The properties of the vacuum are addressed in the two- and four-dimensional quark models for QCD. It is demonstrated that the two-dimensional QCD ('t Hooft model) possesses only one possible vacuum state - the solution to the mass-gap equation, which provides spontaneous breaking of the chiral symmetry (SBCS). On the contrary, the four-dimensional theory with confinement modeled by the linear potential supplied by the Coulomb OGE interaction, not only has the chirally-noninvariant ground vacuum state, but it possesses an excited vacuum replica, which also exhibits SBCS and can realize as a metastable intermediate state of hadronic systems. We discuss the influence of the latter on physical observables as well as on the possibility to probe the vacuum background fields in QCD.Comment: RevTeX4, 26 pages, 8 EPS figures, extended references, corrected some typos, to appear in Phys.Rev.

We argue that the low-lying scalar-meson nonet makes part of a subset of a family of infinitely many scalar-meson nonets, which in turn makes part of a family of infinitely many quark-antiquark bound states and resonances. We outline the properties of this subset.Comment: Talk presented at the workshop on "Scalar Mesons and Related Topics" honoring the 70th birthday of Michael Scadron, 11 pages, 7 figure

Abstract. The interpretation of the Landau gauge lattice gluon propagator as a massive type bosonic propagator is investigated. Three different scenarios are discussed: i) an infrared constant gluon mass; ii) an ultraviolet constant gluon mass; iii) a momentum dependent mass. We find that the infrared data can be associated with a massive propagator up to momenta ∼ 500 MeV, with a constant gluon mass of 723(11) MeV, if one excludes the zero momentum gluon propagator from the analysis, or 648(7) MeV, if the zero momentum gluon propagator is included in the data sets. The ultraviolet lattice data is not compatible with a massive type propagator with a constant mass. The scenario of a momentum dependent gluon mass gives a decreasing mass with the momentum, which vanishes in the deep ultraviolet region. Furthermore, we show that the functional forms used to describe the decoupling like solution of the Dyson-Schwinger equations are compatible with the lattice data with similar mass scales.

The isospin, spin and parity dependent potential of a pair of B mesons is computed using Wilson twisted mass lattice QCD with two flavours of degenerate dynamical quarks. The B meson is addressed in the static-light approximation, i.e. the b quarks are infinitely heavy. From the results of the B B meson-meson potentials, a simple rule can be deduced stating which isospin, spin and parity combinations correspond to attractive and which to repulsive forces. We provide fits to the ground state potentials in the attractive channels and discuss the potentials in the repulsive and excited channels. The attractive channels are most important since they can possibly lead to a bound four-quark state, i.e. abbud tetraquark. Using these attractive potentials in the Schrödinger equation, we find indication for such a tetraquark state of two static bottom antiquarks and two light u/d quarks with mass extrapolated down to the physical value.

We study the SU(3) gluon propagator in renormalizable R ξ gauges implemented on a symmetric lattice with a total volume of (3.25 fm)4 for values of the gauge fixing parameter up to ξ = 0.5. As expected, the longitudinal gluon dressing function stays constant at its tree-level value ξ. Similar to the Landau gauge, the transverse R ξ gauge gluon propagator saturates at a nonvanishing value in the deep infrared for all values of ξ studied.