Glueball

Abstract: We review the theoretical basis and the applications to hadronic physics of the QCD sum rules invented by Shifman, Vainshtein and Zakharov.

Abstract: The spectrum of glueballs below 4 GeV in the SU(3) pure-gauge theory is investigated using Monte Carlo simulations of gluons on several anisotropic lattices with spatial grid separations ranging from 0.1 to 0.4 fm. Systematic errors from discretization and finite volume are studied, and the continuum spin quantum numbers are identified. Care is taken to distinguish single glueball states from two-glueball and torelon-pair states. Our determination of the spectrum significantly improves upon previous Wilson action calculations.

Abstract: Glueballs, hybrids and multiquark states are predicted as bound states in models guided by quantum chromo dynamics (QCD), by QCD sum rules or QCD on a lattice. Estimates for the (scalar) glueball ground state are in the mass range from 1000 to 1800 MeV, followed by a tensor and a pseudoscalar glueball at higher mass. Experiments have reported evidence for an abundance of meson resonances with 0 - + , 0 ++ and 2 ++ quantum numbers. In particular, the sector of scalar mesons is full of surprises starting from the elusive σ and κ mesons. The a 0 ( 980 ) and f 0 ( 980 ) , discussed extensively in the literature, are reviewed with emphasis on their Janus-like appearance as K K ¯ molecules, tetraquark states or q q ¯ mesons. Most exciting is the possibility that the three mesons f 0 ( 1370 ) , f 0 ( 1500 ) , and f 0 ( 1710 ) might reflect the appearance of a scalar glueball in the world of quarkonia. However, the existence of f 0 ( 1370 ) is not beyond doubt and there is evidence that both f 0 ( 1500 ) and f 0 ( 1710 ) are flavour octet states, possibly in a tetraquark composition. We suggest a scheme in which the scalar glueball is dissolved into the wide background into which all scalar flavour-singlet mesons collapse. There is an abundance of meson resonances with the quantum numbers of the η . Three states are reported below 1.5 GeV / c 2 whereas quark models expect only one, perhaps two. One of these states, ι ( 1440 ) , was the prime glueball candidate for a long time. We show that ι ( 1440 ) is the first radial excitation of the η meson. Hybrids may have exotic quantum numbers which are not accessible by q q ¯ mesons. There are several claims for J PC = 1 - + exotics, some of them with properties as predicted from the flux tube model interpreting the quark–antiquark binding by a gluon string. The evidence for these states depends partly on the assumption that meson–meson interactions are dominated by s-channel resonances. Hybrids with non-exotic quantum numbers should appear as additional states. Light-quark mesons exhibit a spectrum of (squared) masses which are proportional to the sum of orbital angular momentum and radial quantum numbers. Two states do not fall under this classification. They are discussed as hybrid candidates. The concept of multiquark states has received revived interest due to new resonances in the spectrum of states with open and hidden charm. The new states are surprisingly narrow and their masses and their decay modes often do not agree with simple quark-model expectations. Lattice gauge theories have made strong claims that glueballs and hybrids should appear in the meson spectrum. However, the existence of a scalar glueball, at least with a reasonable width, is highly questionable. It is possible that hybrids will turn up in complex multibody final states even though so far, no convincing case has been made for them by experimental data. Lattice gauge theories fail to identify the nonet of scalar mesons. Thus, at the present status of approximations, lattice gauge theories seem not to provide a trustworthy guide into unknown territory in meson spectroscopy.

Abstract: We study the formation of a mass gap, or effective gluon mass (and consequent dimensionful parameters such as the string tension, glueball mass, $〈\mathrm{Tr}{{G}_{\ensuremath{\mu}\ensuremath{ u}}}^{2}〉$, correlation lengths) in continuum QCD, using a special set of Schwinger-Dyson equations. These equations are derived from a resummation of the Feynman graphs which represent certain gauge-invariant color-singlet Green's functions, and are themselves essentially gauge invariant. This resummation is essential to the multiplicative renormalizability of QCD in the light-cone gauge, which we adopt for technical reasons. We close the dynamical equations by "solving" a Ward identity, a procedure which, while exact in the infrared regime, is subject to ambiguities and corrections in the ultraviolet regime which are beyond the scope of the present work. (These ambiguities are less prominent for QCD in three dimensions, which we discuss also.) As discussed in an earlier work, quark confinement arises from a vortex condensate supported by the mass gap. Numerical calculations of the mass gap are presented, suggesting an effective gluon mass of 500\ifmmode\pm\else\textpm\fi{}200 MeV and a ${0}^{+}$ glueball mass of about twice this value.

Abstract: We study gravity duals of large N nonsupersymmetric gauge theories with matter in the fundamental representation by introducing a D7-brane probe into deformed AdS backgrounds. In particular, we consider a D7-brane probe in both the AdS Schwarzschild black hole solution and in the background found by Constable and Myers, which involves a nonconstant dilaton and S5 radius. Both these backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the Psi-bar Psi condensate and meson spectrum associated with these backgrounds. In the AdS–black-hole background, a quark-bilinear condensate develops only at a nonzero quark mass. We speculate on the existence of a third order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the Constable-Myers background, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson in the limit of small quark mass. The existence of the condensate ensures that the D7-brane never reaches the naked singularity at the origin of the deformed AdS space.