Hadron Resonance Gas Model with Induced Surface Tension

Here we present a physically transparent generalization of the multicomponent Van der Waals equation of state in the grand canonical ensemble. For the one-component case the third and fourth virial coefficients are calculated analytically. It is shown that an adjustment of a single model parameter allows us to reproduce the third and fourth virial coefficients of the gas of hard spheres with small deviations from their exact values. A thorough comparison of the compressibility factor and speed of sound of the developed model with the one and two component Carnahan-Starling equation of state is made. It is shown that the model with the induced surface tension is able to reproduce the results of the Carnahan-Starling equation of state up to the packing fractions 0.2-0.22 at which the usual Van der Waals equation of state is inapplicable. At higher packing fractions the developed equation of state is softer than the gas of hard spheres and, hence, it breaks causality in the domain where the hadronic description is expected to be inapplicable. Using this equation of state we develop an entirely new hadron resonance gas model and apply it to a description of the hadron yield ratios measured at AGS, SPS, RHIC and ALICE energies of nuclear collisions. The achieved quality of the fit per degree of freedom is about 1.08. We confirm that the strangeness enhancement factor has a peak at low AGS energies, while at and above the highest SPS energy of collisions the chemical equilibrium of strangeness is observed. We argue that the chemical equilibrium of strangeness, i.e. $\gamma_s \simeq 1$, observed above the center of mass collision energy 4.3 GeV may be related to the hadronization of quark gluon bags which have the Hagedorn mass spectrum, and, hence, it may be a new signal for the onset of deconfinement

Bogolyubov-Hartree-Fock approach to studying the QCD ground state

The quark's behaviour while influenced by a strong stochastic gluon field is analyzed. An approximate procedure for calculating the effective Hamiltonian is developed and the corresponding ground state within the Hartree-Fock-Bogolyubov approach is found. The comparative analysis of various Hamiltonian models is given and transition to the chiral limit in the Keldysh model is discussed in detail.Comment: 18 pages, 4 figures, new version of the manuscrip

Quark Gluon Bags as Reggeons

The influence of the medium dependent finite width of QGP bags on their equation of state is analyzed within an exactly solvable model. It is argued that the large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances, but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase. The model allows us to estimate the minimal value of the width of QGP bags from a variety of the lattice QCD data and get that the minimal resonance width at zero temperature is about 600 MeV, whereas the minimal resonance width at the Hagedorn temperature is about 2000 MeV. As shown these estimates are almost insensitive to the number of the elementary degrees of freedom. The recent lattice QCD data are analyzed and it is found that besides sigma T**4 term the lattice QCD pressure contains T-linear and T**4 ln T terms in the range of temperatures between 240 MeV and 420 MeV. The presence of the last term in the pressure bears almost no effect on the width estimates. Our analysis shows that at hight temperatures the average mass and width of the QGP bags behave in accordance with the upper bound of the Regge trajectory asymptotics (the linear asymptotics), whereas at low temperatures they obey the lower bound of the Regge trajectory asymptotics (the square root one). Since the model explicitly contains the Hagedorn mass spectrum, it allows us to remove an existing contradiction between the finite number of hadronic Regge families and the Hagedorn idea of the exponentially growing mass spectrum of hadronic bags.Comment: One section removed, a few references added, the Regge trajectories of free QGP bags are considere

Physical mechanism of the (tri)critical point generation

We discuss some ideas resulting from a phenomenological relation recently declared between the tension of string connecting the static quark-antiquark pair and surface tension of corresponding cylindrical bag. This relation analysis leads to the temperature of vanishing surface tension coefficient of the QGP bags at zero baryonic charge density as T_\sigma = 152.9 +- 4.5 MeV. We develop the view point that this temperature value is not a fortuitous coincidence with the temperature of (partial) chiral symmetry restoration as seen in the lattice QCD simulations. Besides, we argue that T_\sigma defines the QCD (tri)critical endpoint temperature and claim that a negative value of surface tension coefficient recently discovered is not a sole result, but should also exist in ordinary liquids at the supercritical temperatures.Comment: Talk given at the Conference "Critical Point and Onset of Deconfinement (CPOD)" that held on August 23 - 29, 2010, JINR, Dubna, Russia. Contains minimal change

Fresh look at the Hagedorn mass spectrum as seen in the experiments

The medium dependent finite width is introduced into an exactly solvable model with the general mass-volume spectrum of the QGP bags. The model allows us to estimate the minimal value of the QGP bags' width from the lattice QCD data. The large width of the QGP bags not only explains the observed deficit in the number of hadronic resonances comparing to the Hagedorn mass spectrum, but also clarifies the reason why the heavy QGP bags cannot be directly observed as metastable states in a hadronic phase.Comment: 6 pages, no figures, accepted to Europhys. Let

Asymptotic Regge Trajectories of Non-strange Mesons

We analyze the asymptotic behavior of Regge trajectories of non-strange mesons. In contrast to an existing belief, it is demonstrated that for the asymptotically linear Regge trajectories the width of heavy hadrons cannot linearly depend on their mass. Using the data on masses and widths of rho_J, omega_J, a_J and f_J mesons for the spin values J \leq 6, we extract the parameters of the asymptotically linear Regge trajectory predicted by the finite width model of quark gluon bags. As it is shown the obtained parameters for the data set B correspond to the cross-over temperature lying in the interval 170.9-175.3 MeV which is consistent with the kinetic freeze-out temperature of early hadronizing particles found in relativistic heavy ion collisions at and above the highest SPS energy.Comment: 14 pages, 3 figure

Charge separation relative to the reaction plane in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}= 2.76 TeV

Measurements of charge dependent azimuthal correlations with the ALICE detector at the LHC are reported for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV. Two- and three-particle charge-dependent azimuthal correlations in the pseudo-rapidity range $|\eta| < 0.8$ are presented as a function of the collision centrality, particle separation in pseudo-rapidity, and transverse momentum. A clear signal compatible with a charge-dependent separation relative to the reaction plane is observed, which shows little or no collision energy dependence when compared to measurements at RHIC energies. This provides a new insight for understanding the nature of the charge dependent azimuthal correlations observed at RHIC and LHC energies.Comment: 12 pages, 3 captioned figures, authors from page 2 to 6, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/286

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio