Static Quark-antiquark Pair Research Articles

Velocity dependence of baryon screening in a hot strongly coupled plasma

The L-dependence of the static potential between Nc quarks arranged in a circle of radius L (a baryon) immersed in the hot plasma of a gauge theory with Nc colors defines a screening length Ls. We use the AdS/CFT correspondence to compute this screening length for the case of heavy quarks in the plasma of strongly coupled N=4 super Yang-Mills theory moving with velocity v relative to the baryon. We find that in the v -> 1 limit, Ls \propto (1-v^2)^{1/4}/T, and find that corrections to this velocity dependence are small at lower velocities. This result provides evidence for the robustness of the analogous behavior of the screening length defined by the static quark-antiquark pair, which has been computed previously and in QCD is relevant to quarkonium physics in heavy ion collisions. Our results also show that as long as the hot wind is not blowing precisely perpendicular to the plane of the baryon configuration that we analyze, the Nc different quarks are not all affected by the wind velocity to the same degree, with those quarks lying perpendicular to the wind direction screened most effectively.

Color Screening Melts Quarkonium

We calculate quarkonium spectral functions in a quark-gluon plasma using a potential model based on full QCD lattice calculations of the free energy of a static quark-antiquark pair. We estimate the binding energy and the thermal width of different quarkonium states. The estimated upper limit for the dissociation temperatures is considerably lower than the ones suggested in the recent literature.

Heavy quark thermodynamics in full QCD

We analyse the large-distance behaviour of static quark–anti-quark pair correlations in QCD. The singlet free energy is calculated and the entropy contribution to it is identified allowing us to calculate the excess internal energy. The free energy has a sharp drop in the critical region, leading to sharp peaks in both excess entropy and internal energy.

A heavy quark–antiquark pair in hot QCD

Thermodynamics of a heavy quark–antiquark pair in SU ( 3 ) -QCD is studied both below and above the deconfinement critical temperature T c . In the quenched case, a model of the string passing through heavy valence gluons yields a correct estimate of T c and the critical behavior of the string tension below T c . For two light flavors, entropy and internal energy below T c can be obtained from the partition function of heavy–light mesons and baryons. To calculate the free energy of the system above T c , we apply second-order perturbation theory in the interaction of the quark–gluon plasma constituents with the static quark–antiquark pair. The results for the entropy and internal energy, obtained both below and above T c , are compared with recent lattice data.

Color screening and quark-quark interactions in finite temperature QCD

We analyze the screening of static diquark sources in 2-flavor QCD and compare results with the screening of static quark-antiquark pairs. We show that a two quark system in a fixed color representations is screened at short distances like a single quark source in the same color representation whereas at large distances the two quarks are screened independently. At high temperatures we observe that the relative strength of the interaction in diquark and quark-antiquark systems, respectively, obeys Casimir scaling. We use this result to examine the possible existence of heavy quark-quark bound states in the high temperature phase of QCD. We find support for the existence of $bb$ states up to about $2T_c$ while $cc$ states are unlikely to be formed above $T_c$.

Stability of strings dual to flux tubes between static quarks in [formula omitted] SYM

Computing heavy quark–antiquark potentials within the AdS/CFT correspondence often leads to behaviors that differ from what one expects on general physical grounds and field-theory considerations. To isolate the configurations of physical interest, it is of utmost importance to examine the stability of the string solutions dual to the flux tubes between the quark and antiquark. Here, we formulate and prove several general statements concerning the perturbative stability of such string solutions, relevant for static quark–antiquark pairs in a general class of backgrounds, and we apply the results to N = 4 SYM at finite temperature and at generic points of the Coulomb branch. In all cases, the problematic regions are found to be unstable and hence physically irrelevant.

Dynamics of flux tubes in largeNgauge theories

The gluonic field created by a static quark anti-quark pair is described via the AdS/CFT correspondence by a string connecting the pair which is located on the boundary of AdS. Thus the gluonic field in a strongly coupled large N CFT has a stringy spectrum of excitations. We trace the stability of these excitations to a combination of large N suppressions and energy conservation. Comparison of the physics of the N=infinity flux tube in the {\cal N}=4 SYM theory at weak and strong coupling shows that the excitations are present only above a certain critical coupling. The density of states of a highly excited string with a fold reaching towards the horizon of AdS is in exact agreement at strong coupling with that of the near-threshold states found in a ladder diagram model of the weak-strong coupling transition. We also study large distance correlations of local operators with a Wilson loop, and show that the fall off at weak coupling and N=infinity (i.e. strictly planar diagrams) matches the strong coupling predictions given by the AdS/CFT correspondence, rather than those of a weakly coupled U(1) gauge theory.

EXPLORING THE SPECTRUM OF QCD USING A SPACE-TIME LATTICE

Some past and ongoing explorations of the spectrum of QCD using Monte Carlo simulations on a space-time lattice are described. Glueball masses in the pure-gauge theory are reviewed, and the energies of gluonic excitations in the presence of a static quark-antiquark pair are discussed. Current efforts to compute the baryon spectrum using extended three-quark operators are also presented, emphasizing the need to use irreducible representations of the cubic point group to identify spin quantum numbers in the continuum limit.

Screening of heavy quark free energies at finite temperatureand non-zero baryon chemical potential

We analyze the dependence of heavy quark free energies on the baryon chemical potential (mu_b) in 2-flavour QCD using improved (p4) staggered fermions with a bare quark mass of m/T = 0.4. By performing a 6th order Taylor expansion in the chemical potential which circumvents the sign problem. The Taylor expansion coefficients of colour singlet and colour averaged free energies are calculated and from this the expansion coefficients for the corresponding screening masses are determined. We find that for small mu_b the free energies of a static quark anti-quark pair decrease in a medium with a net excess of quarks and that screening is well described by a screening mass which increases with increasing mu_b. The mu_b-dependent corrections to the screening masses are well described by perturbation theory for T > 2 T_c. In particular, we find for all temperatures above T_c that the expansion coefficients for singlet and colour averaged screening masses differ by a factor 2.

Vacuum type of SU(2) gluodynamics in maximally Abelian and Landau gauges

The vacuum type of SU(2) gluodynamics is studied using Monte-Carlo simulations in maximally Abelian (MA) gauge and in Landau (LA) gauge, where the dual Meissner effect is observed to work. The dual Meissner effect is characterized by the coherence and the penetration lengths. Correlations between Wilson loops and electric fields are evaluated in order to measure the penetration length in both gauges. The coherence length is shown to be fixed in the MA gauge from measurements of the monopole density around the static quark-antiquark pair. It is also shown numerically that a dimension 2 gluon operator A^+A^-(s) and the monopole density has a strong correlation as suggested theoretically. Such a correlation is observed also between the monopole density and A^2(s)= A^+A^-(s) + A^3A^3(s) condensate if the remaining U(1) gauge degree of freedom is fixed to U(1) Landau gauge (U1LA). The coherence length is determined numerically also from correlations between Wilson loops and A^+A^-(s) and A^2(s) in MA + U1LA gauge. Assuming that the same physics works in the LA gauge, we determine the coherence length from correlations between Wilson loops and A^2(s). Penetration lengths and coherence lengths in the two gauges are almost the same. The vacuum type of the confinement phase in both gauges is near to the border between the type 1 and the type 2 dual superconductors.

Static potential and local color fields in unquenched latticeQCD3

String breaking by dynamical quarks in three-dimensional lattice QCD is analyzed through measurements of the potential and the local color-electric field strength generated by a static quark-antiquark pair. Simulations were done for unquenched SU(2) color with two flavors of staggered light quarks. An improved gluon action was used, which allows simulations to be done on coarse lattices, providing an extremely efficient means to access the large quark separations and long propagation times at which string breaking occurs. The static sources were generated using Wilson loop operators, hence no light valence quarks are present in the resulting trial states. Results give unambiguous evidence of string breaking. First the static potential is shown to saturate at twice the heavy-light meson mass at large separations. Then it is demonstrated that the local color-electric field strength in the region between the heavy quarks tends towards vacuum values at large separations, the first time that this most graphic effect of quark vacuum polarization on the confining flux-tube has been realized in lattice QCD. Implications of these results for unquenched simulations of four-dimensional QCD are drawn.

Observation of modified hadronization in relativistic Au+Au collisions: a promising signature for deconfined quark–gluon matter

Measurements of identified particles from Au+Au collisions at are reviewed. Emphasis is placed on nuclear modification, baryon-to-meson ratios, and elliptic flow at intermediate transverse momentum (1.5 < pT < 5 GeV/c). Possible connections between (1) these measurements, (2) the running coupling for static quark–anti-quark pairs at finite temperature, and (3) the creation of a deconfined quark–gluon phase are presented. Modifications to hadronization in Au+Au collisions are proposed as a likely signature for the creation of deconfined coloured matter.

Effective string excitation energies

In the presence of a static quark–antiquark pair, the spectrum of the low-lying states in SU( N ) gauge theories is discrete and likely to be described, at large quark separations r , by an effective string theory. The expansion of the excitation energies in powers of 1/ r , which derives from the latter, involves an increasing number of unknown couplings that characterize the string self-interactions. Using open–closed string duality, we show that the possible values of the couplings are constrained by a set of algebraic relations. In particular, the corrections of order 1/ r 2 must vanish, while the 1/ r 3 terms (which we work out for the few lowest levels) depend on a single adjustable coupling only.

Static quark-antiquark free energy and the running coupling at finite temperature

We analyze the free energy of a static quark-antiquark pair in quenched QCD at short and large distances. From this we deduce running couplings, ${g}^{2}$ ($r$, $T$), and determine the length scale that separates at high temperature the short distance perturbative regime from the large distance nonperturbative regime in the QCD plasma phase. Ambiguities in the definition of a coupling beyond the perturbative regime are discussed in their relation to phenomenological considerations on heavy quark bound states in the quark gluon plasma. Our analysis suggests that it is more appropriate to characterize the nonperturbative properties of the QCD plasma phase close to ${T}_{c}$ in terms remnants of the confinement part of the QCD force rather than a strong Coulombic force.

Free energy of a static quark-antiquark pair and the renormalized Polyakov loop in three flavor QCD

We study the free energy of a static quark-antiquark ($Q\overline{Q}$) pair at finite temperature in three flavor QCD with degenerate quark masses using ${N}_{\ensuremath{\tau}}=4$ and $6$ lattices with Asqtad staggered fermion action. The static free energy was calculated for different values of the quark mass and the entropy contribution at large distances has been extracted. We also calculate the renormalized Polyakov loop following the approach by Kaczmarek et al.

The Casimir energy paradox of the QCD string

It is widely thought that the early onset of the asymptotic Casimir energy with unit conformal charge signals bosonic string formation of the confining flux connecting a static quark-antiquark pair in QCD. This is observed on a scale where most of the string eigenmodes do not exist and the few stable modes above the ground state are displaced. Hints for the resolution of this paradox are suggested.

Non-perturbative renormalization of the static axial current in quenched QCD

We non-perturbatively calculate the scale dependence of the static axial current in the Schrödinger functional scheme by means of a recursive finite-size scaling technique, taking the continuum limit in each step. The bare current in the O( a) improved theory as well as in the original Wilson regularization is thus connected to the renormalization group invariant one. The latter may then be related to the current at the B-scale defined such that its matrix elements differ from the physical (QCD) ones by O(1/ M). At present, a (probably small) perturbative uncertainty enters in this step. As an application, we renormalize existing unimproved data on F B bare and extrapolate to the continuum limit. We also study an interesting function h( d/ L, u) derived from the Schrödinger functional amplitude describing the propagation of a static quark–antiquark pair.

Fine structure of the QCD string spectrum.

Using advanced lattice methods in quantum chromodynamics, three distinct scales are established in the excitation spectrum of the gluon field around a static quark-antiquark pair as the color source separation R is varied. On the shortest length scale, the excitations are consistent with states created by local gluon field operators arising from a multipole operator product expansion. An intermediate crossover region below 2 fm is identified with a dramatic rearrangement of the level orderings. On the largest length scale of 2-3 fm, the spectrum agrees with that expected for stringlike excitations. The energies nearly reproduce asymptotic pi/R string gaps, but exhibit a fine structure, providing important clues for developing an effective bosonic string description.

Non-perturbative formulation of the static color octet potential

By dressing Polyakov lines with appropriate functionals of the gauge fields, we construct observables describing a fundamental representation static quark–antiquark pair in the singlet, adjoint and average channels of SU( N) pure gauge theory. Each of the potentials represents a gauge invariant eigenvalue of the Hamiltonian. Numerical simulations are performed for SU(2) in 2+1 dimensions. The adjoint channel is found to be repulsive at small and confining at large separations, suggesting the existence of a metastable ( N 2−1)-plet bound state. For small distances and temperatures above the deconfinement transition, the leading order perturbative prediction for the ratio of singlet and adjoint potentials is reproduced by the lattice data.

The Nf = 0 heavy quark potential and perturbation theory

The potential of a static quark-antiquark pair is studied in the range 0.05 fm ≤ r ≤ 0.8 fm, employing a sequence of lattices up to 64 4. The continuum quantities are evaluated by extrapolation of the data at finite lattice spacing. The results are compared with the perturbation theory predictions obtained from the solution of the renormalization group equation for the coupling. The renormalization scheme must be chosen carefully. No evidence for large non-perturbative effects at short distances is seen.