Effective potential between two gluons from the scalar glueball

Starting from the 0⁺⁺ glueball mass and wave function computed from lattice QCD, we compute the local potential between two constituent gluons. Since the properties of constituent gluons are still a matter of research, we allow for them to be either massless, or massive with a mass around 0.7GeV. Both pictures are actually used in the literature. When the gluons are massless, the corresponding local potential is shown to be compatible with a Cornell form, that is a linear confinement plus a short-range Coulomb part, with standard values for the flux tube energy density and for the strong coupling constant. When the gluons are massive, the confining potential is a saturating one, commonly used to simulate string-breaking effects. These results fill a gap between lattice QCD and phenomenological models: The picture of the scalar glueball as a bound state of two constituent gluons interacting via a phenomenological potential is shown to emerge from pure gauge lattice QCD computations. Moreover, we show that the allowed potential shape is constrained by the mass of the constituent gluons.     

Excited flux tube from q¯g hybrid mesons

In the framework of quark models, hybrid mesons are either seen as two-body qˉ systems with an excited flux tube connecting the quark to the antiquark or as three-body qˉg systems including a constituent gluon. In this work we show that, starting from the three-body wave function of the qˉg hybrid meson in which the gluonic degrees of freedom are averaged, the excited flux tube picture emerges as an equivalent qˉ potential. This equivalence between the excited flux tube and the constituent-gluon approach is confirmed for heavy hybrid mesons but, for the first time, it is shown to hold in the light sector too, provided the contribution of the quark dynamics is correctly taken into account.     

Casimir scaling, glueballs, and hybrid gluelumps

Assuming that the Casimir scaling hypothesis is well verified in QCD, masses of glueballs and hybrid gluelumps (gluon attached to a point-like cˉ pair) are computed within the framework of the rotating string formalism. In our model, two gluons are attached by an adjoint string in a glueball, while the gluon and the colour octet cˉ pair are attached by two fundamental strings in a hybrid gluelump. Masses for such exotic hadrons are computed with very few free parameters. These predictions can serve as a guide for experimental searches. In particular, the ground-state glueballs lie on a Regge trajectory and the lightest 2⁺⁺ state has a mass compatible with some experimental candidates.     

Constituent gluon interpretation of glueballs and gluelumps

Arguments are given that support the interpretation of the lattice QCD glueball and gluelump spectra in terms of bound states of massless constituent gluons with helicity 1. In this scheme, we show that the mass hierarchy of the currently known gluelumps and glueballs is mainly due to the number of constituent gluons and can be understood within a simple flux tube model. It is also argued that the lattice QCD 0^+- glueball should be seen as a four-gluon bound state. We finally predict the mass of the 0^- state, not yet computed in lattice QCD.     

QCD Coulomb gauge approach to exotic hadrons

The Coulomb gauge Hamiltonian model is used to calculate masses for selected J^PC states consisting of exotic combinations of quarks and gluons: ggg glueballs (oddballs), qˉg hybrid mesons and qˉqˉ tetraquark systems. An odderon Regge trajectory is computed for the J^- glueballs with intercept much smaller than the pomeron, explaining its nonobservation. The lowest 1^-+ hybrid-meson mass is found to be just above 2.2GeV while the lightest tetraquark state mass with these exotic quantum numbers is predicted around 1.4GeV consistent with the observed π(1400).     

A new energy-dependent quark interaction from a Tamm-Dancoff reduction of an effective field theory quark model

A new quark interaction is derived, by means of a Tamm-Dancoff reduction, from an effective field theory constituent quark model. In contrast to the standard Coulombic potential, the obtained interaction is nonlocal and energy dependent. Furthermore, it becomes positive and rises up to a maximum value when the interquark distance increases, partially resembling some aspects of the phenomenological Cornell potential.     

The radiative decay ϕ → γππ in a coupled-channel model and the structure of f0(980)

A coupled-channel model is used to study the nature of the scalar mesons produced in the decay ϕ → γππ. The K molecular picture of f₀(980) is found to be in a good agreement with the recent experimental data from SND and CMD-2. The structure of the light scalar mesons is elucidated by investigating the S-matrix poles and the q spectral density.     

Retardation effects in the rotating string model

A new method to study the retardation effects in mesons is presented. It is based on a generalized rotating string model, in which a nonzero value of the relative time between the quark and the antiquark is allowed. This approach leads to a retardation term in the Hamiltonian which behaves as a perturbation of the nonretarded Hamiltonian and preserves the Regge trajectories for light mesons. The straight-line ansatz is used to describe the string, and the relevance of this approximation is tested. It is shown that the string is actually curved because of retardation, but this bending does not bring a relevant contribution to the energy spectrum of the model.     

AdS-QCD quark–antiquark potential,meson spectrum and tetraquarks

The AdS/QCD correspondence predicts the structure of the quark–antiquark potential in the static limit. We use this piece of information together with the Salpeter equation (Schrödinger equation with relativistic kinematics) and a short range hyperfine splitting potential to determine quark masses and the quark potential parameters from the meson spectrum. The agreement between theory and experimental data is satisfactory, provided one considers only mesons comprising at least one heavy quark. We use the same potential (in the one-gluon-exchange approximation) and these data to estimate the constituent diquark masses. Using these results as input we compute tetraquark masses using a diquark–antidiquark model. The masses of the states X(3872) or Y(3940) are predicted rather accurately. We also compute tetraquark masses with open charm and strangeness. Our result is that tetraquark candidates such as D _s (2317), D _s (2457) or X(2632) can hardly be interpreted as diquark–antidiquark states within the present approach.     

The 27-plet baryons with spin 3/2 under SU(3) symmetry

We investigate the spin-3/2 baryons in the 27-plet based on flavor SU(3) symmetry. For J ^p = 3/2⁺, we find all the candidates for non-exotic members. For J ^p = 3/2^-, we predict a new non-exotic member Λ(1780). Fitting the mass spectrum and calculating the widths of the members show an approximate symmetry of the 27-plet of SU(3). We find that the exotic members have relatively large widths and the Ξ(1950) has spin and parity J ^p = 3/2^-. The possibility of assigning the non-exotic candidates to an octet is also analyzed.     

Comparative Regge analysis of Λ,ΣΛ(1520) and Θ<Superscript>+</Superscript> production in γp,πp and pp reactions

Using the Quark-Gluon Strings Model --combined with Regge phenomenology-- we perform a comparative analysis of Λ, Σ⁰, Λ(1520) and Θ⁺ production in binary reactions induced by photon, pion and proton beams on the nucleon. We find that the existing experimental data on the γp↦K⁺Λ differential and total cross-sections can be described very well by the model for photon energies 1-16 GeV and - t < 2 GeV² assuming a dominant contribution of the K^* Regge trajectory. Moreover, using the same parameters we also reproduce the total γp↦K⁺Σ⁰ and γp↦K⁺Λ(1520) cross-sections suggesting a “universality” of the Regge model. In order to check the consistency of the approach we evaluate the differential and total cross-sections for the reaction π^-p↦K⁰Λ which is also found to be dominated by the K^* Regge trajectory. Using the apparent “universality” of the Regge model we extend our scheme to the analysis of the binary reactions γp↦¯⁰Θ⁺, π^-p↦K^-Θ⁺ and pp↦Σ⁺Θ⁺ as well as the exclusive and inclusive Θ⁺ production in the reactions pp↦p¯⁰Θ⁺ and pp↦Θ⁺X. Our detailed studies demonstrate that Θ⁺ production does not follow the “universality” principle, thus suggesting an essentially different internal structure of the exotic baryon relative to conventional hyperons or hyperon resonances.     

Productions of X(1835) as baryonium with sizable gluon content

X(1835) has been treated as a baryonium with sizable gluon content, and to be almost flavor singlet. This picture allows us to rationally understand X(1835) production in J/ψ radiative decays, and its large couplings with pˉ, η^′ππ. The processes ϒ(1S) → γX(1835) and J/ψ → ωX(1835) have been examined. It has been found that Br(ϒ(1S) → γX(1835))Br(X(1835) → pˉ) < 6.45×10^-7, which is compatible with CLEO's recent experimental result (Phys. Rev. D 73, 032001 (2006) hep-ex/0510015). The branching fractions Br(J/ψ → ωX(1835)), Br(J/ψ → ρX(1835)) with X(1835) → pˉ and X(1835) → η^′π⁺π^- have been estimated by the quark-pair creation model. We show that they are heavily suppressed, so the signal of X(1835) is very difficult, if not impossible, to be observed in these processes. The experimental checks for these estimations are expected. The existence of the baryonium nonet is conjectured, and a model-independent derivation of their production branching fractions is presented.     

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     

The WKB method for the Dirac equation with the vector and scalar potentials

The WKB approximation is developed for the Dirac equation with the spherically symmetrical vector and scalar potentials. The relativistic wavefunctions are constructed, new quantization rule containing the spin-orbital interaction is obtained. For spherically symmetrical model of the Stark effect the quasi-classical spectrum of relativistic hydrogen-like atom is calculated. Application of the WKB method to the mass spectrum of the hydrogen-like quark systems was done.     

Towards an understanding of heavy baryon spectroscopy

The recent observation at CDF and D0 of Σ _b , Σ _b ^* and Ξ _b baryons opens the door to the advent of new states in the bottom baryon sector. The states measured provide sufficient constraints to fix the parameters of phenomenological models. One may therefore consistently predict the full bottom baryon spectra. For this purpose we have solved exactly the three-quark problem by means of the Faddeev method in momentum space. We consider our guidance may help experimentalists in the search for new bottom baryons and their findings will help in constraining further the phenomenological models. We identify particular states whose masses may allow to discriminate between the dynamics for the light quark pairs predicted by different phenomenological models. Within the same framework we also present results for charmed, doubly charmed, and doubly bottom baryons. Our results provide a restricted possible assignment of quantum numbers to recently reported charmed-baryon states. Some of them are perfectly described by D-wave excitations with J ^P = 5/2⁺, as the Λ _c (2880), Λ _c (3055), and Λ _c (3123). Communicated by V. Vento     

Nucleon magnetic moments in an extended chiral constituent quark model

We present results for the nucleon magnetic moments in the context of an extended chiral constituent quark model based on the mechanism of the Goldstone boson exchange, as suggested by the spontaneous breaking of chiral symmetry in QCD. The electromagnetic charge-current operator is consistently deduced from the model Hamiltonian, which includes all force components for the pseudoscalar, vector and scalar meson exchanges. Thus, the continuity equation is satisfied for each piece of the interaction, avoiding the introduction of any further parameter. A good agreement with experimental values is found. The role of isoscalar two-body operators, not constrained by the continuity equation, is also investigated.     

Another tetraquark structure in the <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">χ</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>1</Subscript> invariant mass distribution

In this article, we assume that there exists a scalar hidden charm tetraquark state in the π ⁺ χ _c1 invariant mass distribution, and we study its mass using the QCD sum rules. The numerical result M _Z =(4.36±0.18) GeV is consistent with the mass of the Z(4250). The Z(4250) may be a tetraquark state, but other possibilities, such as a hadro-charmonium resonance and a molecular state, are not excluded.     

Possible tetraquark states in the <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">χ</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>1</Subscript> invariant-mass distribution

In this article, we assume that there exist hidden charmed tetraquark states with spin–parity J ^P=1⁻, and we calculate their masses with the QCD sum rules. The numerical result indicates that the masses of the vector hidden charmed tetraquark states are about M _Z =(5.12±0.15) GeV or M _Z =(5.16±0.16) GeV, which are inconsistent with the experimental data on the π ⁺ χ _c1 invariant-mass distribution. The hidden charmed mesons Z ₁, Z ₂ or Z may be scalar hidden charmed tetraquark states, hadro-charmonium resonances or molecular states.     

Roles of quarks and gluons in the spin structure of nucleons

The spin structure of protons will be discussed by using MIT-bag model and considering constituent quarks to be combined from current quarks and gluons. It will be shown that the gluonic degrees of freedom play an important role in prediction of the recent EMC results.