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, 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. The flux tube model allows for a parameter-free computation of its mass, which is in good agreement with lattice QCD.
Assuming that the Casimir scaling hypothesis is well verified in QCD, masses of glueballs and hybrid gluelumps (gluon with a point-like $c\bar c$ pair) are computed within 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 $c\bar c$ 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 a…
We show that C-odd gluelumps can be successfully described as bound states of a single transverse constituent gluon evolving in the flux-tube-like potential generated by a static color-octet source. The use of a helicity degree of freedom rather than a spin one for the constituent gluon forbids the states that are not observed in lattice QCD. Our model leads to a gluelump mass spectrum in remarkable agreement with the available lattice data provided that an additional parity-splitting mass term is introduced. We argue that such a term is due to instanton-induced interactions in gluelumps.
Lattice computations with excited SU(3) representations suggest that the confining gluon-gluon interaction complies with the Casimir scaling. The constituent gluon models have also been assuming the Casimir scaling. Inspired in type-II superconductors, we explore a new scenario for the gluon-gluon interaction where the adjoint string is replaced by a pair of fundamental strings, resulting in a factor of 2, smaller than 9/4. To test our proposal we construct a simple constituent gluon model, extrapolated from the funnel potential for quarkonium, and apply it to compute the wave-function of glue…
Spectrum of gluons in the adjoint source field is computed analytically using the QCD string Hamiltonian, containing only one parameter - string tension, fixed by meson and glueball spectrum. Spin splitting is shown to be small. A good agreement is observed with spatially generated gluelump states measured on the lattice. Important role of gluelumps defining the behaviour of field-strength correlators is stressed and correspondence with earlier computations of the latter is established.
The quantum numbers and mass hierarchy of the glueballs observed in $(2+1)$-dimensional lattice QCD with gauge group SU($N_c$) are shown to be in agreement with a constituent picture. The agreement is maintained when going from glueballs to gluelumps, and when the gauge group SO($2N_c$) is taken instead of SU($N_c$).
The 3d gluodynamics which governs the large T quark gluon plasma is studied in the framework of the field correlator method. Field correlators and spacial string tension are derived through the gluelump Green's functions. The glueball spectrum is calculated both in C=-1 as well as in C=+1 sectors, and multigluon bound states in the form of "gluon rings" and "gluon stars" are computed explicitly. Good overall agreement with available lattice data is observed.
In this talk the pomeron conjecture is reviewed and constituent gluon models are derived. In a simple two-gluon glueball spectrum the pomeron trajectory and the daughter trajectories are computed. The open problems of two-gluon glueballs are discussed, including transversality and Yang's theorem, the spin tensor interactions, the structure of the string and decays. The related systems of charmed hybrids and of the gluelump are also addressed. To conclude, different aspects of glueballs that could be measured at PANDA are highlighted.
In this work we use a mapping technique to derive in the context of a constituent gluon model an effective Hamiltonian that involves explicit gluon degrees of freedom. We study glueballs with two gluons using the Fock-Tani formalism. In the present work we consider two possibilities for $0^{++}$: (i) as a pure $s\bar{s}$ and calculate, in the context of a quark interchange picture, the cross-section; (ii) as a glueball where a new calculation for this cross-section is made, in the context of the constituent gluon model, with gluon interchange.
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 0.7 GeV. 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…
In this work we use a mapping technique to derive in the context of a constituent gluon model an effective Hamiltonian that involves explicit gluon degrees of freedom. We study glueballs with two gluons using the Fock-Tani formalism. In the present work we calculate the glueball-glueball potential, in the context of the constituent gluon model, with gluon interchange.
We analyze the mixing of the scalar glueball with the scalar-isoscalar quarkonia states above 1 GeV in a non-local covariant constituent approach. Similarities and differences to the point-particle Klein-Gordon limit and to the quantum mechanical case are elaborated. Model predictions for the two-photon decay rates in the covariant mixing scheme are indicated.
Modeling glueballs as bound states of transverse constituent gluons allows to understand the main features of the lattice QCD glueball spectrum. In particular it has been shown in previous works that the lightest C-even glueballs can be seen as bound states of two transverse constituent gluons interacting via a funnel potential. In the present study we show that such an effective potential emerges from the available lattice QCD data. Starting from the scalar glueball mass and wave function computed in lattice QCD, we indeed compute the equivalent local potential between two transverse constitu…
We present a model for odd-$C$ (negative charge parity) glueballs with three constituent gluons. The model is an extension of a previous study of two-gluon glueballs. We show that, even if spin-1 gluons seem to reproduce properly the lattice QCD spectrum for $C=+$ states, the extension for $C=-$ cannot match with the lattice results. Resorting to the helicity formalism, we show how transverse gluons fit in better agreement the lattice QCD spectrum.
Confinement in QCD is caused by vacuum fluctuations of gluon fields. There are two numerically different scales, characterizing nonperturbative QCD vacuum dynamics: a "small" scale, corresponding to gluon condensate, critical temperature etc, which is about 0.2-0.3 GeV, and a "large" one, given by inverse confining string width, glueball and gluelump masses etc, which is about 1.5-2.5 GeV. We discuss this mismatch in a picture where confinement is ensured by two-point gauge-invariant field strength correlator of special type. It supports most of perturbative and nonperturbative dynamics, while…
In a model with dynamical gluon mass, we investigate the bound states of two and three gluons via a Schrödinger equation. The short distance potential is approximated by one-gluon-exchange while the long distance part is assumed to be of a breakable string. We estimate the masses and in particular the {\it sizes} of low-lying bound states with no orbital angular momentum. By considering quantum-mechanical smearing of the gluon fields and normalizing to lattice results on $M_{0^{++}}$ and $M_{2^{++}}$, we find that the $0^{++}$ glueball is rather small in size compared with the others. The fitt…
In this work we use a mapping technique to derive in the context of a constituent gluon model an effective Hamiltonian that involves explicit gluon degrees of freedom. We study glueballs with two gluons using the Fock-Tani formalism.
In this paper we first emphasize the importance of the Pomeron (IP) for its asymptotically saturation the unitarity condition alone. After proper modified the field theory model for IP developed by Landshoff and Nochtmann, we argue that the exchange of IP in high energy $h-h'$ scattering embodies the hypothesis of the maximum non-perturbative strong interaction reaction (MNSIR) in which a constituent quark converts into a current quark and emits a color octet non-perturbative gluer. We think the IP is composed from the conjugated pair of such gluer. In the circle of non-perturbative fundamenta…
We report a glueball Regge trajectory emerging from diagonalizing a confining Coulomb gauge Hamiltonian for constituent gluons. Using a BCS vacuum ansatz and gap equation, the dressed gluons acquire a mass, of order 800 $MeV$, providing the quasiparticle degrees of freedom for a TDA glueball formulation. The TDA eigenstates for two constituent gluons have orbital, $L$, excitations with a characteristic energy of 400 $MeV$ revealing a clear Regge trajectory for $\vec{J} = \vec{L} + \vec{S}$, where $S$ is the total (sum) gluon spin. Significantly, the $S = 2$ glueball spectrum coincides with the…
The closed relativistic string carrying two point-like masses is considered as the model of a glueball with two constituent gluons. Here the gluon-gluon interaction is simulated by a pair of strings. For this system exact solutions of classical equations of motions are obtained. They describe rotational states of the string resulting in the set of quasilinear Regge trajectories with different behavior.
The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs is reexamined. The starting point is the fundamental QCD field angular momentum operator written in terms of the chromoelectric and chromomagnetic fields. First, we look at the restrictions placed on the structure of glueballs from the requirement that the QCD field angular momentum operator should satisfy the standard commutation relationshi…
Accurate non-perturbative calculations of glueballs are performed using light-front quantised SU(N) gauge theory, to leading order of the 1/N expansion. Based on early work of Bardeen and Pearson, disordered gauge-covariant link variables M on a coarse transverse lattice are used to approximate the physical gauge degrees of freedom. Simple energetics imply that, at lattice spacings of order the inverse QCD scale, the effective light-front Hamiltonian can be expanded in gauge-invariant powers of M: a colour-dielectric expansion. This leads to a self-consistent constituent structure of boundstat…
The relativistic flux tube model is an effective description of confined quarks and gluons in which the confining interaction is carried by the flux tube, a Nambu-Goto string. We first show that the relativistic flux tube model can be applied to glueballs seen as bound states of transverse constituent gluons. After a comparison of that approach with usual spinless Salpeter Hamiltonians, we compute glueball masses and decay widths. Comments about the $η$-$η'$-pseudosclar glueball problem, the glueball--Pomeron conjecture, and finite-temperature effects are finally given. We also point out the e…
It is argued that strong dynamics in the quark-gluon plasma and bound states of quarks and gluons is mostly due to nonperturbative effects described by field correlators. The emphasis in the paper is made on two explicit calculations of these effects from the first principles: one analytic using gluelump Green's functions and another using independent lattice data on correlators. The resulting hadron spectra are investigated in the range T_c < T < 2T_c. The spectra of charmonia, bottomonia, light s-sbar mesons, glueballs and quark-gluon states calculated numerically are in general agreement wi…
Glueballs are considered to be bound states of constituent gluons. Relativistic wave equation for two massive gluons interacting by the funnel-type potential is analyzed. Using two exact asymptotic solutions of the equation, we derive an interpolating mass formula and calculate glueball masses in agreement with the lattice data. We obtain the complex non-linear Pomeron trajectory, $α_P(t)$, in the whole region of $t$. The real part of the trajectory corresponds to the soft Pomeron, parameters of which are found from the fit of recent HERA data.
The masses of two-gluon glueballs are studied with a semirelativistic potential model whose interaction is a scalar linear confinement supplemented by a one-gluon exchange mechanism. The gluon is massless but the leading corrections of the dominant part of the Hamiltonian are expressed in terms of a state dependent constituent gluon mass. The Hamiltonian depends only on 3 parameters: the strong coupling constant, the string tension, and a gluon size which removes all singularities in the leading corrections of the potential. Accurate numerical calculations are performed with a Lagrange mesh me…
The constituent nature of candidate gluonic mesons can be studied by comparing their production in quark and gluon jets. The production rate for such mesons depends on the colour confinement processes at the end of the perturbative evolution. Whereas we expect enhanced production of hybrids in the fragmentation region of a gluon jet, the rate for glueballs depends on the relative importance of colour triplet and colour octet neutralization. These neutralization processes can be studied independently in events with large rapidity gaps. If octet processes turn out important the recently suggeste…
Glueballs are particles whose valence degrees of freedom are gluons and therefore in their description the gauge field plays a dominant role. We review recent results in the physics of glueballs with the aim set on phenomenology and discuss the possibility of finding them in conventional hadronic experiments and in the Quark Gluon Plasma. In order to describe their properties we resort to a variety of theoretical treatments which include, lattice QCD, constituent models, AdS/QCD methods, and QCD sum rules. The review is supposed to be an informed guide to the literature. Therefore, we do not d…
Bound state of two massive constituent gluons is studied in the potential approach. Relativistic quasi-classical wave equation with the QCD-inspired scalar potential is solved by the quasi-classical method in the complex plane. Glueball masses are calculated with the help of the universal mass formula. The hadron Regge trajectories are given by the complex non-linear function in the whole region of the invariant variable $t$. The Chew-Frautschi plot of the leading glueball trajectory, $α_P(t)$, has the properties of the t-channel Pomeron, which is dual to the glueball states in the s channel. …
Glueballs and hybrids are predicted to exist but searches for them have failed to provide conclusive evidence. One--gluon exchange is not an important part of strong interactions in this energy regime. Instead, quarks seem to interact indirectly, via changes of the QCD vacuum. Strong interactions seem to be governed by instanton--induced interactions; the chiral soliton model gives a more suitable interpretation of the $Θ^+(1540)$ than models based on the dynamics of four quarks and one antiquark.
The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons and the colored valence gluons shows that QCD can be viewed as the restricted QCD (RCD) made of the binding gluons which has the valence gluons as colored source, and simplifies the QCD dynamics greatly. In particular, it tells that the gauge covariant valence gluons can be treated as the constituents of hadrons, and generalizes the quark model to the quark and valence gluon model. So it provides a comprehensive picture of glueballs and their mixing with quarkoniums, and predicts new hybrid hadrons…
The phenomena of strong running coupling and hadron mass generating have been studied in the framework of a QCD-inspired relativistic model of quark-gluon interaction with infrared confined propagators. We derived a meson mass equation and revealed a specific new behaviour of the mass-dependent strong coupling $\hatα_s(M)$ defined in the time-like region. A new infrared freezing point $\hatα_s(0)=1.03198$ at origin has been found and it did not depend on the confinement scale $Λ>0$. Independent and new estimates on the scalar glueball mass, 'radius' and gluon condensate value have been perform…
Nonperturbative QCD approach is systematically derived starting from the QCD Lagrangian. Treating spin effects as a perturbation, one obtains the universal effective Hamiltonian describing mesons, hybrids and glueballs. Constituent mass of quark and gluon is calculated via string tension. The resulting spectrum of mesons, hybrids and glueballs obtained is in good overall agreement with lattice data and experiment.
In the last decade, lattice QCD has been able to compute the low-lying glueball spectrum with accuracy. Like other effective approaches of QCD, potential models still have difficulties to cope with gluonic hadrons. Assuming that glueballs are bound states of valence gluons with zero current mass, it is readily understood that the use of a potential model, intrinsically non covariant, could be problematic in this case. The main challenge for this kind of model is actually to find a way to introduce properly the more relevant degree of freedom of the gluon: spin or helicity. In this work, we use…
The systematic approach to study bound states in gluodynamics is presented. The method utilizes flow equations together with low-energy phenomenology, that provides the perturbative renormalization scaling in conjuction with the change of the basis to constituent gluon states. The renormalized effective Hamiltonian of gluodynamics up to the second order is obtained at low energies, which provides a kind of constituent gluon model for glueball bound states. The approach allows to include perturbative QCD corrections into nonperturbative calculations of many-body techniques. The performed numeri…
The non-Abelian nature of QCD suggests that particles that have a gluon constituent, such as glueballs or hybrids, should exist. Experiments WA76, WA91 and WA102 have performed a dedicated search for these states in central production using the CERN Omega Spectrometer. New results from central production show that there is a kinematical filter which can select out glueball candidates from known qqbar states. A further study of this at high energies is essential in order to get information on the M(X0) > 2 GeV region. This paper describes how this could be done using the the ALICE detector at t…
In constituent models, glueballs are described as bound states of effective gluons. The dynamical mass generation lead to a gluon mass without violating gauge invariance. One can then consider three degrees of freedom for those effective massive gluons. However, models with only two degrees of freedom are shown to be in better agreement with the lattice glueball spectrum. I review both models for two- and three-gluon models and explain why even though the gluon gains a mass, it behaves as a massless particle with only two degrees of freedom.
A simple relativistic quantum field model with the Yukawa-type interaction is considered to demonstrate that the analytic confinement of the constituent ("quarks") and carrier ("gluons") particles explains qualitatively the basic dynamical properties of the spectrum of mesons considered as two-particle stable bound states of quarks and gluons: the quarks and gluons are confined, the glueballs represent bound states of massless gluons, the masses of mesons are larger than the sum of the constituent quark masses and the Regge trajectories of mesonic orbital excitations are almost linear.
We estimate the potential energy for a system of three static gluons in Lattice QCD. This is relevant for the different models of three-body glueballs have been proposed in the literature, either for gluons with a constituent mass, or for massless ones. A Wilson loop adequate to the static hybrid three-body system is developed. We study different spacial geometries, to compare the starfish model with the triangle model, for the three-gluon potential. We also study two different colour structures, symmetric and antisymmetric, and compare the respective static potentials. A first simulation is p…
A systematic procedure to consistently formulate a field theoretical, QCD bound state problem with a fixed number of constituents is outlined. The approach entails applying the Hamiltonian flow equations, which are a set of continuous unitary transformations, to a QCD motivated Hamiltonian with a confining interaction. The method is developed in detail for gluodynamics in the Coulomb gauge to obtain an effective block-diagonal Hamiltonian appropriate to a reduced Fock space with fixed number of dynamical gluons. Standard many-body techniques are used to numerically diagonalize this Hamiltonian…
A perturbative expansion for QED and QCD bound states is formulated in $A^0=0$ gauge. The constituents of each Fock state are bound by their instantaneous interaction. In QCD an O($α_s^0$) confining potential arises from a homogeneous solution of Gauss' constraint. The potential is uniquely determined by the QCD action, up to a universal scale. The Cornell potential is reproduced for quarkonia, and corresponding ones found for higher Fock states, baryons and glueballs.
Based on the constituent quasiparticle model of quark-gluon plasma (QGP), the matrix elements of the density operator and the Wigner function in the color phase space are presented in form of color path integrals over Wiener and SU(3) group Haar measures. Monte Carlo calculations of quark and gluon momentum distributions and spatial pair distribution functions have been carried out for the strongly coupled QGP plasma in thermal equilibrium at zero baryon chemical potential. The Debye screening mass and the running coupling constant have been obtained from the spatial pair distribution function…
We systematically compute the effective short-range potentials arising from second order QCD-diagrams related to bound states of quarks, antiquarks, and gluons. Our formalism relies on the assumption that the exchanged gluons are massless, while the constituent gluons as well as the lightest quarks acquire a nonvanishing constituent mass because of confinement. The potentials we obtain include the first relativistic corrections, thus spin-spin terms, spin-orbit terms, etc. Such effective potentials are expected to be relevant for the building of accurate potential models describing usual hadro…
We study the photon spectrum in the radiative decays of the charmonium $\frac{1}Γ\frac{dΓ(J/ψ\rightarrowγgg)}{dz}$ as an excellent scene for hunting the exotic mesons (hybrids $q\bar{q}g$ and glueballs $gg$) and an ideal frame for the theoretical and phenomenological investigations of the gluon nature in IR, by subtle estimation of its non-zero effective mass which seems required in Quark-Gluon Constituent Model (QGCM) for identifying the nature of these exotic species.
The systematic approach to study bound states in quantum chromodynamics is presented. The method utilizes nonperturbative flow equations in the confining background, that makes possible to perform perturbative renormalization and to bring the QCD Hamiltonian to a block-diagonal form with the number of quasiparticles conserving in each block. The effective block-diagonal Hamiltonian provides constituent description for hadron observables. The renormalized to the second order effective Hamiltonian of gluodynamics in the Coulomb gauge is obtained at low energies. The masses for scalar and pseudos…
Since gluons in QCD are interacting fundamental constituents just as quarks are, we expect that in addition to mesons made from a quark and an antiquark, there should also be glueballs and hybrids (bound states of quarks, antiquarks and gluons). In general, these states would mix strongly with the conventional q-bar-q mesons. However, they can also have exotic quantum numbers inaccessible to q-bar-q mesons. Confirmation of such states would give information on the role of "dynamical" color in low energy QCD. In the quenched approximation we present a lattice calculation of the masses of mesons…
In this article, we study the mass spectrum of the baryon-antibaryon bound states $p\bar{p}$, $Σ\barΣ$, $Ξ\barΞ$, $Λ\barΛ$, $p\bar{N}(1440)$, $Σ\barΣ(1660)$, $Ξ\barΞ^\prime$ and $Λ\barΛ(1600)$ with the Bethe-Salpeter equation. The numerical results indicate that the $p\bar{p}$, $Σ\barΣ$, $Ξ\barΞ$, $p\bar{N}(1440)$, $Σ\barΣ(1660)$, $Ξ\barΞ^\prime$ bound states maybe exist, and the new resonances X(1835) and X(2370) can be tentatively identified as the $p\bar{p}$ and $p\bar{N}(1440)$ (or $N(1400)\bar{p}$) bound states respectively with some gluon constituents, and the new resonance X(2120) may b…
