The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Our results are in good agreement with other approaches and lattice calculation for the odderon trajectory but differ strongly from lattice in the $J^{+-}$ sector. We propose a possible explanation for this problem.
The three-gluon glueball states are studied with the generalization of a semirelativistic potential model giving good results for two-gluon glueballs. The Hamiltonian depends only on 3 parameters fixed on two-gluon glueball spectra: the strong coupling constant, the string tension, and a gluon size which removes singularities in the potential. The Casimir scaling determines the structure of the confinement. Low-lying $J^{PC}$ states are computed and compared with recent lattice calculations. A good agreement is found for $1^{--}$ and $3^{--}$ states, but our model predicts a $2^{--}$ state muc…
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…
A Reply to "Comment on `Finding the $0^{--}$ Glueball' " [arXiv:1702.06634] and comment on `Is the exotic $0^{--}$ glueball a pure gluon state?' [arXiv:1611.08698]
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.
Signatures of dominant and central production of glueballs (binary gluonic mesons) in heavy ion and hadromic collisions are discussed. Search strategies are proposed.
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 th…
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.
We review the phenomenological and theoretical evidences for dynamical gluon mass generation and the main features of the glueball spectrum in (pure gauge) Yang-Mills theories. The mixing between glueball and conventional $\bar q q$ states in $f_0$ scalar mesons is discussed. For pseudoscalar mesons, the inclusion of the glue field in an effective low energy theory is presented leading to a third isoscalar $η''$ partner of the $η$ and $η'$. Branching ratios for processes involving $η''$ are given and, when available, compatible with data for $η(1405)$.
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.
We study the scalar, vector and tensor two-gluon and trigluon glueball spectra in the framework of 5-dimension dynamical holographic QCD model, where the metric structure is deformed self-consistently by the dilaton field. For comparison, the glueball spectra are also calculated in the hard-wall and soft-wall holographic QCD models. In order to distinguish glueballs with even and odd parities, we introduce the positive and negative coupling between the dilaton field and glueballs, and for higher spin glueballs, we introduce a deformed 5-dimension mass. With this set-up, there is only one free …
We discuss the recent observation of f_0(980) in charmless B-decays and in gluon jets which hints toward a gluonic coupling of this meson similar to eta'. Further predictions on B-decays into scalar particles are presented. Charmless B decays also show a broad K Kbar (and possibly pi pi) S-wave enhancement which we relate to the 0^{++} glueball. These gluonic mesons represent a sizable fraction of the theoretically derived decay rate for b -> sg.
We discuss the energy loss of energetic parton jets in quark-gluon plasma above the deconfinement temperature $T_c$ by the interaction with scalar and pseudoscalar glueballs. It is shown that the loss by this mechanism is quite important and may play the important role of the observed jet-quenching.
An unambiguous identification of glueballs in experiments will be of great significance, because their existence is an important test of QCD. The proposal, advanced here, is to experimentally search for glueballs as peaks in the invariant mass of a leading K_S-pair fragmenting from an energetic gluon jet out of high-statistics three-jet events in hadronic decays of the weak neutral Z boson. Using a physically motivated model of the gluon-glueball fragmentation function, we find a substantial fragmentation rate into a leading glueball. It is very likely that a search, along the lines suggested …
In the preceding paper, a rigorous three-dimensional relativistic equation for two-gluon bound states was derived from the QCD with massive gluons and represented in the angular momentum representation. In order to apply this equation to calculate the glueball spectrum, in this paper, the equation is recast in an equivalent three-dimensional relativistic equation satisfied by the two-gluon positive energy state amplitude. The interaction Hamiltonian in the equation is exactly derived and expressed as a perturbative series. The first term in the series describes the one-gluon exchange interacti…
A rigorous three-dimensional relativistic equation satisfied by two-gluon bound states is derived from the QCD with massive gluons. With the gluon fields and the quark fields being expanded in terms of the gluon multipole fields and the spherical Dirac spinors respectively, the equation is well established in the angular momentum representation and hence is much convenient for solving the problem of two-gluon glueball spectra. In particular, the interaction kernel in the equation is exactly derived and given a closed expression which includes all the interactions taking place in the two-gluon …
In this paper we continue previous efforts in the literature to determine phenomenological values for the gluon mass by confronting theoretical results obtained in a theory of massive gluons with experimental values or results directly referring to the nontrivial structure of the Yang-Mills vacuum, e.g. to the presence of the gluon condensate. The decays of heavy quarkonia into 3 gluons and 2 gluons + photon are considered in detail as well as the correlators of the electromagnetic current and the scalar glueball current. Based on the analysis for the latter quantities a value for the gluon ma…
One-loop quark contributions to the dimension-four gluon condensate term in the operator product expansion (OPE) of the scalar glueball correlation function are calculated in the MS-bar scheme in the chiral limit of $n_f$ quark flavours. The presence of quark effects is shown not to alter the cancellation of infrared (IR) singularities in the gluon condensate OPE coefficients. The dimension-four gluonic condensate term represents the leading power corrections to the scalar glueball correlator and, therein, the one-loop logarithmic contributions provide the most important condensate contributio…
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…
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 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…
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.
We present a new calculation of the mass and width of the exotic $0^{--}$ glueball in the framework of the QCD sum rules. We next construct a new current which couples to a pure $0^{--}$ gluon state and derive consistent and stable sum rules. A previously used current in this approach was shown to be inconsistent. We obtain for this state a mass $M_G=6.3^{+0.8}_{-1.1}$ GeV and an upper limit for the total width $Γ_G\leq 235$ MeV. These values can be used as an important guide for the experimental search of this exotic state. We argue that the mixing of this glueball state with $0^{--}$ tetraqu…
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…
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.
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 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…
Using a simple relativistic QFT model of scalar fields we demonstrate that the analytic confinement (propagator is an entire function in the complex p^2-plane) and the weak coupling constant lead to the Regge behaviour of the two-particle bound states. In QCD we assume that the gluon vacuum is realized by the selfdual homogeneous classical field which is the solution of the Yang-Mills equations. This assumption leads to analytical confinement of quarks and gluons. We extract the colorless 0(++) two-glouon state from the QCD generating functional in the one-gluon exchange approximation. The mas…
Using a simple relativistic QFT model of scalar fields we demonstrate that the analytic confinement (propagator is an entire function in the complex $p^2$--plane) and the weak coupling constant lead to the Regge behaviour of the two-particle bound states. In QCD we assume that the gluon vacuum is realized by the self-dual homogeneous classical field which is the solution of the Yang-Mills equations. This assumption leads to analytical confinement of quarks and gluons. We extract the colorless $0^{++}$ two-gluon state from the QCD generating functional in the one-gluon exchange approximation. T…
Nonlocal gluon condensates are vacuum expectations of the product of gluon field strength tensors. Short-distance expansions of two-, three-, and four-gluon condensates are presented up to dimension-8 local operators. We propose a method for calculating the Wilson coefficients based on the presented expansions and the Feynman diagram technique in the background field approach. The method is demonstrated using the glueball current correlators as examples. Methodological aspects of the background field approach are discussed in relation to glueball studies within QCD sum rules. We confirm the re…
The spectrum of two-gluon glueballs below 3 GeV is investigated in a potential model with dynamical gluon mass using variational method. The short distance potential is approximated by one-gluon exchange, while the long distance part is taken as a breakable string. The mass and size of the radial as well as orbital excitations up to principle quantum number n=3 are evaluated. The predicted mass ratios are compared with experimental and lattice results.
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.
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…
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…
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.
Using a bound-state model of weakly bound gluons for glueballs made of two gluons and a natural generalization of the perturbative QCD formalism for exclusive hadronic processes, we present results for glueball production in radiative J/psi, Upsilon decays into several possible glueball states, including L \not= 0 ones. We perform a detailed phenomenological analysis, presenting results for the more favored experimental candidates and for decay angular distributions.
We present the new developments in the physics of XYZ mesons and glueballs and discuss the connection between properties of the $XYZ$ mesons and glueballs, and the structure of the QCD vacuum. It is shown that the mixing between quark and gluon degree of freedoms induced by the nontrivial topological structure of the QCD vacuum might affect strongly the properties of the exotic hadrons. A new interpretation of the $XYZ$ mesons as the mixing between radial excitations of light quark-antiquark systems and states with heavy quark content is suggested. We introduce also a new mechanism of quarkoni…
The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons (the neurons) and the colored valence gluons (the chromons) gauge independently naturally generalizes the quark model to the quark and chromon model which could play the central role in hadron spectroscopy. We discuss the color reflection symmetry, the fundamental symmetry of the quark and chromon model, and explain how it describes the glueballs and the glueball-quarkonium mixing in QCD. We present the numerical analysis of glueball-quarkonium mixing in $0^{++}$, $2^{++}$, and $0^{-+}$ sectors bel…
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…
Based on correction from instanton-gluon interference to correlation function, the properties of the $0^{-+}$ pseudoscalar glueball is investigated in a family of finite-width Gaussian sum rules. In the framework of semiclassical expansion for quantum chromodynamics $(\textrm{QCD})$ in the instanton liquid background, the contribution arising from the the interference between instantons and the quantum gluon fields is calculated, and included in the correlation function together with pure-classical contribution from instantons and the perturbative one. The interference contribution is turned t…
In a recent article, W.-S. Hou and G.-G. Wong [Phys. Rev. D {\bf 67}, 034003 (2003)] have investigated the spectrum of two-gluon glueballs below 3 GeV in a potential model with a dynamical gluon mass. We point out that, among the 18 states calculated by the authors, only three are physical. The other states either are spurious or possess a finite mass only due to an arbitrary restriction of the variational parameter.
The formation and spectrum of two-particle bound states are investigated within a simple relativistic quantum field model with the Yukawa-type interaction. Within this approach, relatively weakly interacting quarks and gluons form stable bound states under the analytic confinement. By introducing a minimal set of free parameters (the quark masses, the coupling constant and the confinement 'radius') and by solving the Bethe-Salpeter equation with one-gluon exchange, we satisfactorily explain the experimental data for most known mesons and the glueball.
We discuss a notion of gluon-glueball duality analogous to quark-hadron duality. We apply this idea to the radiative decay of heavy orthoquarkonium, $Q\bar Q \to γg g$, which has been used to search for glueballs. The duality is first introduced in two simplified contexts: (i) a hypothetical version of QCD without any light quarks and (ii) QCD in the large-$N_c$ limit. We then discuss how an approximate form of this duality could hold in real QCD, based on a hierarchy of time scales in the temporal evolution of the $gg$ subsystem in radiative orthoquarkonium decay. We apply this notion of gluo…
Recently Buniy and Kephart made an astonishing empirical observation, which anyone can reproduce at home. Measure the {\it lengths} of closed knots tied from ordinary rope. The ``double do-nut'', and the beautiful trefoil knot are examples. Tie the knots tightly, and glue or splice the tails into a seamless unity. Compare two knots with corresponding members of the mysterious particle states known as ``glueball'' candidates in the literature. Propose that the microscopic glueball mass ought to be proportional to the macroscopic mass of the corresponding knot. Fit two parameters, then {\it pred…
We study the spectra of two-gluon glueballs and three-gluon oddballs and corresponding equation of state in $5$-dimensional deformed holographic QCD models in the graviton-dilaton system, where the metric, the dilaton field and dilaton potential are self-consistently solved from each other through the Einstein field equations and the equation of motion of the dilaton field. We compare the models by inputting the dilaton field, inputting the deformed metric and inputting the dilaton potential, and find that with only 2 parameters, the $5$-dimensional holographic QCD model predictions on gluebal…
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.
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.
By studying the $η_c$ exclusive decay to double glueballs, we introduce a model to mimic phenomenologically the gluon-pair-vacuum interaction vertices, namely the $0^{++}$ model. Based on this model, we study glueball production in pseudoscalar quarkonium decays, explicitly $η_c \to f_0(1500)η(1405)$, $η_b\to f_0(1500)η(1405)$ and $η_b\to f_0(1710)η(1405)$ processes. Among them $f_0(1500)$ and $f_0(1710)$ are well-known scalars possessing large glue components and $η(1405)$ is a potential candidate for pseudoscalar glueball. The preliminary calculation results indicate that these processes are…
The existence of glueballs within QCD is uncontroversial but their experimental verification is still in doubt. We discuss the new possibilities for a search of glueballs as the leading object in gluon jets at the LHC. We summarize previous results from LEP which demonstrate a significant excess rate of electrically neutral leading clusters in comparison with MC models.
We study glueball G production in gluonic penguin decay B -> X_s G, using next-to-leading order b -> s g^* gluonic penguin interaction and an effective coupling of a glueball to two gluons. The effective coupling allows us to study the decay rate of a glueball to two pseudoscalars in the framework of chiral perturbation theory. Identifying the f_0(1710) to be a scalar glueball, we then determine the effective coupling strength with the branching ratio of f_0(1710) -> K KBar. We find that the charm penguin to be important and obtain a sizable branching ratio for Br(B -> X_s G) in the range of (…
We investigate AdS/QCD duality for the two-point correlation function of the lowest dimension scalar glueball operator, in the case of the IR soft wall model. We point out the role of the boundary conditions for the bulk-to-boundary propagator in determining the gluon condensates. We show that a low energy QCD theorem can be obtained within the AdS approach, together with a gluon condensate close to the commonly accepted value and robust against perturbation of the background dilaton field.
We calculate the mass of $0^{-+}$ triple-valence-gluon resonance, the trigluon glueball, with QCD sum rules. Its mass is found to be approximately in the region between 1.9 GeV and 2.7 GeV with some theoretical uncertainties. Moreover, it is likely that the new BES measurement of the $p \bar{p}$ enhancement near threshold in the $J/ψ$ decays exhibits the behavior of this trigluon state. Our analyzes favor the baryonium-gluonium mixing picture for the BES observation.
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…
The problem of glueball mass spectra using the relativistic Dirac equation is studied. Also the Breit-Fermi approach used to obtaining hyperfine splitting in glueballs. Our approach is based on the assumption, that the nature and the forces between two gluons are the short-range. We were to calculate the glueball masses with used screened potential.
We study a pure gluon plasma in the context of quasiparticle models, where the plasma is considered as an ideal gas of massive bosons. In order to reproduce SU(3) gauge field lattice data within such a framework, we review briefly the necessity to use a temperature-dependent gluon mass which accounts for color interactions between the gluons near $T_{\text{c}}$ and agrees with perturbative QCD at large temperatures. Consequently, we discuss the thermodynamics of systems with temperature-dependent Hamiltonians and clarify the situation about the possible solutions proposed in the literature to …
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.
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 $T > T_c$. We discuss the other physical consequences resulting from the drastic change of the pseudoscalar glueball mass above …
We study two- and three-gluon glueballs of $C=+$ using the method of QCD sum rules. We systematically construct their interpolating currents, and find that all the spin-1 currents of $C=+$ vanish. This suggests that the ``ground-state'' spin-1 glueballs of $C=+$ do not exist within the relativistic framework. We calculate masses of the two-gluon glueballs with $J^{PC} = 0^{\pm+}/2^{\pm+}$ and the three-gluon glueballs with $J^{PC} = 0^{\pm+}/2^{\pm+}$. We propose to search for the $J^{PC} = 0^{-+}/2^{-\pm}/3^{\pm-}$ three-gluon glueballs in their three-meson decay channels in future BESIII, Gl…
