Static Quark-antiquark Pair Research Articles

Vacuum structure around quark systems

The vacuum structure of QCD with dynamical fermions around a static quark-antiquark pair is explored by calculating the correlation functions < L( r 1) L †( r 2) O( r)> between a static meson and several characteristic observables for which we choose the chiral condensate, the charge density, and the energy density. We find a restoration of chiral symmetry around static color sources as a consequence of gluon string creation and a screening of static quarks by virtual antiquarks in analogy to QED. Our computations explicitly exhibit the formation of a chromoelectric flux tube and its breaking in the presence of dynamical quarks.

Quenched approximation in the quark model.

We present a model calculation of some effects of virtual {ital q{bar q}} pairs in mesons. Specifically, using a model for pair creation that has previously been shown to give a good description of strong meson decays, we calculate the energy shift of a static quark-antiquark pair due to the presence of virtual quark-antiquark pairs. The shift is large and approximately proportional to the distance between the static sources. The linearity of the correction suggests that pair-creation effects can be absorbed into a renormalization of the mesonic string tension. However, this masking can only be approximate, as we show by considering the dependence of the energy shift on the spin state of the sources. We conclude by pointing out the relevance of our results to the {ital N}/{rho}'' problem encountered in lattice QCD calculations.

A finite size analysis of the heavy quark potential in a deconfining medium

From lattice studies of Polyakov loop correlations, we determine the potential for a static quark-antiquark pair in a thermal SU(2) gauge field system above the deconfinement temperature. We perform a high statistics, finite size analysis of the heavy quark potential. We investigate the functional form of the potential at intermediate distances and compare it to continuum perturbation theory predictions.

Monte Carlo evidence for the gluon-chain model of QCD string formation

The Monte Carlo method is used to calculate the overlaps 〈 Ψ string| n gluons〉, where Ψ string[ A] is the Yang-Mills wave functional due to a static quark-antiquark pair, and | n gluons〉 are orthogonal trial states containing n = 0, 1, or 2 gluon operators multiplying the true ground state. The calculation is carried out for SU(2) lattice gauge theory in Coulomb gauge, in D = 4 dimensions. It is found that the string state is dominated, at small q q separations, by the vacuum (“no-gluon”) state, at larger separations by the one-gluon state, and, at the largest separations attempted, the two-gluon state begins to dominate. This behavior is in qualitative agreement with the gluon-chain model, which is a large- N colors motivated theory of QCD string formation.

QCD potentials with dynamical quarks at finite temperatures

We investigate the potential between a static quark-antiquark pair in the full QCD vacuum. The dynamical quark sea is considered both by Kogut-Susskind and Wilson fermions. Two temperatures T below and above the phase transition T c are studied. The behavior of the interquark potential in the full quantum field is driven by the explicitly broken Z 3 symmetry in the fermionic action for T< T c and by an additional spontaneous Z 3 symmetry breaking for T< T c .

Chromoflux distribution in lattice QCD

We study the chromoflux distribution in the presence of a static quark-antiquark pair by using a novel operator for the chromoelectric energy density and variationally improved wave functions. An extrapolition of the data to large time separations of the correlation functions is shown to be essential for obtaining meaningful results. By performing this extrapolation, we obtain the first reliable informations about the structure of the “confinement string”. It turns out to be surprisingly thick for quark-antiquark separations where the potential is dominated by the linear piece. In addition, the agreement of our chromoelectric field strength operator with the conventional plaquette operator provides further evidence for the onset of scaling at β = 5.8.

Non-Abelian Debye screening. II. The singlet potential.

The problems encountered in an earlier attempt to compute the non-Abelian Debye screening mass are rectified by considering the correlation of the eigenvalues of the untraced Polyakov loop. This gauge-invariant function is free from color averaging and is shown to yield the singlet potential of a static quark-antiquark pair at finite temperature. A perturbative computation requires that the electrostatic potential ${A}_{4}$ be endowed with a gauge-symmetry-breaking vacuum expectation value, the occurrence of which would explain the breakdown of perturbation theory encountered in the earlier calculation. While the symmetry breakdown cannot reliably be seen perturbatively, its effects on perturbative calculations can be assessed. It is found that most perturbative results, even the supposedly well-established low-order ones, would be affected. This would take the study of the quark-gluon plasma well out of the reach of perturbation theory and make nonperturbative techniques indispensable even at very high temperatures.

Non-Abelian Debye screening: The color-averaged potential.

The non-Abelian analogue of the Debye screening effect is investigated by means of perturbative calculations in high-temperature Yang-Mills theory. It is recalled that the gluon vacuum-polarization tensor, which is gauge dependent, does not directly yield the Debye screening mass beyond leading order. Instead, the correlation function of two Polyakov loops, representing the color-averaged potential energy of a static quark-antiquark pair, is examined as a possible means of defining a gauge-invariant Debye mass. Though apparently satisfactory to leading order, an examination of higher orders reveals two problems: (i) an unexpected breakdown of perturbation theory in the electrostatic sector and (ii) the emergence of the magnetostatic mass gap as the dominant decay mass of this correlation. These results might be the signal for a breakdown of gauge symmetry in the plasma phase and indicate the need for examining a gauge-invariant electrostatic correlation function that is free from color averaging.

Renormalization group β-function from gluon thermodynamics

The renormalization group β-function of lattice quantum chromodynamics (QCD) with Wilson's action is calculated from gluon thermodynamics. The critical temperature of the deconfining phase transition and the free energy of a static quark-antiquark pair at finite temperature are investigated and used for the determination of the β-function. For lattice couplings 6/ g 2 < 6.10 the β-function dramatically differs from the perturbation theory prediction. Gluon thermodynamics appears to be strictly non-perturbative in this regime. For weaker couplings the β-function gradually begins to approach its two-loop value.

The static potential in quantum chromodynamics

The effective interaction between a static quark-antiquark pair is computed within the framework of 〈 G μv a G a μv 〉 ≠ 0. Due to the static approximation the interaction takes the form of a potential, which is in striking agreement with phenomenological potentials.

How thick are chromo-electric flux tubes?

Abstract We analyse the space dependence of the expectation value of the chromo-electric energy density in the presence of a static quark-antiquark pair by means of the strong coupling expansion on a lattice and by the relativistic string model. Both methods indicate that the transversal width of the field energy distribution increases without bound, when the quark-antiquark separation goes to infinity.

A multipole expansion and the Casimir-Polder effect in quantum chromodynamics

A multipole expansion for correlation functions in quantum chromodynamics in the presence of a static quark-antiquark pair is described. We discover a retardation effect, analogous to the Casimir-Polder effect in atomic physics, which is proven to persist to all finite orders of perturbation theory. The correlation functions studied may be used to gain some insight into the total rates for decays of the form ( Q Q ) n′l′ → ( Q Q ) nl + hadrons among states of a heavy quark Q. We also derive the Casimir-Polder potential between heavy mesons.

A non-perturbative, semi-classical approach to the calculation of the quark force

A non-perturbative, semi-classical method for the calculation of the effective potential between heavy quarks is here proposed. The technique we present is a minimal extension of the classical Yang-Mills equations to operator equations in the space of isospin states of a static quark-antiquark pair. We obtain a set of non-linear partial differential equations which, when expanded in perturbation theory and improved by the renormalization group, reproduce to within 1% accuracy the order α 3 QCD result for the potential.