Perturbative Thermodynamics of Lattice QCD with Chiral-Invariant Four-Fermion Interactions

Lattice QCD with additional chiral-invariant four-fermion interactions is studied at nonzero temperature. Staggered Kogut-Susskind quarks are used. The four-fermion interactions are implemented by introducing bosonic auxiliary fields. A mean field treatment of the auxiliary fields is used to calculate the model's asymptotic scale parameter and perturbative thermodynamics, including the one-loop gluonic contributions to the energy, entropy, and pressure. In this approach the calculations reduce to those of ordinary lattice QCD with massive quarks. Hence, the previous calculations of these quantities in lattice QCD using massless quarks are generalized to the massive case.Comment: 22 pages, RevTeX, 8 EPS figures, uses epsf.sty and feynmf.st

A Family of Equations of State Based on Lattice QCD: Impact on Flow in Ultrarelativistic Heavy-Ion Collisions

We construct a family of equations of state within a quasiparticle model by relating pressure, energy density, baryon density and susceptibilities adjusted to first-principles lattice QCD calculations. The relation between pressure and energy density from lattice QCD is surprisingly insensitive to details of the simulations. Effects from different lattice actions, quark masses and lattice spacings used in the simulations show up mostly in the quark-hadron phase transition region which we bridge over by a set of interpolations to a hadron resonance gas equation of state. Within our optimized quasiparticle model we then examine the equation of state along isentropic expansion trajectories at small net baryon densities, as relevant for experiments and hydrodynamic simulations at RHIC and LHC energies. We illustrate its impact on azimuthal flow anisotropies and transverse momentum spectra of various hadron species

A Note on Asymptotic Freedom at High Temperatures

This short note considers, within the external field approach outlined in hep-ph/0202026, the role of the lowest lying gluon Landau mode in QCD in the high temperature limit. Its influence on a temperature- and field-dependent running coupling constant is examined. The thermal imaginary part of the mode is temperature-independent in our approach and exactly cancels the well-known zero temperature imaginary part, thus rendering the Savvidy vacuum stable. Combining the real part of the mode with the contributions from the higher lying Landau modes and the vacuum contribution, a field-independent coupling alpha_s(T) is obtained. It can be interpreted as the ordinary zero temperature running coupling constant with average thermal momenta \approx 2pi T for gluons and \approx pi T for quarks.Comment: 4 pages; minor changes, version to appear in Phys. Rev.

Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical Potential

We present results of a simulation of 2-flavor QCD on a 4x16^3 lattice using p4-improved staggered fermions with bare quark mass m/T=0.4. Derivatives of the thermodynamic grand canonical partition function Z(V,T,mu_u,mu_d) with respect to chemical potentials mu_(u,d) for different quark flavors are calculated up to sixth order, enabling estimates of the pressure and the quark number density as well as the chiral condensate and various susceptibilities as functions of mu_q = (mu_u + mu_d)/2 via Taylor series expansion. Furthermore, we analyze baryon as well as isospin fluctuations and discuss the relation between the radius of convergence of the Taylor series and the chiral critical point in the QCD phase diagram. We argue that bulk thermodynamic observables do not, at present, provide direct evidence for the existence of a chiral critical point in the QCD phase diagram. Results are compared to high temperature perturbation theory as well as a hadron resonance gas model.Comment: 38 pages, 30 encapsulated postscript figures, typo corrected, 1 footnote adde

The beta function and equation of state for QCD with two flavors of quarks

We measure the pressure and energy density of two flavor QCD in a wide range of quark masses and temperatures. The pressure is obtained from an integral over the average plaquette or psi-bar-psi. We measure the QCD beta function, including the anomalous dimension of the quark mass, in new Monte Carlo simulations and from results in the literature. We use it to find the interaction measure, E-3p, yielding non-perturbative values for both the energy density E and the pressure p. uuencoded compressed PostScript file Revised version should work on more PostScript printers.Comment: 24 page

Transverse Pressure and Strangeness Dynamics in Relativistic Heavy Ion Reactions

Transverse hadron spectra from proton-proton, proton-nucleus and nucleus-nucleus collisions from 2 AGeV to 21.3 ATeV are investigated within two independent transport approaches (HSD and UrQMD). For central Au+Au (Pb+Pb) collisions at energies above $E_{\rm lab}\sim$ 5 AGeV, the measured $K^{\pm}$ transverse mass spectra have a larger inverse slope parameter than expected from the default calculations. The additional pressure - as suggested by lattice QCD calculations at finite quark chemical potential $\mu_q$ and temperature $T$ - might be generated by strong interactions in the early pre-hadronic/partonic phase of central Au+Au (Pb+Pb) collisions. This is supported by a non-monotonic energy dependence of $v_2/$ in the present transport model.Comment: Proceedings of Strange Quark Matter 200

An Experimental Overview of Results Presented at SQM 2006

I have been asked to give an critical overview on the experimental results shown in the conference with a emphasis of what has been learned and the challenges that are ahead in trying to understand the physics of the strongly interacting quark-gluon plasma. I will not try to summarize all of the results presented, rather I will concentrate primarily on RHIC data from this conference. Throughout this summary, I will periodically review some of the previous results for those not familiar with the present state of the field.Comment: 15 pages, 12 Figure

The QCD equation of state for two flavours at non-zero chemical potential

We present results of a simulation of 2 flavour QCD on a $16^3\times4$ lattice using p4-improved staggered fermions with bare quark mass $m/T=0.4$. Derivatives of the thermodynamic grand canonical partition function $Z(V,T,\mu_u,\mu_d)$ with respect to chemical potentials $\mu_{u,d}$ for different quark flavours are calculated up to sixth order, enabling estimates of the pressure and the quark number density as well as the chiral condensate and various susceptibilities as functions of $\mu_{u,d}$ via Taylor series expansion. Results are compared to high temperature perturbation theory as well as a hadron resonance gas model. We also analyze baryon as well as isospin fluctuations and discuss the relation to the chiral critical point in the QCD phase diagram. We moreover discuss the dependence of the heavy quark free energy on the chemical potential.Comment: 4 pages, 7 figures, talk presented at Quark Matter 2005, Budapes

News from Lattice QCD on Heavy Quark Potentials and Spectral Functions of Heavy Quark States

We discuss recent lattice results on in-medium properties of hadrons and focus on thermal properties of heavy quark bound states. We will clarify the relation between heavy quark free energies and potentials used to analyze the melting of heavy quark bound states. Furthermore, we present calculations of meson spectral functions which indicate that the charmonium ground states, J/psi and eta_c, persist in the quark gluon plasma as well defined resonances with no significant change of their zero temperature masses at least up to T ~ 1.5 T_c. We also briefly comment on the current status of lattice calculations at non-vanishing baryon number density.Comment: Plenary talk at the 17th International Conference on Ultra Relativistic Nucleus-Nucleus Collisions (Quark Matter 2004), Oakland, California, 11-17 Jan 2004. Submitted to J.Phys.

Lattice calculations of meson correlators and spectral functions at finite temperature

I review recent progress in relating meson spectral function to imaginary time correlation function at finite temperature calculated on isotropic as well as on anisotropic lattices. Special attention is payed for the lattice artifacts present in calculation of meson spectral functions. Results in the case of light quarks as well as heavy quarks are reviewed which indicate in particular that even in the chiral limit meson spectral functions have non-trivial structure and the ground state quarkonia survive up to temperature 1.5T_cComment: Invited plenary talk presented at SQM03 (Atlantic Beach, March 12-17, 2003), 10 pages LaTeX, uses iopams.sty, iopart.cl