Chiral quark model with infrared cut-off for the description of meson properties in hot matter

A simple chiral quark model of the Nambu--Jona-Lasinio (NJL) type with a quark confinement mechanism is constructed for the description of the light meson sector of QCD at finite temperature. Unphysical quark production thresholds in the NJL model are excluded by an infrared cut-off in the momentum integration within quark loop diagrams. This chiral quark model satisfies the low energy theorems. Using the vacuum masses and decay widths of \pi- and \rho-mesons for fixing the model parameters, the properties of the \sigma- meson are derived. Within the Matsubara formalism, the model is systematically extended to finite temperatures where chiral symmetry restoration due to a dropping constituent quark mass entails a vanishing of the infrared cut-off (deconfinement) at the pion Mott temperature T_c=186 MeV. Besides of the pion mass and weak decay constant, the masses, coupling constants and decay widths of \sigma- and \rho-mesons in hot matter are investigated. The quark-antiquark decay channel of the light mesons is opened for T>T_c only and becomes particularly strong for the \rho- meson. The two-pion decay channel below T_c has almost constant width for the \rho- meson up to T_c, but for the \sigma-meson it closes below T_c such that a scalar meson state with vanishing width is obtained as a precursor of the chiral/deconfinement transition.Comment: Latex file, 23 pages, 7 figure

Who cares? -The unrecognised contribution of homecare nurses to care trajectories

publishedVersio

Measuring Topological Chaos

The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a chaotic flow, the braid generated by the motion of three or more fluid particles is computed. A ``braiding exponent'' is then defined to characterize the complexity of the braid. This exponent is proportional to the usual Lyapunov exponent of the flow, associated with separation of nearby trajectories. Measuring chaos in this manner has several advantages, especially from the experimental viewpoint, since neither nearby trajectories nor derivatives of the velocity field are needed.Comment: 4 pages, 6 figures. RevTeX 4 with PSFrag macro

Fully integrated transport approach to heavy ion reactions with an intermediate hydrodynamic stage

We present a coupled Boltzmann and hydrodynamics approach to relativistic heavy ion reactions. This hybrid approach is based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. Event-by-event fluctuations are directly taken into account via the non-equilibrium initial conditions generated by the initial collisions and string fragmentations in the microscopic UrQMD model. After a (3+1)-dimensional ideal hydrodynamic evolution, the hydrodynamical fields are mapped to hadrons via the Cooper-Frye equation and the subsequent hadronic cascade calculation within UrQMD proceeds to incorporate the important final state effects for a realistic freeze-out. This implementation allows to compare pure microscopic transport calculations with hydrodynamic calculations using exactly the same initial conditions and freeze-out procedure. The effects of the change in the underlying dynamics - ideal fluid dynamics vs. non-equilibrium transport theory - will be explored. The freeze-out and initial state parameter dependences are investigated for different observables. Furthermore, the time evolution of the baryon density and particle yields are discussed. We find that the final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The results of the different calculations for the mean transverse mass excitation function, rapidity and transverse mass spectra for different particle species at three different beam energies are discussed in the context of the available data.Comment: 20 pages, 21 figures, 1 additional figure, minor corrections and revised figures for clarity, version published in PR

Elliptic flow at RHIC: where and when does it formed?

Evolution of the elliptic flow of hadrons in heavy-ion collisions at RHIC energies is studied within the microscopic quark-gluon string model. The elliptic flow is shown to have a multi-component structure caused by (i) rescattering and (ii) absorption processes in spatially asymmetric medium. Together with different freeze-out dynamics of mesons and baryons, these processes lead to the following trend in the flow formation: the later the mesons are frozen, the weaker their elliptic flow, whereas baryon fraction develops stronger elliptic flow during the late stages of the fireball evolution. Comparison with the PHOBOS data demonstrates the model ability to reproduce the v2(eta) signal in different centrality bins.Comment: 11 pages incl. 5 figure

Heavy flavor kinetics at the hadronization transition

We investigate the in-medium modification of the charmonium breakup processes due to the Mott effect for light (pi, rho) and open-charm (D, D*) quark-antiquark bound states at the chiral/deconfinement phase transition. The Mott effect for the D-mesons effectively reduces the threshold for charmonium breakup cross sections, which is suggested as an explanation of the anomalous J/psi suppression phenomenon in the NA50 experiment. Further implications of finite-temperature mesonic correlations for the hadronization of heavy flavors in heavy-ion collisions are discussed.Comment: 4 pages, 2 figures, Contribution to SQM2001 Conference, submitted to J. Phys.

Equation of state at FAIR energies and the role of resonances

Two microscopic models, UrQMD and QGSM, are used to extract the effective equation of state (EOS) of locally equilibrated nuclear matter produced in heavy-ion collisions at energies from 11.6 AGeV to 160 AGeV. Analysis is performed for the fixed central cubic cell of volume V = 125 fm**3 and for the expanding cell that followed the growth of the central area with uniformly distributed energy. For all reactions the state of local equilibrium is nearly approached in both models after a certain relaxation period. The EOS has a simple linear dependence P/e = c_s**2 with 0.12 < c_s**2 < 0.145. Heavy resonances are shown to be responsible for deviations of the c_s**2(T) and c_s**2(mu_B) from linear behavior. In the T-mu_B and T-mu_S planes the EOS has also almost linear dependence and demonstrates kinks related not to the deconfinement phase transition but to inelastic freeze-out in the system.Comment: SQM2008 proceedings, 6 page

Microscopic models and effective equation of state in nuclear collisions at FAIR energies

Two microscopic models, UrQMD and QGSM, were employed to study the formation of locally equilibrated hot and dense nuclear matter in heavy-ion collisions at energies from 11.6 AGeV to 160 AGeV. Analysis was performed for the fixed central cubic cell of volume V = 125 fm**3 and for the expanding cell which followed the growth of the central area with uniformly distributed energy. To decide whether or not the equilibrium was reached, results of the microscopic calculations were compared to that of the statistical thermal model. Both dynamical models indicate that the state of kinetic, thermal and chemical equilibrium is nearly approached at any bombarding energy after a certain relaxation period. The higher the energy, the shorter the relaxation time. Equation of state has a simple linear dependence P = a(sqrt{s})*e, where a = c_s**2 is the sound velocity squared. It varies from 0.12 \pm 0.01 at E_{lab} = 11.6 AGeV to 0.145 \pm 0.005 at E_{lab} = 160 AGeV. Change of the slope in a(sqrt{s}) behavior occurs at E_{lab} = 40 AGeV and can be assigned to the transition from baryon-rich to meson-dominated matter. The phase diagrams in the T - mu_B plane show the presence of kinks along the lines of constant entropy per baryon. These kinks are linked to the inelastic (i.e. chemical) freeze-out in the system.Comment: 14 pages, REVTE