Dirk H. Rischke

The Quark gluon plasma in equilibrium

Abstract Our current knowledge of the quark–gluon plasma in thermodynamical equilibrium is reviewed. The phase diagram of strongly interacting matter is discussed, with emphasis on the quark–hadron phase transition and the colour-superconducting phases of quark matter. Lattice quantum chromodynamics results on the order of the phase transition, the thermodynamical functions, the heavy quark free energy, mesonic spectral functions, and recent results for nonzero quark chemical potential are presented. Analytic attempts to compute the thermodynamical properties of strongly interacting matter, such as perturbation theory, quasiparticle models, “hard-thermal-loop”-resummed perturbation theory, the Polyakov-loop model, as well as linear sigma models are discussed. Finally, colour-superconducting quark matter is considered in the limit of weak coupling. The gap equation and the excitation spectrum are derived. The solution of the gap equation, gap parameters in various colour-superconducting phases, and critical temperatures for the transition to normal-conducting quark matter are presented. A summary of gluon and photon properties in colour superconductors is given.

Derivation of transient relativistic fluid dynamics from the Boltzmann equation

In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inverse Reynolds number. We conclude that the equations of motion can be closed in terms of only 14 dynamical variables, as long as we only keep terms of second order in Knudsen and/or inverse Reynolds number. We show that, even though the equations of motion are closed in terms of these 14 fields, the transport coefficients c information about all the moments of the distribution function. In this way, we can show that the particle-diffusion and shear-viscosity coefficients agree with the values given by the Chapman-Enskog expansion. PACS numbers:

The time-delay signature of quark-gluon plasma formation in relativistic nuclear collisions

Abstract The hydrodynamic expansion of quark-gluon plasmas with spherical and longitudinally boost-invariant geometries is studied as a function of the initial energy density. The sensitivity of the collective flow pattern to uncertainties in the nuclear matter equation of state is explored. We concentrate on the effect of a possible finite width, ΔT ∼ 0.1 T c , of the transition region between quark-gluon plasma and hadronic phase. Although slow deflagration solutions that act to stall the expansion do not exist for ΔT > 0.08 T c , we find, nevertheless, that the equation of state remains sufficiently soft in the transition region to delay the propagation of ordinary rarefaction waves for a considerable time. We compute the dependence of the pion-interferometry correlation function on ΔT , since this is the most promising observable for time-delayed expansion. The signature of time delay, proposed by Pratt and Bertsch, is an enhancement of the ratio of the inverse width of the pion correlation function in out-direction to that in side-direction. One of our main results is that this generic signature of quark-gluon plasma formation is rather robust to the uncertainties in the width of the transition region. Furthermore, for longitudinal boost-invariant geometries, the signal is likely to be maximized around RHIC energies

Relativistic hydrodynamics for heavy-ion collisions. I. General aspects and expansion into vacuum☆

Abstract We present algorithms to solve relativistic hydrodynamics in (3+1)-dimensional situations without apparent symmetry to simplify the solution. In simulations of heavy-ion collisions, these numerical schemes have to deal with the physical vacuum and with equations of state with a first order phase transition between hadron matter and a quark-gluon plasma, i.e. rather special conditions fluid-dynamical algorithms are usually not confronted with. Therefore, prior to applying them directly to the simulation of heavy-ion collisions, one should investigate their performance in well-controlled situations. We consider here the one-dimensional expansion of baryon-free nuclear matter into the vacuum, which is an analytically solvable test problem that incorporates both the aspect of the vacuum as well as that of a phase transition in the equation of state. The dependence of the lifetime of the mixed phase on the initial energy density is discussed.

Excluded volume effect for the nuclear matter equation of state

We present the thermodynamically consistent procedure to introduce the excluded volume effect into the equation of state of nuclear matter. Implications are discussed in the framework of a mean-field model for hadrons with eigenvolume.

Phase diagram of neutral quark matter: Self-consistent treatment of quark masses

We study the phase diagram of dense, locally neutral three-flavor quark matter within the framework of the Nambu\char21{}Jona-Lasinio model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagram in the plane of temperature and quark chemical potential is presented. The results for two qualitatively different regimes, intermediate and strong diquark coupling strength, are presented. It is shown that the role of gapless phases diminishes with increasing diquark coupling strength.

Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory

We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latters definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.

Influence of Shear Viscosity of Quark-Gluon Plasma on Elliptic Flow in Ultrarelativistic Heavy-Ion Collisions

We investigate the influence of a temperature-dependent shear viscosity over entropy density ratio η/s on the transverse momentum spectra and elliptic flow of hadrons in ultrarelativistic heavy-ion collisions. We find that the elliptic flow in √S(NN)=200  GeV Au+Au collisions at RHIC is dominated by the viscosity in the hadronic phase and in the phase transition region, but largely insensitive to the viscosity of the quark-gluon plasma (QGP). At the highest LHC energy, the elliptic flow becomes sensitive to the QGP viscosity and insensitive to the hadronic viscosity.

Vacuum properties of mesons in a linear sigma model with vector mesons and global chiral invariance

We present a two-flavor linear sigma model with global chiral symmetry and vector and axial-vector mesons. We calculate {pi}{pi} scattering lengths and the decay widths of scalar, vector, and axial-vector mesons. It is demonstrated that vector and axial-vector meson degrees of freedom play an important role in these low-energy processes and that a reasonable theoretical description requires globally chirally invariant terms other than the vector-meson mass term. An important question for meson vacuum phenomenology is the quark content of the physical scalar f{sub 0}(600) and a{sub 0}(980) mesons. We investigate this question by assigning the quark-antiquark {sigma} and a{sub 0} states of our model with these physical mesons. We show via a detailed comparison with experimental data that this scenario can describe all vacuum properties studied here except for the decay width of the {sigma}, which turns out to be too small. We also study the alternative assignment f{sub 0}(1370) and a{sub 0}(1450) for the scalar mesons. In this case the decay width agrees with the experimental value, but the {pi}{pi} scattering length a{sub 0}{sup 0} is too small. This indicates the necessity to extend our model by additional scalar degrees of freedom.

Color superconductivity in weak coupling

We derive perturbatively the gap equations for a color-superconducting condensate with total spin J=0 in dense QCD. At zero temperature, we confirm the results of Son for the dependence of the condensate on the coupling constant, and compute the prefactor to leading logarithmic accuracy. At nonzero temperature, we find that to leading order in weak coupling, the temperature dependence of the condensate is identical to that in BCS-like theories. The condensates for total spin J=1 are classified; to leading logarithmic accuracy these condensates are of the same order as those of spin J=0. (c) 2000 The American Physical Society.