The experimental status of glueballs

Glueballs and other resonances with large gluonic components are predicted as bound states by Quantum Chromodynamics (QCD). The lightest (scalar) glueball is estimated to have a mass in the range from 1 to 2 GeV/c²; pseudoscalar and tensor glueballs are expected at higher masses. Many different experiments exploiting a large variety of production mechanisms have presented results in recent years on light mesons with J^PC=0⁺⁺, 0⁻⁺, and 2⁺⁺ quantum numbers. This review looks at the experimental status of glueballs. Good evidence exists for a scalar glueball which is mixed with nearby mesons, but a full understanding is still missing. Evidence for tensor and pseudoscalar glueballs are weak at best. Theoretical expectations of phenomenological models and QCD on the lattice are briefly discussed.     

The DD* interaction with isospin zero in an extended hidden gauge symmetry approach

The DD^* interaction via a ρ or ω exchange is constructed within an extended hidden gauge symmetry approach, where the strange quark is replaced by the charm quark in the SU(3) flavor space. With this DD^* interaction, a bound state slightly lower than the DD^* threshold is generated dynamically in the isospin zero sector by solving the Bethe-Salpeter equation in the coupled-channel approximation, which might correspond to the X(3872) particle announced by many collaborations. This formulism is also used to study the BB^* interaction, and a BB^* bound state with isospin zero is generated dynamically, which has no counterpart listed in the review of the Particle Data Group. Furthermore, the one-pion exchange between the D meson and the D^* is analyzed precisely, and we do not think the one-pion exchange potential need be considered when the Bethe-Salpeter equation is solved.     

Ultralight glueballs in Quark-Gluon Plasma

We consider the dynamics of the scalar and pseudoscalar glueballs in the Quark-Gluon Plasma (QGP). By using the instanton model for the QCD vacuum we give the arguments that the nonperturbative gluon-gluon interaction is qualitatively different in the confinement and deconfinement phases. Based on this observation it is shown that above T _c the values of the scalar and pseudoscalar glueball masses might be very small. The estimation of the temperature of scale invariance restoration, at which the scalar glueball becomes massless, is given. We also discuss the Bose—Einstein condensation of the glueballs and the superfluidity of the glueball matter in QGP.     

Spotting glueballs in collinear gluon jets

We suggest looking for pure gluon hadronic states (glueballs) in ?→ 3g → low spherically final state (collinear gluon jets). In these events one gluon has the maximum energy, $\text{M?}\text{2}$, favouring fragmentation into a glueball. The signature for a true C = G + glueball is its prominence at the ? resonance in e⁺e^? →? → (glueball → four charged pions) + … and its absence in q$\text{q}$ jets off (we do not expect significant quark fragmentation into glueballs).     

Quark chiral condensate from the overlap quark propagator

From the overlap lattice quark propagator calculated in the Landau gauge,we determine the quark chiral condensate by fitting operator product expansion formulas to the lattice data.The quark propagators are computed on domain wall fermion configurations generated by the RBC-UKQCD Collaborations with N_f = 2 + 1flavors.Three ensembles with different light sea quark masses are used at one lattice spacing 1/a = 1.75(4) Ge V.We obtain ψψ (2 GeV)MS =(-304(15)(20) MeV)~3in the SU(2) chiral limit.     

Study of X(5568) in a unitary coupled-channel approximation of BK and B_sπ

The potential of the B meson and the pseudoscalar meson is constructed up to the next-to-leading order Lagrangian, and then the BK and B_sπ interaction is studied in the unitary coupled-channel approximation. A resonant state with a mass about 5568 MeV and J~P= 0~+is generated dynamically, which can be associated with the X(5568) state announced by the D0 Collaboration recently. The mass and the decay width of this resonant state depend on the regularization scale in the dimensional regularization scheme, or the maximum momentum in the momentum cutoff regularization scheme. The scattering amplitude of the vector B meson and the pseudoscalar meson is calculated, and an axial-vector state with a mass near 5620 MeV and J~P= 1~+is produced. Their partners in the charm sector are also discussed.     

Measurement of the absolute branching fraction of D+→K0e+ve via K0→π0π0

By analyzing 2.93 fb^-1 data collected at the center-of-mass energy √s=3.773 GeV with the BESIII detector, we measure the absolute branching fraction of the semileptonic decay D⁺→K⁰e⁺v_e to be B(D⁺→K⁰e⁺v_e)=(8.59±0.14±0.21)% using K⁰→K_S⁰→π⁰π⁰, where the first uncertainty is statistical and the second systematic. Our result is consistent with previous measurements within uncertainties..     

Glueballs and the superfluid phase of Two-Color QCD

We present the first results on scalar glueballs in cold, dense matter using lattice simulations of two-color QCD. The simulations are carried out on a 6³×12 lattice and use a standard hybrid molecular dynamics algorithm for staggered fermions for two values of quark mass. The glueball correlators are evaluated via a multi-step smearing procedure. The amplitude of the glueball correlator peaks in correspondence with the zero temperature chiral transition, μ _c=m _π /2, and the propagators change in a significant way in the superfluid phase, while the Polyakov loop is nearly insensitive to the transition. Standard analysis suggest that lowest mass in the 0⁺⁺ gluonic channel decreases in the superfluid phase, but these observations need to be confirmed on larger and more elongated lattices. These results indicate that a non-zero density induces non-trivial modifications of the gluonic medium.     

Hybrids: Mixed states of quarks and gluons

We calculate the spectrum of the four ground state hybrid $\text{(}\text{q}\text{qg}\text{)}$ nonets, J^PC = (0, 1, 2)^?+, 1^??, using the MIT bag model to first order in cavity perturbation theory. Quark and gluon self-energies are included by a fit to the s-wave mesons and baryons and to the glueball candidate i(1440). We find a large gluon self-energy which substantially increases our predictions of the glueball and hybrid masses. We discuss the phenomenology of hybrids, including a suggestion that the A₃ (1670) and a second peak at 1850 MeV in the fπ channel may be mixtures of the isovector $\text{q}\text{q}$ d-wave state with the $\text{q}\text{qg}$ s-wave.     

Toroidal bags

In the framework of the bag model of hadrons glueballs have a toroidal shape. Previous calculations with a spherical bag suggest glueball masses as low as 940 MeV. We examine the possibility that, with the correct bag topology, glueballs are pushed to higher mass. Inside a fixed toroidal cavity of rectangular cross-section (theT-bag) we find evidence that this is not the case. We attempt an extraction of theJ ^p of the lowest mode and discuss spectroscopic implications of the results.     

A Lattice Study of the Glueball Spectrum

Glueball Spectrum is studied using an improved gluonic action on asymmetric lattices in the pure SU(3) gauge theory.The smallest spatial lattice spacing is about 0.08 fm which makes the extrapolation to the continuum limit more reliable.In particular.attention is paid to the scalar glueball mass which is known to have problems in the extrapolation.Converting our lattice results to physical units using the scale set by the static quark potential,we obtain the following results for the glueball masses:MG(0 )=1730(90)MeV for the scalar glueball mass and MG(2 )=2400(95)MeV for the tensor glueball.     

Role of glueballs in non-perturbative quark–gluon plasma

Discussed is how non-perturbative properties of quark gluon plasma, recently discovered in RHIC experiment, can be related to the change of properties of scalar and pseudoscalar glueballs. We set up a model with the Cornwall–Soni's glueball–gluon interaction, which shows that the pseudoscalar glueball becomes massless above the critical temperature of deconfinement phase transition. This change of properties gives rise to the change of sign of the gluon condensate at T>Tc$T>T_c$. We discuss the other physical consequences resulting from the drastic change of the pseudoscalar glueball mass above the critical temperature.     

QCD sum rules for heavy quark systems

In this paper we present in a detailed and coherent fashion our work on QCD sum rules for equal mass heavy quark meson states. We discuss the technical procedures used to calculate the perturbative and non-perturbative contributions to the vacuum polarization, which have been calculated for all currents up to and including spin 2⁺⁺. Using dispersion relations, sum rules are derived. Extensive applications are made to the lowest lying states of the charmonium and upsilon systems. The masses of the S- and P-wave charmonium levels are reproduced to a high degree of accuracy, and the mass of the ¹P₁ level is predicted at 3.51 GeV. For the upsilon system it only appears to be possible to predict the γ-η_b splitting which gives 60 MeV. Very accurate values are given for the current quark masses at p² = ?m_q²: m_c = 1.28 GeV and m_b = 4.25 GeV.     

Scalar mesons in a chiral quark model with glueball

Ground-state scalar isoscalar mesons and a scalar glueball are described in a U(3)×U(3) chiral quark model of the Nambu-Jona-Lasinio (NJL) type with 't Hooft interaction. The latter interaction produces singlet-octet mixing in the scalar and pseudoscalar sectors. The glueball is introduced into the effective meson Lagrangian as a dilaton on the base of scale invariance. The mixing of the glueball with scalar isoscalar quarkonia and amplitudes of their decays into two pseudoscalar mesons are shown to be proportional to current quark masses, vanishing in the chiral limit. Mass spectra of the scalar mesons and the glueball and their main modes of strong decay are described. Received: 14 July 2000 / Accepted: 31 July 2000     

Calculation of the pseudoscalar masses from a QCD effective potential

We calculate the effective two-loop potential of QCD with massive quarks in the CJT composite operator formalism. To perform the wave-function renormalization of composite operators we are lead to a condition which corresponds to the Adler-Dashen requirement in the limit of vanishing quark masses. The condition also assures absence of spontaneous breaking of parity. Pseudoscalar masses are calculated from the second derivatives of the effective potential, and a fit is obtained for quark masses m_u = 3.6 MeV, m_d = 7 MeV, m_s = 152 MeV. We also comment on consistuent quark masses and on the effect of heavy quarks.     

Is J~(PC)=3~(-+) molecule possible?

The confirmation of charged charmonium-like states indicates that heavy quark molecules should exist.Here we discuss the possibility of a molecule state with J P C= 3-+. In a one-boson-exchange model investigation for the S wave C = + D* ˉD*2states, one finds that the strongest attraction is in the case J = 3 and I = 0 for bothπ and σ exchanges. Numerical analysis indicates that this hadronic bound state might exist if a phenomenological cutoff parameter around 2.3 Ge V(1.5 Ge V) is reasonable with a dipole(monopole) type form factor in the one-pionexchange model. The cutoff for binding solutions may be reduced to a smaller value once the σ exchange contribution is included. If a state around the D* ˉD*2threshold(≈4472 Me V) in the channel J/ψω(P wave) is observed, the heavy quark spin symmetry implies that it is not a cˉc meson and the J P C are likely to be 3-+.     

Analysis of the QCD spectrum and chiral symmetry breaking with varying quark masses

The meson spectrum of QCD is studied in the framework of nonperturbative QCD as a function of varying quark masses m _q . It is shown that the total spectrum consists of two branches: 1) the standard one, which may be called the flux-tube spectrum, depending approximately linearly on m _q , and 2) the chiral symmetry breaking (CSB) spectrum for pseudoscalar (PS) flavor nonsinglet mesons with mass dependence √m _q . The formalism for PS mesons is derived from the QCD Lagrangian with m _q corrections, and a unified form of the PS propagator was derived. It is shown that the CSB branch of PS mesons joins to the flux-tube branch at around m _q = 200 MeV. All these results are in close correspondence with recent numerical data on large lattices.     

A basic guide for the glueball spotter

After a brief review of the theoretical and phenomenological motivation for the existence of gluonic resonances, we examine the expected properties of such states, and consider possible tests for their presence in the hadronic spectrum below 1.5 GeV in mass. The scalar mesons can be classified as an approximately ideally mixed nonet with an additional isoscalar, the S¹, with all the expected properties of a scalar glueball. It is suggested that the η′ contains a large proportion of glue as well as strange quarks and that, if the E(1420) is not a pseudoscalar, two further pseudoscalars await discovery in the low-lying meson spectrum. The pomeron, a narrow resonance in the ππ D-wave, must be found with a mass around or slightly below that of the S¹. If the pomeron has a daughter vector glueball which, as has been argued, is fairly close to the φ mass, then it should also have a mother 3^?? glueball with a similar mass. The D(1285) may well be a 2^?+ glueball.     

Meson decays of the glueball

We estimate the decay widths of the 0^±-glueballs by taking account of the mixings with η and η′ through their anomalous coupling. We find a pseudoscalar glueball with a broad decay width, if its mass is larger than m_δ(980) + m_π. On the other hand, a scalar glueball has a narrow decay width. Assuming E(1440) to be the pseudoscalar glueball, we predict Γ_δ(980)ππ≈ 40 MeV.