We study singlet and triplet correlation functions of static quark anti-quark pair defined through gauge invariant time-like Wilson loops and Polyakov loop correlators in finite temperature SU(2) gauge theory. We use the Luescher-Weisz multilevel algorithm, which allows to calculate these correlators at very low temperatures. We observe that the naive separation of singlet and triplet states in general does not hold non-perturbatively, however, is recovered in the limit of small separation and the temperature dependence of the corresponding correlators is indeed very different.
We discuss different static quark correlators, including Wilson loops in 2+1 flavor QCD at non-zero temperature and their relation to in-medium quarkonium properties. We present lattice results on static correlation functions obtained with highly improved staggered fermion action and their implications for potential models.
We study Wilson loops at non-zero temperature and extract the static quark potential from them. The extracted potentials are larger than the singlet free energies and do not show screening for $T<190$ MeV.
We present numerical results on the static quark--anti-quark grand canonical potential in full QCD at non-vanishing temperature ($T$) and quark chemical potential ($μ$). Non-zero $μ$-s are reached by means of multi-parameter reweighting. The dynamical staggered simulations were carried out for $n_f=2+1$ flavors with physical quark masses on $4\times 12^3$ lattices.
We present UKQCD's latest results for the static quark potential and light hadron spectrum obtained from matched simulations using two flavours of dynamical quarks. We report that using matched ensembles helps disentangle screening effects from discretisation errors in the static quark potential.
We study the singlet part of the free energy of a static quark anti-quark pair at finite temperature in three flavor QCD with degenerate quark masses using $N_τ=4$ and 6 lattices with Asqtad staggered fermion action. We look at thermodynamics of the system around phase transition and study its scaling with lattice spacing and quark masses.
We are studying the effects of light dynamical quarks on the excitation energies of a flux tube between a static quark and antiquark. We report preliminary results of an analysis of the ground state potential and the $Σ^{\prime+}_g$ and $Π_u$ potentials. We have measured these potentials on closely matched ensembles of gauge configurations, generated in the quenched approximation and with 2+1 flavors of Asqtad improved staggered quarks.
A comprehensive determination of the rich, low-lying spectrum of gluonic excitations in the presence of a static quark-antiquark pair is presented. Our results are obtained from several simulations on anisotropic lattices using an improved action and a large set of gluonic operators. The hybrid quarkonium states are studied in the quenched approximation using the Born-Oppenheimer expansion and nonrelativistic lattice QCD.
Free energies between static quarks and Debye screening masses in the quark-gluon plasma are studied on the basis of Polyakov-line correlations in lattice simulations of 2+1 flavors QCD with the renormalization-group improved gluon action and the $O(a)$-improved Wilson quark action. We perform simulations at $m_{\rm PS}/m_{\rm V} = 0.63$ (0.74) for light (strange) flavors with lattice sizes of $32^3 \times N_t$ with $N_t=4$--12. We adopt the fixed-scale approach, where temperature can be varied without changing the spatial volume and renormalization factor. We find that, at short distance, the…
We determine the static quark free energies around the transition temperature using 2+1 flavors of staggered fermions. Simulations are carried out on N_t=4,6,8 and 10 lattices using physical quark masses. The free energies extracted from Polyakov-loop correlators are extrapolated to the continuum limit.
We introduce new discretizations of the action for static quarks. They achieve an exponential improvement (compared to the Eichten-Hill regularization) on the signal to noise ratio in static-light correlation functions. This is explicitly checked in a quenched simulation and it is understood quantitatively in terms of the self energy of a static quark and the lattice heavy quark potential at zero distance. We perform a set of scaling tests in the Schroedinger functional and find scaling violations in the O(a) improved theory to be rather small -- for one observable significantly smaller than w…
We investigate correlation functions of the Polyakov loop and static meson/diquark systems with the chiral condensate and the quark number density at finite temperature. In particular the latter observable can give insight in the mechanism of screening and string breaking at finite temperature. We use for our analysis gauge field configurations generated in 2+1 flavor QCD with an improved staggered fermion action with almost physical light quark masses and a physical value of the strange quark mass on lattices with temporal extent Nt=4 and 6.
The grand canonical potential for a static quark-antiquark pair at non-vanishing chemical potential was determined at several temperatures. The dynamical staggered simulations were carried out with 2+1 physical quarks along the Lines of Constant Physiscs (LCP).
Static quark potential is studied using a tadpole improved gauge lattice action. The scale is set using the potential for a wide range of bare parameters. The renormalized anisotropy of the lattice is also measured.
We describe the Wuppertal university pilot project in applied parallel computing. We report on a comprehensive high statistics determination of the static quark-antiquark potential and related quantities from quenched quantum chromodynamics. New data for the string tension and the plaquette action for the region 5.5 < beta < 6.8 is presented.
We update our numerical investigation of topological structures around static quarks in pure gauge QCD by results of the first runs including dynamical quarks. Simulations were performed on an $8^3\times4$ lattice, with $SU(3)$ Wilson action, with 3 flavours of quarks of equal mass, both in the confinement and deconfinement phase. In the confinement phase we observe indications for the existence of a flux tube between a static quark and antiquark, flux-tube breaking for large separations, and local correlation between the topological charge density and chiral condensate. In the deconfinement p…
We discuss perturbative O(g^2a) matching with static heavy quarks and domain-wall light quarks for lattice operators relevant to B-meson decays and $B^0$-$\bar{B}^0$ mixing. The chiral symmetry of the light domain-wall quarks does not prohibit operator mixing at O(a) for these operators. The O(a) corrections to physical quantities are non-negligible and must be included to obtain high-precision simulation results for CKM physics. We provide results using plaquette, Symanzik, Iwasaki and DBW2 gluon actions and applying APE, HYP1 and HYP2 link-smearing for the static quark action.
We present results on the in-medium interactions of static quark anti-quark pairs using realistic 2+1 HISQ flavor lattice QCD. Focus is put on the extraction of spectral information from Wilson line correlators in Coulomb gauge using four complementary methods. Our results indicate that on HISQ lattices, the position of the dominant spectral peak associated with the real-part of the interquark potential remains unaffected by temperature. This is in contrast to prior work in quenched QCD and we present follow up comparisons to newly generated quenched ensembles.
The static gluon-quark-antiquark interaction is investigated using lattice QCD techniques. A Wilson loop adequate to the static hybrid three-body system is developed and, using a $24^3 \times 48$ periodic lattice with $β= 6.2$, the potential energy of the system is measured for different geometries. For the medium range behaviour, when the quarks are far apart, we find a string tension which is compatible with two fundamental strings. On the other hand, when the quark and antiquark are nearby, the string tension is larger than two fundamental strings and is compatible with the Casimir scaling.
We present results for the static three- and four-quark potentials in SU(3) and SU(4) respectively. Using a variational approach, combined with multi-hit for the time-like links, we determine the ground state of the baryonic string with sufficient accuracy to test the $Y-$ and $Δ-$ ansätze for the baryonic Wilson area law. Our results favor the $Δ$ ansatz, where the potential is the sum of two-body terms.
We give the analytical expressions and numerical values of radiative corrections to the covariant derivative operator on the static quark line, used for the lattice calculation of the Isgur-Wise form factors $τ_{1/2}(1)$ and $τ_{3/2}(1)$. Those corrections induce an enhancement of renormalized quantities if an hypercubic blocking is applied to the Wilson line, whereas there is a reduction without such a blocking.
We present a numerical study for different discretisations of the static action, concerning cut-off effects and the growth of statistical errors with Euclidean time. An error reduction by an order of magnitude can be obtained with respect to the Eichten-Hill action, for time separations beyond 1.3 fm, keeping discretization errors small. The best actions lead to a big improvement on the precision of the quark mass Mb and F_Bs in the static approximation.
We summarize our recent lattice gauge theory computation of the $Π_u$ and $Σ_u^-$ hybrid static potentials at small quark-antiquark separations. We provide parameterizations of the resulting lattice data points, which can be used for investigating masses and properties of heavy hybrid mesons in the Born-Oppenheimer approximation.
We report on progress to renormalize non-pertubatively the static heavy quark theory on the lattice. In particular, we present first results for position-space renormalization scheme for heavy-light bilinears. We test our approach on RBC's 16^3 x 32 lattice ensemble with m_pi = 420 MeV, Iwasaki gauge action and domain wall light fermions.
We present results on heavy quark free energies in 2-flavour QCD. The temperature dependence of the interaction between static quark anti-quark pairs will be analyzed in terms of temperature dependent screening radii, which give a first estimate on the medium modification of (heavy quark) bound states in the quark gluon plasma. Comparing those radii to the (zero temperature) mean squared charge radii of cha rmonium states indicates that the $J/ψ$ may survive the phase transition as a bound state, while $χ_c$ and $ψ'$ are expected to show significant thermal modifications at temperatures close …
In the limit of infinitely heavy b-quarks we compute the SU(3)-breaking ratio xi of neutral B-meson mixing matrix elements. We also present results for the ratio of decay constants f_{B_s}/f_{B_d}. Our calculation employs chirality-preserving domain-wall fermions for the light quarks, a static action with link-smearing for the b-quarks, and the Iwasaki gauge action. Here we report on our results from the 16^3 x 32 x 16 ensemble (a^-1 = 1.729(28) GeV) which we use to verify our method. We improve upon our earlier work by including O(alpha_s pa) matching for the computation of the decay constant…
We study the static potential using gauge configurations that include the effects of two flavors of dynamical Kogut-Susskind quarks. The configurations, generated by the MILC collaboration, and used to study the spectrum and heavy-light decay constants, cover a range $5.3 \le 6/g^2 \le 5.6$. There are at least four quark masses for each coupling studied. Determination of $r_0$ from the potential can be used to set a scale. This alternative scale is useful to study systematic errors on the spectrum and decay constants.
We perform the first study for the static penta-quark (5Q) potential in lattice QCD with $β$=6.0 and $16^3 \times 32$ at the quenched level. Accurate results of the 5Q potential are extracted from the 5Q Wilson loop using the smearing method, which enhances the ground-state component. The tetra-quark potential for the $\rm QQ$-$\rm {\bar Q}{\bar Q}$ system is also studied in lattice QCD. The multi-quark potentials are found to be well described as a sum of the one-gluon-exchange Coulomb term and the multi-Y linear confinement term based on the flux-tube picture.
A systematic investigation of Symanzic improvement in the gauge field action is performed for the static quark potential in quenched QCD. We consider Symanzik improved gauge field configurations on a 16^3 X 32 lattice with a relatively coarse lattice spacing of 0.165(2)fm. A matched set of standard Wilson gauge configurations is prepared at β= 5.74 with the same physical volume and lattice spacing and is studied for comparison. We find that, despite the coarse lattice spacing, the unimproved and less-expensive Wilson action does as well as the Symanzik action in allowing us to extract the stat…
We investigate effects of action improvement on the light hadron spectrum and the static quark potential in two-flavor QCD for $a^{-1} \approx 1$ GeV and $m_{PS}/m_V = 0.7-0.9$. We compare a renormalization group improved action with the plaquette action for gluons, and the SW-clover action with the Wilson action for quarks. We find a significant improvement in the hadron spectrum by improving the quark action, while the gluon improvement is crucial for a rotationally invariant static potential. We also explore the region of light quark masses corresponding to $m_{PS}/m_V \geq 0.4$ on a 2.7 fm…
String breaking by dynamical quarks in (2+1)-d lattice QCD is demonstrated in this project, by measuring the static potential and the local color-electric field strength between a heavy quark and antiquark pair at large separations. Simulations are done for unquenched SU(2) color with two flavors of staggered quarks. An improved gluon action is used which allows simulations to be done on coarse lattices, providing an extremely efficient means to access the quark separations and propagation times at which string breaking occurs. The static quark potential is extracted using only Wilson loop ope…
We report results on the static quark potential in two-flavor full QCD. The calculation is performed for three values of lattice spacing $a^{-1}\approx 0.9, 1.3$ and 2.5 GeV on $12^3{\times}24, 16^3{\times}32$ and $24^3{\times}48$ lattices respectively, at sea quark masses corresponding to $m_π/m_ρ\approx 0.8-0.6$. An RG-improved gauge action and a tadpole-improved SW clover quark action are employed. We discuss scaling of $m_ρ/\sqrtσ$ and effects of dynamical quarks on the potential.
We compute hybrid static potentials in $SU(3)$ lattice Yang-Mills theory at short quark-antiquark separations using four different small lattice spacings as small as $0.04\,\text{fm}$. The resulting static potentials are important, e.g. when studying heavy hybrid mesons in the Born-Oppenheimer approximation. We also discuss and exclude possible systematic errors from topological freezing, the finite lattice volume and glueball decays.
We present SU(3) lattice Yang-Mills data for hybrid static potentials from five ensembles with different small lattice spacings and the corresponding parametrizations for quark-antiquark separations $0.08\,\text{fm} \le r \le 1.12\,\text{fm}$. We remove lattice discretization errors at tree level of perturbation theory and partly at order $a^2$ as well as the $a$-dependent self energy. In particular the tree-level improvement of static potentials is discussed in detail and two methods are compared. The resulting parametrizations are expected to represent continuum limit results for hybrid stat…
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 compute the fermionic contribution to the strong coupling $α_{qq}$ extracted from the static force in Lattice QCD up to order $g^4$ in perturbation theory. This allows us to subtract the leading fermionic lattice artifacts from recent determinations of $α_{qq}$ produced in simulations of two dynamical charm quarks. Moreover, by using a suitable parametrization of the $β_{qq}$-function, we can evaluate the charm loop effects on $α_{qq}$ in the continuum limit.
We study the static three quark potential using lattice QCD simulation. At zero temperature, the three quark potential is extracted from the baryonic Wilson loop and fitted to the phenomenological form, the sum of the Coulomb term, linearly rising term and the constant. We compare two types of the linear term, ``$Y$'' and ``$Δ$'' type, and find that the string tension almost coincide with $σ_{Q\bar{Q}}$ in the former case. We also investigate the three quark potential at finite temperature using the Polyakov loop correlation. In the deconfined phase, the screened potential is observed similarl…
We study lattice QCD in the limit that the quark mass and chemical potential are simultaneously made large, resulting in a controllable density of quarks which do not move. This is similar in spirit to the quenched approximation for zero density QCD. In this approximation we find that the deconfinement transition seen at zero density becomes a smooth crossover at any nonzero density, and that at low enough temperature chiral symmetry remains broken at all densities.
We study a new method -- maximal variance reduction -- for reducing the variance of stochastic estimators for quark propagators. We find that while this method is comparable to usual iterative inversion for light-light mesons, a considerable improvement is achieved for systems containing at least one infinitely heavy quark. Such systems are needed for heavy quark effective theory. As an illustration of the effectiveness of the method we present results for the masses of the ground state and excited states of $\bar{Q}q$ mesons and $\bar{Q}qq$ baryons. We compare these results with the experimen…
We report our present status of on-going project on the measurement of the static quark potential in 2+1 flavour domain wall QCD with various improved gauge actions and couplings. Lattice spacing determined from Sommer scale on these ensembles are from 1.6 GeV to 2.0 GeV for $16^3 \times 32$ lattice with fifth dimension size 8. We also examine size of discretization error from scaling of a pair of dimensionless quantities, $(r_0 m_π)^2$ and $r_0 m_ρ$, and found small scaling violation.
We discuss the perturbative $O(α_s a)$ matching in the static heavy and domain-wall light quark system. The gluon action is the Iwasaki action and the link smearing is performed in the static heavy action. The chiral symmetry of the light quark realized by using the domain-wall fermion formulation does not prohibit the mixing of the operators at $O(a)$. The application of $O(a)$ improvement to the actual data shows that the B meson decay constant $f_B$, the matrix elements ${\cal M}_B$ and the B parameter $B_B$ have non-negligible effects, while the effect on the SU(3) breaking ratio $ξ$ is sm…
We study lattice QCD in the limit that the quark mass and chemical potential are simultaneously made large, resulting in a controllable density of quarks which do not move; this is similar in spirit to the quenched approximation for zero density QCD. In this approximation we find that the deconfinement transition seen at zero density becomes a smooth crossover for any nonzero density at which we simulated, and that at low enough temperature chiral symmetry remains broken at all densities.
We present preliminary results for the static quark potential computed on some of the DWF lattice configurations generated by the RBC-UKQCD collaborations. Most of these results were obtained using Wilson lines joining spatial planes fixed into the Coulomb gauge. We compare the results from this method with the earlier ones on $16^3 \times 32$ lattices using Bresenham spatial paths with APE smeared link variables. Some preliminary results on $24^3 \times 64$ lattices are also presented.
We explore the distribution of the energy momentum tensor (EMT) around quark--anti-quark and single quark at nonzero temperature in SU(3) Yang-Mills gauge theory by extending our previous study on the EMT distribution in static quark--anti-quark systems in vacuum. We discuss the disappearance of the flux tube structure observed in the vacuum simulation. We investigate the total stress acting on the mid-plane between a quark and an anti-quark and show that it agrees with the force obtained from the derivative of the free energy. The color Debye screening effect in the deconfined phase is also d…
The spectrum of gluons in the presence of a static quark-antiquark pair is studied using Monte Carlo simulations on anisotropic space-time lattices. For very small quark-antiquark separations R, the level orderings and approximate degeneracies disagree with the expectations from an effective string theory. As the quark-antiquark separation R increases, a dramatic rearrangement of the energies occurs, and above 2 fm, all of the levels studied show behavior consistent with an effective string description. The energy spacings are nearly pi/R, but a tantalizing fine structure remains. In addition …
Polyakov loop correlations at finite temperature in two-flavor QCD are studied in lattice simulations with the RG-improved gluon action and the clover-improved Wilson quark action. From the simulations on a $16^3 \times 4$ lattice, we extract the free energies, the effective running coupling $g_{\rm eff}(T)$ and the Debye screening mass $m_D(T)$ for various color channels of heavy quark--quark and quark--anti-quark pairs above the critical temperature. The free energies are well approximated by the screened Coulomb form with the appropriate Casimir factors. The magnitude and the temperature de…
The colour fields, created by a static gluon-quark-antiquark system, are computed in quenched SU(3) lattice QCD, in a $24^3\times 48$ lattice at $β=6.2$ and $a=0.07261(85)\,fm$. We study two geometries, one with a U shape and another with an L shape. The particular cases of the two gluon glueball and quark-antiquark are also studied, and the Casimir scaling is investigated in a microscopic perspective. This also contributes to understand confinement with flux tubes and to discriminate between the models of fundamental versus adjoint confining strings, analogous to type-II and type-I supercondu…
We propose a formulation of the QCD partition function which leads to a series expansion of the quark determinant in any given baryonic sector. The r-th term gives the gauge-invariant contribution of the valence quarks plus r quark-antiquark pairs. This expansion can be used to investigate any baryonic sector, starting from the nucleon up to high baryonic densities.
We calculate the static quark and anti-quark potential both in quenched and two-flavor dynamical quark lattice QCD using DBW2 gauge and domain-wall quark actions. Lattice spacings from Sommer scale are determined. We find (i) mixing of excited states is different in between quenched and dynamical, (ii) lattice spacing $a_{r_0}\sim a_{m_ρ}$ in dynamical and (iii) coefficient of Coulomb term being $α_{N_f=0}<α_{N_f=2}$ at $a^{-1}\sim$ 2 GeV.
The static potentials for quark-antiquark-gluon and 3-gluon systems are computed with lattice QCD methods. For the quark-antiquark-gluon hybrid meson the static potential is obtained for different values of the angle between the quark-gluon and antiquark-gluon segments. The simulations support the formation of an adjoint string for small angles, while for large angles, the adjoint string is replaced by two fundamental strings connecting the gluon and the quarks. For the 3-gluon glueball, we discuss the corresponding Wilson loops and show that the gluons are connected by fundamental strings whe…
We calculate bottom-hadron mass splittings with respect to $B_d$ and $Λ_b$ using full QCD with 2+1 flavors of dynamical Kogut-Susskind sea quarks and domain-wall valence quarks along with a static heavy quark. Our lattices have spatial volume of $(2.5{fm})^3$ with lattice spacing about 0.124 fm and a range of pion masses as low as 291 MeV. Our results are in agreement with experimental observations and other lattice calculations within our statistical and systematic errors. In particular, we find the mass of the $Ω_b$ to be consistent with the recent CDF measurement. We also predict the mass f…
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 …
Recently, cluster methods have been used to solve a variety of sign problems including those that arise in the presence of fermions. In all cases an analytic partial re-summation over a class of configurations in the path integral was necessary. Here the new ideas are illustrated using the example of QCD at a finite density of static quarks. In this limit the sign problem simplifies since the fermionic part decouples. Furthermore, the problem can be solved completely when the gauge dynamics is replaced by a Potts model. On the other hand in QCD with light quarks the solution will require a par…
We calculate glueball and torelon masses as well as the lowest lying hybrid potential in addition to the static ground state potential in lattice simulations of QCD with two flavours of dynamical Wilson fermions. The results are obtained on lattices with $16^3\times 32$ and $24^3\times 40$ sites at $β=5.6$, corresponding to a lattice spacing, $a^{-1}=2.65^{+5}_{-8}$ GeV, as determined from the Sommer force radius, at physical sea quark mass. The range spanned in the present study of five different quark masses is reflected in the ratios, $0.83\geq m_π/m_ρ\geq 0.57$.
We study the free energy of a static quark anti-quark pair at finite temperature in three flavor QCD with degenerate quark masses using N_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.
We investigate the distribution of energy-momentum tensor (EMT) around a static quark in the deconfined phase of SU(3) Yang-Mills theory. The EMT defined through the gradient-flow formalism is used for the numerical analysis of the EMT distribution around the Polyakov loop with the continuum extrapolation. Using EMT, one can study the mechanical distortion of the color gauge field induced by the static charge. We find substantial separation in the absolute values of the EMT eigenvalues which is not observed in Maxwell theory. The separation grows as temperature is lowered toward the critical t…
