Light-cone Wilson loop in classical lattice gauge theory

The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity.Comment: 20 pages. v2: more elaboration on systematic errors; published versio

Thermal imaginary part of a real-time static potential from classical lattice gauge theory simulations

Recently, a finite-temperature real-time static potential has been introduced via a Schr\"odinger-type equation satisfied by a certain heavy quarkonium Green's function. Furthermore, it has been pointed out that it possesses an imaginary part, which induces a finite width for the tip of the quarkonium peak in the thermal dilepton production rate. The imaginary part originates from Landau-damping of low-frequency gauge fields, which are essentially classical due to their high occupation number. Here we show how the imaginary part can be measured with classical lattice gauge theory simulations, accounting non-perturbatively for the infrared sector of finite-temperature field theory. We demonstrate that a non-vanishing imaginary part indeed exists non-perturbatively; and that its value agrees semi-quantitatively with that predicted by Hard Loop resummed perturbation theory.Comment: 18 pages. v2: clarifications and a reference added; published versio

Mesonic screening masses at high temperature and finite density

We compute the first perturbative correction to the static correlation lengths of light quark bilinears in hot QCD with finite quark chemical potentials. The correction is small and positive, with mu-dependence depending on the relative sign of chemical potentials and the number of dynamical flavors. The computation is carried out using a three-dimensional effective theory for the lowest fermionic Matsubara mode. We also compute the full correlator in free theory and find a rather complicated general mu-dependence at shorter distances. Finally, rough comparisons with lattice simulations are discussed.Comment: 24 pages, 5 figures, JHEP style. Minor corrections and clarifications, version to appear in JHE

Four-loop pressure of massless O(N) scalar field theory

Inspired by the corresponding problem in QCD, we determine the pressure of massless O(N) scalar field theory up to order g^6 in the weak-coupling expansion, where g^2 denotes the quartic coupling constant. This necessitates the computation of all 4-loop vacuum graphs at a finite temperature: by making use of methods developed by Arnold and Zhai at 3-loop level, we demonstrate that this task is manageable at least if one restricts to computing the logarithmic terms analytically, while handling the ``constant'' 4-loop contributions numerically. We also inspect the numerical convergence of the weak-coupling expansion after the inclusion of the new terms. Finally, we point out that while the present computation introduces strategies that should be helpful for the full 4-loop computation on the QCD-side, it also highlights the need to develop novel computational techniques, in order to be able to complete this formidable task in a systematic fashion.Comment: 34 page

Intermediate distance correlators in hot Yang-Mills theory

Lattice measurements of spatial correlation functions of the operators FF and FF-dual in thermal SU(3) gauge theory have revealed a clear difference between the two channels at "intermediate" distances, x ~ 1/(pi T). This is at odds with the AdS/CFT limit which predicts the results to coincide. On the other hand, an OPE analysis at short distances (x << 1/(pi T)) as well as effective theory methods at long distances (x >> 1/(pi T)) suggest differences. Here we study the situation at intermediate distances by determining the time-averaged spatial correlators through a 2-loop computation. We do find unequal results, however the numerical disparity is small. Apart from theoretical issues, a future comparison of our results with time-averaged lattice measurements might also be of phenomenological interest in that understanding the convergence of the weak-coupling series at intermediate distances may bear on studies of the thermal broadening of heavy quarkonium resonances.Comment: 31 page

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

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

O(2) symmetry breaking vs. vortex loop percolation

We study with lattice Monte Carlo simulations the relation of global O(2) symmetry breaking in three dimensions to the properties of a geometrically defined vortex loop network. We find that different definitions of constructing a network lead to different results even in the thermodynamic limit, and that with typical definitions the percolation transition does not coincide with the thermodynamic phase transition. These results show that geometrically defined percolation observables need not display universal properties related to the critical behaviour of the system, and do not in general survive in the field theory limit.Comment: 14 pages; references added, version to appear in Phys.Lett.