.Comment: 4 pages, 3 figure

Hydro+: hydrodynamics with parametric slowing down and fluctuations near the critical point

The search for the QCD critical point in heavy-ion collision experiments requires dynamical simulations of the bulk evolution of QCD matter as well as of fluctuations. We consider two essential ingredients of such a simulation: a generic extension of hydrodynamics by a_parametrically_ slow mode or modes ("Hydro+") and a description of fluctuations out of equilibrium. By combining the two ingredients we are able to describe the bulk evolution and the fluctutations within the same framework. Critical slowing down means that equilibration of fluctuations could be as slow as hydrodynamic evolution and thus fluctuations could significantly deviate from equilibrium near the critical point. We generalize hydrodynamics to partial-equilibrium conditions where the state of the system is characterized by the off-equilibrium magnitude of fluctuations in addition to the usual hydrodynamic variables -- conserved densities. We find that the key element of the new formalism -- the extended entropy taking into account the off-equilibrium fluctuations -- is remarkably similar to the 2PI action in quantum field theory. We show how the new Hydro+ formalism reproduces two major effects of critical fluctuations on the bulk evolution: the strong frequency dependence of the anomalously large bulk viscosity as well as the stiffening of the equation of state with increasing frequency or wave-number. While the agreement with known results confirms its validity, the fact that Hydro+ achieves this within a local and deterministic framework gives it significant advantages for dynamical simulations.Comment: 46 pages, 5 figure