We extend previous calculations of leading-order correlation functions of spin-0 and spin-1 light quarkonium hybrids to include QCD condensates of dimensions five and six, with a view to improving the stability of QCD sum-rules analyses in previously unstable channels. Based on these calculations, prior analyses in the literature, and its phenomenological importance, we identify the exotic $J^{PC}=0^{+-}$ channel as the most promising for detailed study. Using Gaussian sum-rules constrained by the Hölder inequality, we calculate masses of light (nonstrange and strange) quarkonium hybrid mesons with $J^{PC}=0^{+-}$. We consider single narrow, single wide, and double narrow resonance models, and find that the double narrow resonance model yields the best agreement between QCD and phenomenology. In both non-strange and strange cases, we find hybrid masses of $2.60$ GeV and $3.57$ GeV.
The 125 GeV resonance discovered at the LHC could be a heavy quarkonium pseudoscalar meson. The diagonalization of the mass matrix of the isoscalar quarkonium states $|ζ>$ and $|ζ^{0'}>$ produces the states identified with the pseudoscalar heavy quarkonium mesons $ζ^0$ and $ζ^{0'}$. For a mixing angle $ϕ\sim 36\,^{\circ}$ the mass of the bound state pseudoscalar resonance $ζ^0$ is $m_{ζ^0}\sim 125$ GeV. The decay rates of the quarkonium $ζ^0$ meson are estimated and compared to the standard model Higgs boson predictions. The importance of determining the spin-parity of the 125 GeV resonance is…
Modifications of the mass spectrum the quarkonium induced by its virtual dissociation into a pair of heavy mesons is considered. Coupling between quark and mesonic channels results in noticeable corrections to spin-dependent mass splitting. In particular, the observable hierarchy of mass splittings in the $χ_c, χ_b$ and $χ'_b$ multiplets is reproduced.
This talk summarizes recent developments in quarkonium spectroscopy. I comment on the relation between the Z_b(10610) and Z_b(10650) and recently observed Z_c(3900) and Z_c(4025) states. Then I discuss a number of calculations using non-relativistic effective field theory for the X(3872), Z_b(10610), and Z_b(10650), under the assumption that these are shallow molecular bound states of charm or bottom mesons.
We compute the c \bar{b} spectrum from a first principle Salpeter equation obtained in a preceding paper. For comparison we report also the heavy-light quarkonium spectrum and the hyperfine separations previously presented only in a graphical form. Notice that all results are parameter free.
In this article, we study the vector meson transitions among the charmonium and bottomonium states with the heavy quark effective theory in an systematic way, and make predictions for the ratios among the vector meson decay widths of a special multiplet to another multiplet. The predictions can be confronted with the experimental data in the future.
The exclusive processes are considered, where a point-like source of heavy quark-antiquark pairs $Q \bar Q$, e.g. their electromagnetic current, produces a pair consisting of a heavy quarkoniumlike exotic meson (tetraquark) or baryon (pentaquark) and a light meson or an antibaryon. For a sufficiently large mass of the heavy quark $m_Q$ there is a range of the energy $E$ above the $Q \bar Q$ threshold, where $E \ll m_Q$ and still the energy is large compared to the strong interaction scale, $E \gg Λ_{QCD}$. It is shown that in this energy range, where the heavy quarks are nonrelelativistic, a s…
We use QCD Laplace sum-rules to explore mixing between conventional mesons and hybrids in the heavy quarkonium vector $J^{PC}\!=\!1^{--}$ channel. Our cross-correlator includes perturbation theory and contributions proportional to the four-dimensional and six-dimensional gluon condensates. We input experimentally determined charmonium and bottomonium hadron masses into both single and multi-resonance models in order to test them for conventional meson and hybrid components. In the charmonium sector we find evidence for meson-hybrid mixing in the $J/ψ$ and a $\approx4.3$ GeV resonance. In the b…
The processes of P-wave Quarkonium exclusive decays to two mesons are investigated, in which the final state vector mesons with various polarizations are considered separately. In the calculation, the initial heavy quarkonia are treated in the framework of non-relativistic quantum chromodynamics, whereas for light mesons, the light cone distribution amplitudes up to twist-3 are employed. It turns out that the higher twist contribution is significant and provides a possible explanation for the observation of the hadron helicity selection rule violated processes $χ_{c1}\rightarrow ϕϕ,ωω$ by the …
Since nine years experiments have been observing a host of exotic states decaying into heavy quarkonia. The interpretation of most of them still remains uncertain and, in some cases, controversial, notwithstanding a considerable progress has been made on the quality of the experimental information available and a number of ideas and models have been put forward to explain the observations. In this mini-review we will summarize the measurements, with the most recent updates, and list the useful ones yet to be done. We will discuss the problem of the spin of the X, which could hide some major su…
The pseudoscalar quarkonia exclusive decays to light mesons still poses a challenge to the theoretical understanding of quarkonium properties in decay. In this work, we evaluate the processes of pseudoscalar heavy quarkonium decays into vector meson pairs, especially the helicity suppressed processes of $η_b\rightarrow J/ψJ/ψ$ and $η_c\rightarrow VV$. In the frame of NRQCD, the branching fraction of $Br[η_b\rightarrow J/ψJ/ψ]$ are evaluated at the next-to-leading order of perturbative QCD; and within the light-cone distribution formalism, we calculate also the higher twist effects in these pro…
Investigations on heavy quarkonium hybrid mesons with exotic quantum numbers $J^{PC}=2^{+-}$
College of Physical Science and Technology, Bohai University（渤海大学物理科学与技术学院）；School of Physics, Southeast University（东南大学物理学院）；School of Physics, Sun Yat-Sen University（中山大学物理学院）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
We explore conventional meson-hybrid mixing in $J^{PC}=1^{++}$ heavy quarkonium using QCD Laplace sum-rules. We calculate the cross-correlator between a heavy conventional meson current and heavy hybrid current within the operator product expansion, including terms proportional to the four- and six-dimensional gluon condensates and the six-dimensional quark condensate. Using experimentally determined hadron masses, we construct models of the $1^{++}$ charmonium and bottomonium mass spectra. These models are used to investigate which resonances couple to both currents and thus exhibit conventio…
At the large transverse momentum region, the production of heavy-heavy bound-states such as charmonium, bottomonium, and $\bar bc$ mesons in high energy $e^+e^-$ and hadronic collisions is dominated by parton fragmentation. We calculate the heavy quark fragmentation functions into the D-wave quarkonium and $\bar bc$ mesons to leading order in the strong coupling constant and in the non-relativistic expansion. In the $\bar b c$ meson case, one set of its D-wave states is expected to lie below the open flavor threshold. The total fragmentation probability for a $\bar b$ antiquark to split into t…
The Belle II experiment at the SuperKEKB energy-asymmetric $e^+e^-$ collider is a substantial upgrade of the B factory facility at KEK in Tsukuba, Japan. It aims to record a factor of 50 times more data than its predecessor. The experiment completed a commissioning run in 2018, and began full operation in early 2019. Belle II is uniquely capable of studying the so-called XYZ particles: heavy exotic hadrons consisting of more than three quarks. First discovered by Belle, these now number in the dozens, and represent the emergence of a new category within quantum chromodynamics. This talk will p…
The N-dimensional radial Schrodinger equation with an extended Cornell potential is solved. The analytical exact iteration method is applied. The energy eigenvalues are calculated in the N-dimensional space. The charmonium meson, the bottomonium meson and the bc meson masses are calculated in the N-dimensional space. The special cases are obtained from the general case. The study of the effect of dimensionality number is studied. The mean value of the radius and the mean square velocity of charmonium meson, bottomonium meson, and bc meson are calculated. The present results are improved in com…
In this work, we present an updated study about the interactions of quarkonia with surrounding hadronic medium. The meson-meson interactions are described with a chiral effective Lagrangian within the framework of unitarized coupled channel amplitudes. In particular, we extend a previous work performed in the charmonium sector by calculating the cross-sections for $Υ$ scattering by light pseudoscalar mesons ($π, K, η$) and vector mesons ($ρ, K^\ast, ω$). We evaluate the relevant channels and compare the results with existing literature. The analysis is completed by including the finite-tempera…
We use QCD Laplace sum-rules to study meson-hybrid mixing in vector ($1^{--}$) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multi-resonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compa…
Flavor-exotic tetraquark mesons have recently been observed in the heavy-quark pair sectors of QCD, including two isospin multiplets in the b b-bar sector, Z_b(10610) and Z_b(10650), and one isospin multiplet in the c c-bar sector, Z_c(3900). We identify Z_b and Z_c as tetraquark mesons that are analogs of quarkonium hybrids with the gluon field replaced by an isospin-1 excitation of the light-quark fields. Given the identification of Y(4260) and Z_c(3900) as a ground-state charmonium hybrid and tetraquark, respectively, lattice QCD calculations of the charmonium spectrum can be used to estima…
In this work we calculate the lifetime of quarkonium moving with velocity $v$ through a quark gluon plasma at temperature $T$. We also investigate the stability of heavy mesons with respect to the effects of color charge screening. An explicit, configuration-space potential is found for the screened interaction between the quarks constituting the meson. We solve the Schrödinger equation for the relative motion of the quarks in this non-spherical potential. In this way, we determine the range of $v,T$ values for which the meson is bound. When a bound state exists, we use the bound-state wavefun…
The XYZ mesons are unexpected mesons containing a heavy quark-antiquark pair that have been discovered during the last decade. The models for the XYZ mesons that have been proposed include conventional quarkonium, quarkonium hybrids, and quarkonium tetraquarks, whose four constituents can be clustered in several possible ways. None of the models have provided a compelling pattern for the XYZ mesons. The most promising theoretical approaches within QCD are lattice QCD for the c c-bar mesons, lattice NRQCD for the b b-bar mesons, and the Born-Oppenheimer approximation. The additional hints that …
We investigate the pair production of S-wave heavy quarkonium at the LHC in the color-singlet mechanism (CSM) and estimate the contribution from the gluon fragmentation process in the color-octet mechanism (COM) for comparison. With the matrix elements extracted previously in the leading order calculations, the numerical results show that the production rates are quite large for the pair production processes at the LHC. The $p_t$ distribution of double $J/ψ$ production in the CSM is dominant over that in the COM when $p_t$ is smaller than about 8GeV. For the production of double $Υ$, the contr…
The mass splitting between the quarkonium spin-singlet state $h$ ($J^{PC} = 1^{+-}$) and the spin average of the quarkonium spin-triplet states $χ$ ($J^{PC} = 0^{++}, 1^{++}, 2^{++}$) is seen to be astonishingly small, not only in the charmonium and bottomonium cases where the relevant masses have been measured, but in positronium as well. We find, both in nonrelativistic quark models and in NRQCD, that this hyperfine splitting is so small that it can be used as a test of the pure $Q\bar Q$ content of the states. We discuss the $2P$ states of charmonium in the vicinity of $3.9$ GeV, where the …
We present factorization theorems for two exclusive heavy-quarkonium production processes: production of two quarkonia in e^+e^- annihilation and production of a quarkonium and a light meson in B-meson decays. We describe the general proofs of factorization and supplement them with explicit one-loop analyses, which illustrate some of the features of the soft-gluon cancellations. We find that violations of factorization are generally suppressed relative to the factorized contributions by a factor v^2m_c/Q for each S-wave charmonium and a factor m_c/Q for each L-wave charmonium with L>0. Here, v…
We report on a recent QCD based research on hybrid mesons containing $c\bar c$ or $b\bar b$ quarks. We present results for the spectrum, the decay widths to heavy quarkonium, and the role of mixing with the latter. We point out that mixing with heavy quarkonium provides a potentially large source of spin symmetry breaking. We identify candidates to hybrid mesons among the so called XYZ states in the charmonium and bottomonium spectrum.
The research presented here uses QCD sum rules (QSR) to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third theme involves developing a renormalization methodology for these higher or…
Nucleon electromagnetic form factors are considered in the framework of the generalized Skyrme model with dilaton-quarkonium field. In our recent publication we have got big discrepancies between calculated form factors and dipole approximation formula. Here we have reasonably good accordance between them in finite impulse region after vector meson dominance have been taken into account. Omega and Rho -meson have been included into only hadron structure of the photon.
We revisit holographic mesons in the D4/D6 model to study holographic light vector mesons and the properties of heavy quarkonium in confining and deconfining phases. To treat the light mesons and heavy quarkonium on the same footing, we use the same compactification scale MKK in both systems. We observe that like scalar and pseudo-scalar mesons the vector meson mass is linearly proportional to the square root of the quark mass, when the quark mass is large. With a MKK fixed by light meson masses, we calculate the mass of heavy quarkonium in confining and deconfining phases. We also obtain the …
The 125 GeV resonance discovered at the LHC could be a heavy quarkonium, spin 0 pseudoscalar meson $ζ^0$. The decay rates of the $ζ^0$ meson resonance are calculated and compared to the standard model Higgs boson decay rates. The branching ratios and signal strengths for $ζ\rightarrowγγ$, $ζ\rightarrow Zγ$, $ζ\rightarrow ZZ^*$ and $ζ\rightarrow WW^*$ are approximately the same as the Higgs boson branching ratios and signal strengths. The decay rates for $ζ\rightarrowτ^+τ^-$, $ζ\rightarrow b\bar b$ and $ζ\rightarrow c\bar c$ are suppressed compared to the Higgs boson decay rates. Accurate branc…
In this contribution, we discuss the possible importance of continuum-coupling (or threshold) effects in heavy quarkonium spectroscopy. Our calculations are carried out in a coupled-channel model, where meson-meson higher Fock (or molecular-type) components are introduced in $Q \bar Q$ bare meson wave functions by means of a pair-creation mechanism. After providing a quick resume of the main characteristics of the coupled-channel model, we briefly discuss its application to the calculation of the masses of heavy quarkonium-like $χ_{\rm c}(2P)$ and $χ_{\rm b}(3P)$ states with threshold correcti…
To illustrate the campaign to understand heavy quarkonium systems, I focus on a puzzling new state, $X(3872) \to π^+π^- J/ψ$. Studying the influence of open-charm channels on charmonium properties leads us to propose a new charmonium spectroscopy: additional discrete charmonium levels that can be discovered as narrow resonances of charmed and anticharmed mesons. I recall some expectations for a new spectroscopy of mesons with beauty and charm, the $B_c$ ($b\bar{c}$) system. Throughout, I call attention to open issues for theory and experiment.
Two-photon decays of light scalar mesons are discussed within the quarkonium and tetraquark asignements: in both cases the decay rate of the sigma resonances turns out to be smaller than 1 keV.
Heavy quarkonia, Bc-meson, and CS-meson masses are calculated within the framework of the N-dimensional radial Schrodinger equation. The Cornell potential is extended by including the harmonic oscillator potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov-Uvarov (NV) method. The energy eigenvalues are obtained in the three-dimensional space. The mass of spectra of charmonium, bottomonium, and mesons are calculated. The effect of dimensionality number on the mass of quarkonium is investigated. A comparison with oth…
The photonuclear production of vector mesons in ultraperipheral heavy ion collisions is investigated within the collinear approach using different parameterizations for the nuclear gluon distribution. The integrated cross section and the rapidity distribution for the $AA \to V AA$ ($V = J/Ψ, Υ$) process are computed for energies of RHIC and LHC. A comparison with the recent PHENIX data on coherent production of $J/Ψ$ mesons is also presented. We demonstrate that the study of the exclusive quarkonium photoproduction can be used to constrain the nuclear effects in the gluon distribution.
We outline the proofs of the factorization theorems for exclusive two-body charmonium production in B-meson decay and e^+e^- annihilation to all orders in perturbation theory in quantum chromodynamics. We find that factorized expressions hold up to corrections of order m_c/m_b in B-meson decay and corrections of order m_c^2/s in e^+e^- annihilation, where m_c is the charm-quark mass, m_b is the bottom-quark mass, and root-s is the e^+e^- center-of-momentum energy.
Double $J/ψ$ production on the order of 20-30 pb has been observed by the NA3 collaboration. These $ψψ$ pairs, measured in $π^- N$ interactions at 150 and 280 GeV$/c$ and in $pN$ interactions at 400 GeV$/c$, carry a large fraction of the projectile momentum, $x_{ψψ} \geq 0.6$ for the 150 GeV$/c$ beam and $\geq 0.4$ at 280 GeV$/c$. We examine several sources of $ψψ$ pair production within QCD, including ${\cal O}(α_s^4)$ $ψψ$ production, leading-twist $b \overline b$ production and decay, and the materialization of heavy-quark Fock states in the projectile. We estimate the production cross sect…
A mixing of near-threshold quarkonium-like resonances with heavy meson-antimeson pairs results in an enhancement of heavy quark spin symmetry breaking, since the meson pairs are not eigenstates of the heavy quark spin. The decomposition of $P$-wave states of meson pairs in terms of the heavy-quark-pair spin states is considered in the channel with $J^{PC}=1^{--}$, which is directly produced in $e^+e^-$ annihilation. Specific processes are suggested for experimental study of the effects of the mixing with heavy meson pairs and of the internal spin structure of bottomonium and charmonium resonan…
We consider the recently suggested model for some resonances near the open charm threshold as bound states of charmonium inside excited light mesons. It is argued in the soft-wall holographic model of QCD that such states of heavy quarkonium necessarily exist at sufficiently large spin of the light meson. The bound state is provided by the dilaton exchange through the 5D bulk. We also argue that the decay of such bound systems into mesons with open heavy flavors due to splitting of the heavy quarkonium can be treated as semiclassical tunneling and is suppressed. This behavior is in agreement w…
In the framework of a specific scheme of the QCD sum rules for $S$-wave levels of the heavy quarkonium, one derives an expression, relating the energetic density of quarkonium states and universal characteristics in the heavy quarkonium physics, such as the difference between the masses of a heavy quark $Q$ and meson $(Q\bar q)$ and the number of heavy quarkonium levels below the threshold of $(Q\bar Q) \to (Q\bar q) + (\bar Q q)$ decay.
We review selected lattice results on the charmonium spectrum and first attempts to search for the existence of exotic states. The hadro-quarkonium model was proposed to interpret some of the exotic states as a quarkonium core inside a hadron. We present a lattice study of the hadro-quarkonium model in the limit of static quarks. The charm quark decouples in low energy observables and binding energies of charmonium. In a model calculation we are able to evaluate the corrections to decoupling of the charm quark in the continuum.
In the framework of a specific scheme of the QCD sum rules for $S$-wave levels of the heavy quarkonium, one derives expressions, relating the leptonic constants, the energetic density of quarkonium states and universal characteristics in the heavy quarkonium physics, such as the difference between the masses of heavy quark $Q$ and meson $(Q\bar q)$ and the number of heavy quarkonium levels below the threshold of $(Q\bar Q) \to (Q\bar q) + (\bar Q q)$ decay.
The decays of a light scalar meson into a vector meson and a photon ($S\to Vγ)$ are evaluated in the tetraquark and quarkonium assignments of the scalar states. A link with the radiative decays $ϕ\to Sγ$ is established: experimental results for $S\to Vγ$ will allow to understand if the direct, quark-loop contribution to $ϕ\to Sγ$ or the kaon-loop contribution is dominant. Also strong decays $S\to PP$ -where $P$ denotes a pseudoscalar meson- are investigated: the tetraquark assignment works better than the quarkonium one. It is then also discussed why the tetraquark assignment is favoured with …
Using a specific scheme of the QCD sum rules for heavy quarkonium in the leading approximation over the inverse heavy quark mass, one gets the estimate of the difference between the masses of the heavy meson and heavy quark $\bar Λ= 0.59\pm 0.02$ GeV.
Hard diffractive photo- and electroproduction of heavy vector mesons ($J/ψ$ and $Υ$) is evaluated within the leading $α_s\ln{Q^2 \overΛ_{QCD}^2}$ approximation of QCD. In difference from our earlier work on that subject, also the production of transversely polarized vector mesons is calculated. Special emphasis is placed on the role of the vector meson's $q\bar q$ light-cone wave function. In that context, conventional non-relativistic quarkonium models and a light-front QCD bound state calculation are critically examined and confronted with QCD expectations. Our numerical analysis finds a sig…
Encouraged by recent developments in AdS/QCD models for light quark system, we study heavy quarkonium in the framework of the AdS/QCD models. We calculate the masses of $c\bar c$ vector meson states using the AdS/QCD models at zero and at finite temperature. Among the models adopted in this work, we find that the soft wall model describes the low-lying heavy quark meson states at zero temperature relatively well. At finite temperature, we observe that once the bound state is above $T_c$, its mass will increase with temperature until it dissociates at a temperature of around $494 {\rm MeV}$. It…
The discovery of hadronic states beyond the conventional two-quark meson and three-quark baryon picture in the last two decades is one of the most amazing accomplishments in fundamental physics research. Many experiments contributed to this field despite of the original goals of the design. We review the experimental progress on the study of the quarkoniumlike states -- states with at least one heavy quark-antiquark pair and possible light quarks, also known as XYZ states. We give a general review and then focus on the new experimental results on the X(3872) and its bottom-quark partner X_b, t…
In this work, we perform a detailed study of transition form factors for axial-vector meson production via the two-photon fusion process $γ^* γ^* \to 1^{++}$, with space-like virtual photons in the initial state and a $P$-wave axial-vector quarkonium in the final state. In this analysis, we employ the formalism of light-front quarkonium wave functions obtained from a solution of the Schrödinger equation for a selection of interquark potentials for $Q \bar Q$ interaction. We found the helicity structure and covariant decomposition of the matrix elements that can be generically applied for any $…
We investigate in detail the role of heavy meson loops in the transition from $J^{PC}=1^{--}$ sources to candidates for QCD "exotics", such as $Z_c(3900)$, $Z_b(10610)$ and $Z_b'(10650)$. We demonstrate that, if a vector state strongly couples to a heavy meson pair in an $S$--wave and this system decays to another heavy meson pair (e.g. via pion emission), again in an $S$-wave, the pertinent diagrams get enhanced significantly, if the intermediate states are (near) on--shell and have small relative momenta. In a limited kinematic range this mechanism generates "singularity regions" that lead t…
For the flavor-singlet heavy quark systems of quarkonia, we compute the masses of the first radial excitation of mesons in four different channels: pseudo-scalar ($η_{c,b}(2S)$), vector ($ψ(2S),Υ(2S)$), scalar ($χ_{c_0,b_0}(2P)$) and axial vector ($χ_{c_1,b_{1}}(2P)$), as well as the weak decay constants of the $η_{c,b}(2S)$ and $ψ(2S),Υ(2S)$. The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equations treatment of a vector$\times$vector contact interaction. The results found for the meson masses are in good agreement experimental data and earlier model calcu…
We shortly report on the two-photon decay width of the light $σ$-meson interpreted as a quarkonium state. Results are given in dependence on the $σ$-mass and the constituent mass of the light quark. The triangle quark-loop diagram, responsible for the two-photon transition, is carefully evaluated: a term in the transition amplitude, often omitted in literature, results in destructive interference with the leading term. As a result we show that the two-photon decay width of the $σ$ in the quarkonium picture is less than 1 keV for the physical range of parameters.
Many of the XYZ mesons discovered in the last decade can be identified as bound states of a heavy quark and antiquark in Born-Oppenheimer (B-O) potentials defined by the energy of gluon and light-quark fields in the presence of static color sources. The mesons include quarkonium hybrids, which are bound states in excited flavor-singlet B-O potentials, and quarkonium tetraquarks, which are bound states in flavor-nonsinglet B-O potentials. The deepest hybrid potentials are known from lattice QCD calculations. The deepest tetraquark potentials can be inferred from lattice QCD calculations of stat…
A quantum relativistic model is proposed to represent the confining potential of $c \bar{c}$ and $b \bar{b}$ mesons by using the Klein Gordon oscillator. We have solved the two-body problem obtaining the eigenvalues and the corresponding mass spectra, which fit very well with experimental data. We compare the results of our model with others obtained from different quark binding potentials.
We review lattice QCD results for glueballs (including a discussion of mixing with scalar mesons), hybrid mesons and exotic mesons (such as $B_s B_s$ molecules).
The evidence for the existence of mesons with exotic quantum numbers and of hybrid candidates with non-exotic quantum numbers is critically reviewed, including candidates with hidden charm. Aims and methods of future searches for hybrid mesons are briefly discussed.
