We present a detailed calculation of the transition temperature in QCD with two light and one heavier (strange) quark mass on lattices with temporal extent Nτ = 4 and 6. Calculations with improved staggered fermions have been performed for various light to strange quark mass ratios in the range, 0.05 ≤m l /ms ≤ 0.5, and with a strange quark mass fixed close to its physical value. From a combined extrapolation to the chiral (m l → 0) and continuum (aT ≡ 1/Nτ → 0) limits we find for the transition temperature at the physical point Tcr0 = 0.457(7) where the scale is set by the Sommer-scale parameter r0 defined as the distance in the static quark potential at which the slope takes on the value, (dVqq(r)/dr) r=r 0 = 1.65/r 2 0 . Using the currently best known value for r0 this translates to a transition temperature Tc = 192(7)(4) MeV. The transition temperature in the chiral limit is about 3% smaller. We discuss current ambiguities in the determination of Tc in physical units and also comment on the universal scaling behavior of thermodynamic quantities in the chiral limit.

We present results on the equation of state in QCD with two light quark flavors and a heavier strange quark. Calculations with improved staggered fermions have been performed on lattices with temporal extent Nτ = 4 and 6 on a line of constant physics with almost physical quark mass values; the pion mass is about 220 MeV, and the strange quark mass is adjusted to its physical value. High statistics results on large lattices are obtained for bulk thermodynamic observables, i.e. pressure, energy and entropy density, at vanishing quark chemical potential for a wide range of temperatures, 140 MeV ≤ T ≤ 800 MeV. We present a detailed discussion of finite cut-off effects which become particularly significant for temperatures larger than about twice the transition temperature. At these high temperatures we also performed calculations of the trace anomaly on lattices with temporal extent Nτ = 8. Furthermore, we have performed an extensive analysis of zero temperature observables including the light and strange quark condensates and the static quark potential at zero temperature. These are used to set the temperature scale for thermodynamic observables and to calculate renormalized observables that are sensitive to deconfinement and chiral symmetry restoration and become order parameters in the infinite and zero quark mass limits, respectively.

We study charmonium correlators in pseudoscalar and vector channels at finite temperature using lattice QCD simulation in the quenched approximation. Anisotropic lattices are used in order to have sufficient numbers of degrees of freedom in the Euclidean temporal direction. We focus on the low energy structure of the spectral function, corresponding to the ground state in the hadron phase, by applying the smearing technique to enhance the contribution to the correlator from this region. We employ two analysis procedures: the maximum entropy method (MEM) for the extraction of the spectral function without assuming a specific form, to estimate the shape of the spectral function, and the standard χ 2 fit analysis using typical forms in accordance with the result of MEM, for a more quantitative evaluation. To verify the applicability of the procedures, we first analyze the smeared correlators as well as the point correlators at zero temperature. We find that by shortening the t-interval used for the analysis (a situation inevitable at T > 0) the reliability of MEM for point correlators is lost, while it subsists for smeared correlators. Then the smeared correlators at T ≃ 0.9Tc and 1.1Tc are analyzed. At T ≃ 0.9Tc, the spectral function exhibits a strong peak, well approximated by a delta function corresponding to the ground state with almost the same mass as at T = 0. At T ≃ 1.1Tc, we find that the strong peak structure still persists at almost the same place as below Tc, but with a finite width of a few hundred MeV. This result indicates that the correlators possess a nontrivial structure even in the deconfined phase.

We discuss a constant contribution to meson correlators at finite temperature. In the deconfinement phase of QCD, a colored single quark state is allowed as a finite energy state, which yields to a contribution of wraparound quark propagation to temporal meson correlators. We investigate the effects in the free quark case and quenched QCD at finite temperature. The ``scattering'' contribution causes a constant mode in meson correlators with zero spatial momentum and degenerate quark masses, which can dominate the correlators in the region of large imaginary times. In the free spectral function, the contribution yields a term proportional to $\omega\delta(\omega)$. Therefore this contribution is related to transport phenomena in the quark gluon plasma. It is possible to distinguish the constant contribution from the other part using several analysis methods proposed in this paper. As a result of the analyses, we find that drastic changes in charmonium correlators for $\chi_c$ states just above the deconfinement transition are due to the constant contribution. The other differences in the $\chi_c$ states are small. It may indicate the survival of $\chi_c$ states after the deconfinement transition until, at least, $1.4T_c$.Comment: 11pages, 18figures, published versio

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