Quark Mass and Flavour Dependence of the QCD Phase Transition

We analyze the quark mass and flavour dependence of the QCD phase transition temperature. When the lightest pseudo-scalar meson mass (m_PS) is larger than 2 GeV the critical temperature is controlled by the gluonic sector of QCD alone. For smaller values of the lightest meson mass the pseudo-critical temperature decreases slowly with m_PS. For a large regime of meson masses the pseudo-critical temperature of 2-flavour QCD is about 10% larger than in the 3-flavour case. On lattices with temporal extent N_t=4 an extrapolation to the chiral limit yields T_c = 173(8) MeV and 154(8) MeV for 2 and 3-flavour QCD, respectively. We also analyze dynamical quark mass effects on the screening of the heavy quark potential. A detailed analysis of the heavy quark free energy in 3-flavour QCD shows that close to T_c screening effects are approximately quark mass independent already for pseudo-scalar meson masses m_PS = 800 MeV and screening sets in at distances r = 0.3 fm.Comment: 25 pages, LaTeX2e File, 11 EPS-file

Group projection method in statistical systems

We discuss an application of group theoretical methods to the formulation of the thermodynamics of systems constrained by the conservation laws described by a semi--simple compact Lie group. A general projection method that allows to construct a partition function for a given irreducible representation of the Lie group is outlined. Applications of the method in Lattice Gauge Theory (LGT) for non--zero baryon number and in the phenomenological description of particle production in ultrarelativistic heavy ion collisions are also indicated.Comment: Invited talk presented at the XXIV International Colloquium on Group Theoritical Methods in Physic

Magnetic Screening in Hot Non-Abelian Gauge Theory

We analyze the large distance and low-momentum behavior of the magnetic gluon propagator of the SU(2) gauge theory at finite temperature. Lattice calculations within the 4-dimensional as well as the effective, dimensionally reduced 3-dimensional gauge theories in generalized Landau gauges and MAG show that the magnetic propagator is strongly infrared suppressed in Landau gauges but stays large and finite in MAG. Despite these differences in the low-momentum behavior of the propagator calculated in different gauges the magnetic fields are exponentially screened in all gauges considered. From the propagator calculated in maximally Abelian gauge we find for the screening mass, m_M = (1.48 +/- 0.17) T at T=2 T_c.Comment: 11 pages, LaTeX2e, new data added, conclusions unchanged. The final version to appear in Phys. Lett.

Heavy ion collisions and lattice QCD at finite baryon density

We discuss a relation between the QCD thermodynamics obtained from a statistical analysis of particle production in heavy ion collisions at SPS and RHIC energies and recent LGT results at finite chemical potential. We show that basic thermodynamic properties obtained from the phenomenological statistical operator of a hadron resonance gas that describes particle yields in heavy ion collisions are consistent with recent LGT results. We argue that for $T\leq T_c$ the equation of state derived from Monte--Carlo simulations of two quark--flavor QCD at finite chemical potential can be well described by a hadron resonance gas when using the same set of approximations as used in LGT calculations. We examine the influence of a finite quark mass on the position of the deconfinement transition in temperature and chemical potential plane.Comment: To appear in the proceedings of 17in International Conference on Ultra Relativistic Nucleus-Nucleus Collisions (Quark Matter 2004), Oakland, California, 11-17 Jan 200

Flavor and Quark Mass Dependence of QCD Thermodynamics

We calculate the transition temperature in 2 and 3-flavor QCD using improved gauge and staggered fermion actions on lattices with temporal extent Nt=4. We find Tc=173(8)MeV and 154(8)MeV for nf=2 and 3, respectively. In the case of 3-flavor QCD we present evidence that the chiral critical point, i.e. the second order endpoint of the line of first order chiral phase transitions, belongs to the universality class of the 3d Ising model.Comment: Talk given at Lattice 2000 (Finite Temperature), 4 pages, 6 EPS-figure

The QCD phase diagram: A comparison of lattice and hadron resonance gas model calculations

We compare the lattice results on QCD phase diagram for two and three flavors with the hadron resonance gas model (HRGM) calculations. Lines of constant energy density $\epsilon$ have been determined at different baryo-chemical potentials $\mu_B$. For the strangeness chemical potentials $\mu_S$, we use two models. In one model, we explicitly set $\mu_S=0$ for all temperatures and baryo-chemical potentials. This assignment is used in lattice calculations. In the other model, $\mu_S$ is calculated in dependence on $T$ and $\mu_B$ according to the condition of vanishing strangeness. We also derive an analytical expression for the dependence of $T_c$ on $\mu_B/T$ by applying Taylor expansion of $\epsilon$. In both cases, we compare HRGM results on $T_c-\mu_B$ diagram with the lattice calculations. The agreement is excellent, especially when the trigonometric function of $\epsilon$ is truncated up to the same order as done in lattice simulations. For studying the efficiency of the truncated Taylor expansion, we calculate the radius of convergence. For zero- and second-order radii, the agreement with lattice is convincing. Furthermore, we make predictions for QCD phase diagram for non-truncated expressions and physical masses. These predictions are to be confirmed by heavy-ion experiments and future lattice calculations with very small lattice spacing and physical quark masses.Comment: 25 pages, 8 eps figure

Hadron resonance gas and nonperturbative QCD vacuum at finite temperature

We study the nonperturbative QCD vacuum with two light quarks at finite temperature in the framework of hadron resonance gas. Temperature dependence of the quark and gluon condensates in the confined phase are obtained. We demonstrate that the quark condensate and one half (chromo-electric component) of gluon condensate evaporate at the same temperature, which corresponds to the temperature of quark-hadron phase transition. Critical temperature is T_c~190 MeV when temperature shift of hadron masses is taken into account.Comment: 8 pages, 4 figures; to appear in JETP Lett.; v2: references adde

Charge fluctuations in chiral models and the QCD phase transition

We consider the Polyakov loop-extended two flavor chiral quark--meson model and discuss critical phenomena related with the spontaneous breaking of the chiral symmetry. The model is explored beyond the mean-field approximation in the framework of the functional renormalisation group. We discuss properties of the net-quark number density fluctuations as well as their higher cumulants. We show that with the increasing net-quark number density, the higher order cumulants exhibit a strong sensitivity to the chiral crossover transition. We discuss their role as probes of the chiral phase transition in heavy-ion collisions at RHIC and LHC.Comment: 4 pages, 3 figures, to appear in the proceedings of Quark Matter 2011, 23-28 May 2011, Annecy, Franc

Baryon-strangeness correlations: a diagnostic of strongly interacting matter

The correlation between baryon number and strangeness elucidates the nature of strongly interacting matter, such as that formed transiently in high-energy nuclear collisions. This diagnostic can be extracted theoretically from lattice QCD calculations and experimentally from event-by-event fluctuations. The analysis of present lattice results above the critical temperature severely limits the presence of q-qbar bound states, thus supporting a picture of independent (quasi)quarks.Comment: 4 pages, 2 eps figures, Revised: several sign typos have been fixed (the PRL version is correct