Wilson Loop in Classical Lattice Gauge Theory and the Thermal Width of Heavy Quarkonium

We present an estimate for the imaginary part of the recently introduced finite temperature real-time static potential. It can be extracted from the time evolution of the Wilson loop in classical lattice gauge theory. The real-time static potential determines, through a Schroedinger-type equation and a subsequent Fourier-transform of its solution, the spectral function of heavy quarkonium in finite-temperature QCD. We also compare the results of the classical simulations with those of Hard Thermal Loop improved simulations, as well as with analytic expectations based on resummed perturbation theory.Comment: 7 pages, 3 figures, XXV International Symposium on Lattice Field Theor

The non-perturbative QCD Debye mass from a Wilson line operator

According to a proposal by Arnold and Yaffe, the non-perturbative g^2T-contribution to the Debye mass in the deconfined QCD plasma phase can be determined from a single Wilson line operator in the three-dimensional pure SU(3) gauge theory. We extend a previous SU(2) measurement of this quantity to the physical SU(3) case. We find a numerical coefficient which is more accurate and smaller than that obtained previously with another method, but still very large compared with the naive expectation: the correction is larger than the leading term up to T ~ 10^7 T_c, corresponding to g^2 ~ 0.4. At moderate temperatures T ~ 2 T_c, a consistent picture emerges where the Debye mass is m_D ~ 6T, the lightest gauge invariant screening mass in the system is ~ 3T, and the purely magnetic operators couple dominantly to a scale ~ 6T. Electric (~ gT) and magnetic (~ g^2T) scales are therefore strongly overlapping close to the phase transition, and the colour-electric fields play an essential role in the dynamics.Comment: 10 pages; typos corrected, to appear in Phys.Lett.

Lattice constraints on the thermal photon rate

We estimate the photon production rate from an SU(3) plasma at temperatures of about 1.1Tc and 1.3Tc. Lattice results for the vector current correlator at spatial momenta k ~ (2-6)T are extrapolated to the continuum limit and analyzed with the help of a polynomial interpolation for the corresponding spectral function, which vanishes at zero frequency and matches to high-precision perturbative results at large invariant masses. For small invariant masses the interpolation is compared with the NLO weak-coupling result, hydrodynamics, and a holographic model. At vanishing invariant mass we extract the photon rate which for k \gsim 3T is found to be close to the NLO weak-coupling prediction. For k \lsim 2T uncertainties remain large but the photon rate is likely to fall below the NLO prediction, in accordance with the onset of a strongly interacting behaviour characteristic of the hydrodynamic regime.Comment: 20 pages. v2: clarifications adde

A non-perturbative estimate of the heavy quark momentum diffusion coefficient

We estimate the momentum diffusion coefficient of a heavy quark within a pure SU(3) plasma at a temperature of about 1.5Tc. Large-scale Monte Carlo simulations on a series of lattices extending up to 192^3*48 permit us to carry out a continuum extrapolation of the so-called colour-electric imaginary-time correlator. The extrapolated correlator is analyzed with the help of theoretically motivated models for the corresponding spectral function. Evidence for a non-zero transport coefficient is found and, incorporating systematic uncertainties reflecting model assumptions, we obtain kappa = (1.8 - 3.4)T^3. This implies that the "drag coefficient", characterizing the time scale at which heavy quarks adjust to hydrodynamic flow, is (1.8 - 3.4) (Tc/T)^2 (M/1.5GeV) fm/c, where M is the heavy quark kinetic mass. The results apply to bottom and, with somewhat larger systematic uncertainties, to charm quarks.Comment: 18 pages. v2: clarifications adde

Critical point and scale setting in SU(3) plasma: An update

We explore a method developed in statistical physics which has been argued to have exponentially small finite-volume effects, in order to determine the critical temperature Tc of pure SU(3) gauge theory close to the continuum limit. The method allows us to estimate the critical coupling betac of the Wilson action for temporal extents up to Nt ~ 20 with < 0.1% uncertainties. Making use of the scale setting parameters r0 and sqrt{t0} in the same range of beta-values, these results lead to the independent continuum extrapolations Tc r0 = 0.7457(45) and Tc sqrt{t0} = 0.2489(14), with the latter originating from a more convincing fit. Inserting a conversion of r0 from literature (unfortunately with much larger errors) yields Tc / LambdaMSbar = 1.24(10).Comment: 12 pages. v2: clarifications and references added, published versio

Heavy Quark Interactions and Quarkonium Binding

We consider heavy quark interactions in quenched and unquenched lattice QCD. In a region just above the deconfinement point, non-Abelian gluon polarization leads to a strong increase in the binding. Comparing quark-antiquark and quark-quark interaction, the dependence of the binding on the separation distance $r$ is found to be the same for the colorless singlet $Q\bar Q$ and the colored anti-triplet $QQ$ state. In a potential model description of in-medium $J/\Psi$ behavior, this enhancement of the binding leads to a survival up to temperatures of 1.5 $T_c$ or higher; it could also result in $J/\Psi$ flow.Comment: 8 pages, 8 Figures; invited talk at "Strangeness in Quark Matter 2008", Beijing/China, to appear in the Proceeding

Heavy quark medium polarization at next-to-leading order

We compute the imaginary part of the heavy quark contribution to the photon polarization tensor, i.e. the quarkonium spectral function in the vector channel, at next-to-leading order in thermal QCD. Matching our result, which is valid sufficiently far away from the two-quark threshold, with a previously determined resummed expression, which is valid close to the threshold, we obtain a phenomenological estimate for the spectral function valid for all non-zero energies. In particular, the new expression allows to fix the overall normalization of the previous resummed one. Our result may be helpful for lattice reconstructions of the spectral function (near the continuum limit), which necessitate its high energy behaviour as input, and can in principle also be compared with the dilepton production rate measured in heavy ion collision experiments. In an appendix analogous results are given for the scalar channel.Comment: 43 pages. v2: a figure and other clarifications added, published versio

Towards the continuum limit in transport coefficient computations

The analytic continuation needed for the extraction of transport coefficients necessitates in principle a continuous function of the Euclidean time variable. We report on progress towards achieving the continuum limit for 2-point correlator measurements in thermal SU(3) gauge theory, with specific attention paid to scale setting. In particular, we improve upon the determination of the critical lattice coupling and the critical temperature of pure SU(3) gauge theory, estimating r0*Tc ~ 0.7470(7) after a continuum extrapolation. As an application the determination of the heavy quark momentum diffusion coefficient from a correlator of colour-electric fields attached to a Polyakov loop is discussed.Comment: 7 pages. To appear in the Proceedings of the 31st International Symposium on Lattice Field Theory, July 29 - August 3, 2013, Mainz, German

The spectrum of the three-dimensional adjoint Higgs model and hot SU(2) gauge theory

We compute the mass spectrum of the SU(2) adjoint Higgs model in 2+1 dimensions at several points located in the (metastable) confinement region of its phase diagram. We find a dense spectrum consisting of an almost unaltered repetition of the glueball spectrum of the pure gauge theory, and additional bound states of adjoint scalars. For the parameters chosen, the model represents the effective finite temperature theory for pure SU(2) gauge theory in four dimensions, obtained after perturbative dimensional reduction. Comparing with the spectrum of screening masses obtained in recent simulations of four-dimensional pure gauge theory at finite temperature, for the low lying states we find quantitative agreement between the full and the effective theory for temperatures as low as T = 2 Tc. This establishes the model under study as the correct effective theory, and dimensional reduction as a viable tool for the description of thermodynamic properties. We furthermore compare the perturbative contribution O(g.T) with the non-perturbative contributions O(g^2.T) and O(g^3.T) to the Debye mass. The latter turns out to be dominated by the scale g^2.T, whereas higher order contributions are small corrections.Comment: LaTeX. Typos corrected and references adde