We represent the Polyakov loop correlator as a spectral sum of correlators of eigenvectors of the lattice Dirac operator. This spectral representation is studied numerically using quenched SU(3) configurations below and above the deconfinement temperature. We analyze whether the individual Dirac eigenvector correlators differ in the confined and deconfined phases. The decay properties of the normalized Dirac eigenvector correlators turn out to be essentially identical in the two phases, but the amplitudes change. This change of the amplitudes shifts the relative contributions of the individual Dirac eigenvector correlators and is the driving mechanism for the transition from the confining static potential into the deconfining one.
We consider the four point connected correlator representing a static quark-antiquark pair separated by a spatial distance R, propagating for a Euclidean time T. This function is computed by lattice Monte Carlo in SU(2) pure gauge theory at lattice couplings $β=2.2$ and $β=2.5$ in both Coulomb and Landau gauges. The Coulomb gauge correlator is well behaved, and is dominated at large T by a state whose energy grows linearly as $σR$, with $σ$ the known asymptotic string tension. The connected correlator in Landau gauge behaves differently. At intermediate R there is clear evidence of a linear po…
We study the correlators of Polyakov loops, and the corresponding gauge invariant free energy of a static quark-antiquark pair in 2+1 flavor QCD at finite temperature. Our simulations were carried out on $N_t$ = 6, 8, 10, 12, 16 lattices using a Symanzik improved gauge action and a stout improved staggered action with physical quark masses. The free energies calculated from the Polyakov loop correlators are extrapolated to the continuum limit. For the free energies we use a two step renormalization procedure that only uses data at finite temperature. We also measure correlators with definite E…
We discuss color screening in 2+1 flavor QCD in terms of free energies of a static quark-antiquark pair. Thermal modifications of long distance correlations in quark-antiquark systems are studied in terms of static meson correlators. We calculate the Polyakov loop correlator, the color-singlet Wilson line correlator in Coulomb gauge and the cyclic Wilson loop on lattices using the HISQ/Tree action and almost physical quark mases with $N_τ= 4, 6, 8, 10, 12$. We present results in the continuum limit for temperatures up to $T \lesssim 650$ MeV and discuss the linear divergence of the cyclic Wils…
We test a method for computing the static quark-antiquark potential in lattice QCD, which is not based on Wilson loops, but where the trial states are formed by eigenvector components of the covariant lattice Laplace operator. The runtime of this method is significantly smaller than the standard Wilson loop calculation, when computing the static potential not only for on-axis, but also for many off-axis quark-antiquark separations, i.e., when a fine spatial resolution is required. We further improve the signal by using multiple eigenvector pairs, weighted with Gaussian profile functions of the…
We study screening correlators of quark-antiquark composites at T=2T_c, where T_c is the QCD phase transition temperature, using overlap quarks in the quenched approximation of lattice QCD. As the lattice spacing is changed from 1/4T to a=1/6T and 1/8T, we find that screening correlators change little, in contrast with the situation for other types of lattice fermions. All correlators are close to the ideal gas prediction at small separations. The long distance falloff is clearly exponential, showing that a parametrization by a single screening length is possible at distances z > 1/T. The corr…
We study the correlators of Polyakov loops, and the corresponding gauge invariant free energy of a static quark-antiquark pair in 2+1 flavor QCD at finite temperature. Our simulations were carried out on $N_t$ = 6, 8, 10, 12, 16 lattices using Symanzik improved gauge action and a stout improved staggered action with physical quark masses. The free energies calculated from the Polyakov loop correlators are extrapolated to the continuum limit. For the free energies we use a two step renormalization procedure that only uses data at finite temperature. We also measure correlators with definite Euc…
We determine the mass of the lightest quark-antiquark scalar meson with I=1 using the simulation with two dynamical Domain Wall Fermions. The conventional exponential fit of the scalar correlator is justified in this case giving the mass 1.58 +/- 0.34 GeV. In general the scalar correlator receives also the bubble contribution, which is the intermediate state with two pseudoscalar mesons. This contribution is sizable at light quark masses and has to be incorporated in the fit of the scalar correlator in order to extract the scalar meson mass. We provide predictions for the bubble contribution i…
We present an NLO analysis of the massive vector current correlator at temperatures above a few hundred MeV. The physics of this correlator originates from a transport peak, related to heavy quark diffusion, and from the quark-antiquark threshold, related to quarkonium physics. In the bottom case both can be studied with separate effective theories, but for charm these may not be accurate, so a study within the full theory is needed. Working in imaginary time, the NLO correlator can be computed in unresummed perturbation theory; comparing with lattice data, we find good agreement. Subsequently…
We present a method for computing the static quark-antiquark potential, which is not based on Wilson loops, but where the trial states are formed by eigenvector components of the covariant lattice Laplace operator. We have tested this method in SU(2) Yang-Mills theory and have obtained results with statistical errors of similar magnitude compared to a standard Wilson loop computation. The runtime of the method is, however, significantly smaller, when computing the static potential not only for on-axis, but also for many off-axis quark-antiquark separations, i.e. when a fine spatial resolution …
We study field strength correlators in presence of a static quark-antiquark pair by use of lattice methods. The lattice data have been acquired recently in the context of a determination of relativistic corrections to the static interquark potential. We extract independent estimates of the form factors of two point correlation functions and investigate the effect of higher order correlators. Our results confirm the dominance of the two point correlators in the regions of intermediate and large quark separations, and are compatible with correlation length values obtained from different approach…
We present NLO results for thermal imaginary-time correlators in the vector and scalar channels as a function of the quark mass. The range of quark masses for which a non-relativistic approximation works in the temperature range considered is estimated, and charm quarks turn out to be a borderline case. Comparing with simulation data from fine lattices, we find good agreement in the vector channel but a substantial discrepancy in the scalar one. An explanation for the discrepancy is suggested in terms of physics of the quark-antiquark threshold region. Perturbative predictions for the bottom s…
The complete expression of the heavy quark-antiquark potential up to order $1/m^2$ is known from QCD in terms of Wilson loop expectation values. We use that expression and a mapping, assumed to be valid at large distances, between Wilson loop expectation values and correlators evaluated in the effective string theory, to compute the potential. We obtain previously unknown results for the spin and momentum-independent parts of the potential. These are linearly rising with the distance and may be interpreted as relativistic corrections to the string tension. We confirm known results for the othe…
Colorelectric and Colormagnetic structure of the flux tubes, connecting heavy quark and antiquark, is investigated in the framework of the Field Correlator method which describes all resulting fields in terms of correlators $D^E$ and $D^E_1$. The latter have been computed via gluelumps, which allows to predict the resulting distribution of color fields $\mathbf{E} (\mathbf{r}),$ and colormagnetic currents $\mathbf{k} (\mathbf{r})$ in the flux tubes. It is shown, that at large distances $r\gg λ\approx 0.2$ fm the whole structure of fields and relations between them is similar to that of the dua…
We have studied finite temperature complex static quark-antiquark potentials for 2+1 flavor QCD using highly improved staggered action with physical strange quark masses and light quark masses corresponding to a pion mass of 161 MeV. We calculated the potential using Wilson line correlators fixed in Coulomb gauge. For the extraction, we have used HTL motivated parametrization of the correlators. We found that the real part of the potential is screened above the crossover temperature and it's close to singlet free energies, whereas the imaginary part is increasing with both distance and tempera…
We have constructed the lowest few eigenvectors of the staggered Dirac operator on SU(3) gauge configurations, both quenched and dynamical. We use these modes to study the topological charge and to construct approximate hadronic correlators.
We examine the taste structure of eigenvectors of the staggered-fermion Dirac operator. We derive a set of conditions on the eigenvectors of modes with small eigenvalues (near-zero modes), such that staggered fermions reproduce the 't Hooft vertex in the continuum limit. We also show that, assuming these conditions, the correlators of flavor-singlet mesons are free of contributions singular in $1/m$, where $m$ is the quark mass. This conclusion holds also when a single flavor of sea quark is represented by the fourth root of the staggered-fermion determinant. We then test numerically, using th…
The spin-dependent corrections to the static inter-quark potential are phenomenologically relevant to describing the fine and hyperfine spin splitting of the heavy quarkonium spectra. We investigate these corrections, which are represented as the field strength correlators on the quark-antiquark source, in SU(3) lattice gauge theory. We use the Polyakov loop correlation function as the quark-antiquark source, and by employing the multi-level algorithm, we obtain remarkably clean signals for these corrections up to intermediate distances of around 0.6 fm. Our observation suggests several new fe…
The nature of resonances and excited states near decay thresholds is encoded in scattering amplitudes, which can be extracted from single-particle and multiparticle correlators in finite volumes. Lattice calculations have only recently reached the precision required for a reliable study of such correlators. The distillation method represents a significant improvement insofar as it simplifies quark contractions and allows one to easily extend the operator basis used to construct interpolators. We present preliminary results on charmonium bound states and resonances on the Nf=2+1 CLS ensembles. …
The relativistic corrections to the static potential, i.e. the O(1/m) correction, the O(1/m^2) spin-dependent and momentum-dependent corrections are investigated in SU(3) lattice gauge theory. These corrections are relevant ingredients of an effective field theory for heavy quarkonium called potential nonrelativistic QCD. Utilizing the multilevel algorithm for the field strength correlator on the quark-antiquark source, these corrections are determined at the distances ranged from 0.25 to 1.2 fm. A reasonable scaling behavior and long-range nonperturbative contributions are observed.
Field distributions generated by static quark-antiquark and QQQ sources are calculated analytically in the framework of Gaussian (bilocal) approximation of Field Correlator Method (FCM). Special attention is paid to the QQQ system and asymmetric configurations are also studied. In both quark-antiquark and QQQ cases the string consists mainly of longitudinal color electric field. Transverse color electric field contribution is shown to be less then 3%. Baryon string has an Y-like shape with a deep well at the string junction position. Field distributions for quark-diquark and for three quarks o…
We study quarkonium correlators and spectral functions at zero and finite temperature in QCD with only heavy quarks using potential models combined with perturbative QCD. First, we show that this approach can describe the quarkonium correlation function at zero temperature. Using a class of screened potentials based on lattice calculations of the static quark-antiquark free energy we calculate spectral functions at finite temperature. We find that all quarkonium states, with the exception of the $1S$ bottomonium, dissolve in the deconfined phase at temperatures smaller than $1.5T_c$, in contra…
The transverse profile of the chromoelectric field generated by a quark-antiquark pair in the SU(3) vacuum is analysed within the dual superconductor scenario, then the London penetration depth and coherence length are extracted. The color field is determined on the lattice through a connected correlator of two Polyakov loops measured on smeared configurations.
It appears well accepted in the literature that the correlator of Polyakov loops in a finite temperature system decays with the "average" free energy of the static quark-antiquark system, and can be decomposed into singlet and adjoint (or octet for QCD) contributions. By fixing a gauge respecting the transfer matrix, attempts have been made to extract those contributions separately. In this paper we point out that the "average" and "adjoint" channels of Polyakov loop correlators are misconceptions. We show analytically that all channels receive contributions from singlet states only, and give …
We study the interactions of a static quark antiquark pair at non-zero temperature using realistic 2+1 flavor lattice QCD calculations. The study consists of two parts: the first investigates the properties of Wilson line correlators in Coulomb gauge and compares to predictions of hard-thermal loop perturbation theory. As a second step we extract the spectral functions underlying the correlators using four conceptually different methods: spectral function fits, a HTL inspired fit for the correlation function, Padé rational approximation and the Bayesian BR spectral reconstruction. We find that…
We represent Polyakov loops and their correlators as spectral sums of eigenvalues and eigenmodes of the lattice Dirac operator. The deconfinement transition of pure gauge theory is characterized as a change in the response of moments of eigenvalues to varying the boundary conditions of the Dirac operator. We argue that the potential between static quarks is linked to spatial correlations of Dirac eigenvectors.
We study the spin splitting in the heavy quarkonium hybrid spectrum within the framework of an nonrelativistic effective field theory. We derive for the first time the spin-dependent part of the heavy-quark-antiquark potential for heavy quarkonium hybrids to order $1/m^2$ in the heavy-quark-mass expansion. We find that several operators that are not found in standard quarkonia appear, most remarkably an operator suppressed by only one power of the heavy-quark mass. By matching the weakly-coupled pNRQCD to the effective field theory in the regime of short heavy-quark-antiquark distances, we wor…
We study the flux tubes produced by static quark-antiquark, quark-quark and quark-gluon charges at finite temperature in pure gauge SU(3) lattice QCD. Our sources are static and our lattice correlators are composed of fundamental and adjoint Polyakov loops. To signal the flux tubes, we compute the square densities of the chromomagnetic and chromoelectric fields with plaquettes, in a gauge invariant framework. We study the existence and non-existence of flux tubes both above and below the deconfinement phase transition temperature Tc. Using the Lagrangian density as a probability distribution, …
Propagation of gluons in the confining vacuum is studied in the framework of the background perturbation theory, where nonperturbative background contains confining correlators. Two settings of the problem are considered. In the first the confined gluon is evolving in time together with static quark and antiquark forming the one-gluon static hybrid. The hybrid spectrum is calculated in terms of string tension and is in agreement with earlier analytic and lattice calculations. In the second setting the confined gluon is exchanged between quarks and the gluon Green's function is calculated, givi…
The spin-dependent operators for heavy quarkonium hybrids have been recently obtained in a nonrelativistic effective field theory approach up to next-to-leading order in the heavy-quark mass expansion. In the effective field theory for hybrids several operators not found in standard quarkonia appear, including an operator suppressed by only one power of the heavy-quark mass. We compute the matching coefficients for these operators in the short heavy-quark-antiquark distance regime, $r\ll 1/Λ_{\rm QCD}$, by matching weakly-coupled potential NRQCD to the effective field theory for hybrids. In th…
We investigate the implications of Nambu-Goto (NG), Lüscher-Weisz (LW) and Polyakov-Kleinert (PK) string actions for the Casimir energy of the QCD flux-tube at one and two loop order at finite temperature. We perform our numerical study on the 4-dim pure SU(3) Yang-Mills lattice gauge theory at finite temperature $β=6.0$. The static quark-antiquark potential is calculated using link-integrated Polyakov loop correlators. At a high temperature-close to the critical point- We find that the rigidity and self-interactions effects of the QCD string to become detectable. The remarkable feature of thi…
The concept of a screening mass is a powerful tool to simplify the intricate physics of in-medium test charges surrounded by light charge carriers. While it has been successfully used to describe electromagnetic properties, its definition and computation in QCD is plagued by questions of gauge invariance and the presence of non-perturbative contributions from the magnetic sector. Here we present a recent alternative definition of a gauge invariant Debye mass parameter following closely the original idea of Debye and Hueckel. Our test charges are a static heavy quark-antiquark pair whose comple…
