We estimate the sizeable cross section for deep exclusive electroproduction of an exotic $J^{PC}=1^{-+}$ hybrid meson in the Bjorken regime. The production amplitude scales like the one for usual meson electroproduction, i.e. as $1/Q^2$. This is due to the non-vanishing leading twist distribution amplitude for the hybrid meson, which may be normalized thanks to its relation to the energy momentum tensor and to the QCD sum rules technique. The hard amplitude is considered up to next-to-leading order in $\alpha_{S}$ and we explore the consequences of fixing the renormalization scale ambiguity through the BLM procedure. We study the particular case where the hybrid meson decays through a $\pi\eta $ meson pair. We discuss the $\pi\eta$ generalized distribution amplitude and then calculate the production amplitude for this process. We propose a forward-backward asymmetry in the production of $\pi$ and $\eta$ mesons as a signal for the hybrid meson production. We briefly comment on hybrid electroproduction at very high energy, in the diffractive limit where a QCD Odderon exchange mechanism should dominate. The conclusion of our study is that hard electroproduction is a promissing way to study exotic hybrid mesons, in particular at JLAB, HERA (HERMES) or CERN (Compass).

This work analyses hadronic decays of exotic mesons, with a focus on the lightest one, the $J^{PC}=1^{-+}$ $\pi_{1}$, in a fully relativistic formalism, and makes comparisons with non-relativistic results. We also discuss Coulomb gauge decays of normal mesons that proceed through their hybrid components. The relativistic spin wave functions of mesons and hybrids are constructed based on unitary representations of the Lorentz group. The radial wave functions are obtained from phenomenological considerations of the mass operator. Fully relativistic results (with Wigner rotations) differ significantly from non-relativistic ones. We also find that the decay channels $\pi_{1}\to\pi b_{1}, \pi f_{1}, KK_{1}$ are favored, in agreement with results obtained using other models.

Tests are discussed to distinguish c cbar, hybrid charmonium and molecular interpretations of the narrow Belle resonance at 3872 MeV.

The observation of $\pi_1(1600) \to \pi \rho$ is shown in the flux-tube model to be compatible with this state being a hybrid meson with branching ratio to this channel $\sim 10-25%$. This forces the hybrid $\pi(\sim 1800)$ to have a width to $\pi \rho \sim$ 100-300 MeV, which implies a novel interpretation of data. The $\pi \rho$ widths of other hybrids are related by rather general arguments. These results enable cross sections for photoproduction of hybrids to be predicted.

We calculate rates for hybrid meson production by electromagnetic and weak interactions in the flux-tube model. Applications include photo and electroproduction at Jefferson Laboratory and HERA, and the production of light strange and charmed hybrids in the weak decays of heavy flavours. Photoproduction of some light hybrids is predicted to be prominent in charge exchange reactions, $\gamma p \to n \cal{H}$ and accessible in $\gamma p \to p \cal{H}$. Production of light or charmed hybrids in $B$ and $D$ decays may be feasible with high statistics. Photoproduction of the axial hybrid meson is predicted to be large courtesy of $\pi$ exchange, and its strange counterpart is predicted in $B \to \psi K_H(1^+)$ with $b.r. \sim 10^{-4}$. Production rates for exotic hybrid candidates $1^{-+};(0,2)^{+-}$ are given special attention. Selection rules that can help to distinguish between hybrid and conventional states with the same $J^{PC}$ are noted.

Recent data on charmonium production in B-meson decays suggest that charmonium hybrid mesons with mass ~4 GeV may be produced in B-decay via c\bar{c} colour octet operators. Some of these states are likely to be narrow with clean signatures to J/\psi pi^+ pi^- final states. Experimental signatures and search strategies for existing B-factories are described.

The coupling of a neutral hybrid {1,3,5...}^-+ exotic particle (or current) to two neutral (hybrid) meson particles with the same J^PC and J=0 is proved to be sub-leading to the usual large-N_c QCD counting. The coupling of the same exotic particle to certain two - (hybrid) meson currents with the same J^PC and J=0 is also sub-leading. The decay of a {1,3,5...}^-+ hybrid to eta pi^0, eta' pi^0, eta' eta, eta(1295) pi^0, pi(1300)^0 pi0, eta(1440) pi^0, a_0(980)^0 sigma or f_0(980) sigma is sub-leading, assuming that these final state particles are (hybrid) mesons in the limit of large N_c.

Two mechanisms for the $\pi_1$ ($J^{PC}=1^{-+}$) hybrid meson decay processes $\pi_1\to\eta\pi,\eta'\pi$ are investigated. These mechanisms are applied to $\phi\to\eta\gamma,\eta'\gamma$ and $J/\psi\to\eta\gamma,\eta'\gamma$ decays to illustrate the validity of the decay mechanisms and to obtain independent information on the coupling of $\eta,\eta'$ to quark and gluonic operators. From this information, we find that $\Gamma(\pi_1\to\eta\pi)/\Gamma(\pi_1\to\eta'\pi)$ is substantially different in the two decay mechanisms, and hence future experimental measurements of this ratio will provide valuable information for substantiating the hybrid nature of these states and for determining the mechanism for these hybrid decays.

We consider a simplified constituent model for relativistic strong-interaction decays of hybrid mesons. The model is constructed using rules of renormalization group procedure for effective particles in light-front quantum field theory, which enables us to introduce low-energy phenomenological parameters. Boost covariance is kinematical and special relativity constraints are reduced to the requirements of rotational symmetry. For a hybrid meson decaying into two mesons through dissociation of a constituent gluon into a quark-anti-quark pair, the simplified constituent model leads to a rotationally symmetric decay amplitude if the hybrid meson state is made of a constituent gluon and a quark-anti-quark pair of size several times smaller than the distance between the gluon and the pair, as if the pair originated from one gluon in a gluonium state in the same effective theory.

This work investigates whether the observed 1^-+ exotic mesons are molecular states. We first use a potential model to calculate the spectra and lifetimes of the f_0(980) and a_0(980), taken to be loosely bound molecular states of K Kbar, then apply the same scenario to the 1^-+ exotic states pi_1(1400) and pi_1(1600), assuming them to be pi eta(1295) and pi eta(1440) molecules respectively. We derive the effective potential in the framework of field theory at the hadronic level. Our results indicate that the present data on pi_1(1400) and pi_1(1600) rule out the specific molecular ansatz. We show that the lifetime of a loosely bound heavy-light molecule with enough angular momentum is fully determined by the lifetimes of its constituent mesons.

The current situation for vector meson spectroscopy is outlined, and it is shown that the data are inconsistent with the generally-accepted model for meson decay. A possible resolution in terms of exotic mesons is given. Although this resolves some of the issues, fresh theoretical questions are raised.

A simple dynamical model for the exotic waves with $I^G(J^{PC})=1^-(1^{-+})$ in the reactions $\rho\pi\to\rho\pi$, $\rho\pi\to\eta\pi$, $\rho\pi\to\eta'\pi$, $ \rho\pi\to(K^*\bar K+\bar K^*K)$, and in the related ones, is constructed beyond the scope of the quark-gluon approach. The model satisfies unitarity and analyticity and uses as a "priming" the anomalous non-diagonal $VPPP$ interaction which couples together the four channels $\rho\pi$, $\eta\pi$, $ \eta'\pi$, and $K^*\bar K+\bar K^*K$. The possibility of the resonance-like behavior of the $I^G(J^{PC})=1^-(1^{-+})$ amplitudes belonging to the $\{10\}- \{\bar{10}\}$ and $\{8\}$ representations of SU(3) as well as their mixing is demonstrated explicitly in the 1.3--1.6 GeV mass range which, according to the current experiments, is really rich in exotics.

We investigate the possibility that the light-mass exotic mesons with J^PC=1^-+ observed at BNL and CERN may be resonances in the eta-pi and eta'-pi systems associated with the anomalous glue which generates the eta' mass in QCD.

Lattice QCD gives reliable predictions for hybrid charmonium and multi-GeV glueball masses. Proton-antiproton annihilation may offer an excellent opportunity for the first observation of these states. There are two distinct possible programs: The search for J^PC-exotic and non-J^PC-exotic states. The latter program represents substantially higher cross sections and does not absolutely require partial wave analysis, two very attractive features. The program can be performed with a varying pbar energy <10 GeV and a fixed target.

The current situation for vector meson spectroscopy is outlined, and it is shown that the data are inconsistent with the generally-accepted model for meson decay. A possible resolution in terms of exotic (hybrid) mesons is given. Although this hypothesis resolves some of the issues, fresh theoretical questions are raised. It is argued that high-precision $e^+e^-$ annihilation data provide an excellent laboratory for studying many aspects of nonperturbative QCD.

We discuss two production mechanisms of the $J^{PC}=1^{-+}$ exotic meson, hadroproduction, using pion beams and photoproduction. We show that the ratio of exotic to non-exotic, in particular the $a_2$, meson production cross sections is expected to be by a factor of 5 to 10 larger, in photoproduction then in hadroproduction. Furthermore we show that the low-t photoproduction of exotic meson is enhanced as compared to hadronic production. This findings support the simple quark picture in which exotic meson production is predicted to be enhanced when the beam is a virtual $Q\bar Q$ pair with a spin-1 (photon) rather then with a spin-0 (pion).

We present a short survey of the theoretical expectations on glueballs and hybrids as well as of the present phenomenological status. The possibility to obtain new information on gluonic mesons from the study of gluon jets in comparison to quark jets is discussed.

The D^+ --> omega + pi^+ decay is studied by decomposing its amplitude into a sum of factorizable and non-factorizable ones. Its rate is predicted as a function of mass and width of a hypothetical hybrid meson.

We consider glueball- (hybrid) meson mixing for the low-lying four pseudovector states. The h_1'(1380) decays dominantly to K*K with some presence in rho pi and omega eta. The newly observed h_1(1600) has a D- to S-wave width ratio to omega eta which does not enable differentiation between a conventional and hybrid meson interpretation. We predict the decay pattern of the isopartner conventional or hybrid meson b_1(1650). A notably narrow s sbar partner h_1'(1810) is predicted.

A simple model for the exotic waves with $I^G(J^{PC})=1^-(1^{-+})$ in the reactions $VP\to VP$, $VP\to PP$, and $PP\to PP$ is constructed beyond the scope of the quark-gluon approach. The model satisfies unitarity and analiticity and uses as "a priming" the "anomalous" non-diagonal $VPPP$ interaction which couples together the four channels $\rho\pi$, $\eta\pi$, $\eta'\pi$, and $K^*\bar K+\bar K^*K$. The possibility of the resonance-like behavior of the $I^G(J^{PC})=1^-(1^{-+})$ amplitudes belonging to the $\{10\}- \{\bar{10}\}$ and $\{8\}$ representations of SU(3) as well as their mixing is demonstrated explicitly in the $1.3-1.6$ GeV mass range which, according to the current experimental evidence, is really rich in exotics.

A simple model for the exotic waves with $I^G(J^{PC})=1^-(1^{-+})$ in the reactions $VP\to VP$, $VP\to PP$, and $PP\to PP$ is constructed beyond the scope of the quark-gluon approach. The model satisfies unitarity and analiticity and uses as "a priming" the "anomalous" non-diagonal $VPPP$ interaction which couples together the four channels $\rho\pi$, $\eta\pi$, $\eta'\pi$, and $K^*\bar K+\bar K^*K$. The possibility of the resonance-like behavior of the $I^G(J^{PC})=1^-(1^{-+})$ amplitudes belonging to the $\{10\}- \{\bar{10}\}$ and $\{8\}$ representations of SU(3) as well as their mixing is demonstrated explicitly in the $1.3-1.6$ GeV mass range which, according to the current experimental evidence, is really rich in exotics.

We discuss whether a low-lying hybrid baryon should be defined as a three quark - gluon bound state or as three quarks moving on an excited adiabatic potential. We show that the latter definition becomes exact, not only for very heavy quarks, but also for specific dynamics. We review the literature on the signatures of hybrid baryons, with specific reference to strong hadronic decays, electromagnetic couplings, diffractive production and production in psi decay.

In this contribution I discuss recent developments in light meson spectroscopy, and note specific areas in which DAFNE is an especially appropriate tool for future experiments. One topic of special relevance is the spectroscopy of excited vector mesons; quite narrow vector hybrids are predicted by the flux-tube model, which could be produced by DAFNE when operating in the $M_{e^+e^-}\approx 1.5-2$ GeV range. A second topic, which would be appropriate for a later date because it requires a rather higher beam energy, is the production of C=(+) mesons in $\gamma\gamma$ collisions.

We analyze the process $\vec \gamma +p\to \rho^0 \pi^{+}n$ at low momentum transfer focusing on a possibility of production of an exotic $J^{PC}=1^{-+}$ meson state. In particular we discuss polarization observables and conclude that linear photon polarization is instrumental for separating of the exotic wave.

In this contribution I discuss prospects for photoproducing hybrid mesons at CEBAF, based on recent model results and experimental indications of possible hybrids. One excellent opportunity appears to be a search for the I=1, JPC=2+-, neutral "(b2)o" hybrid in (a2 pi)o through diffractive photoproduction. Other notable possibilities accessible through pi+ or pio exchange photoproduction are I=1, JPC=1-+, charged "pi1+" in f1 pi+, (b1 pi)+ and (rho pi)+; piJ(1770)+ in f2 pi+ and (b1 pi)+; pi(1800)+ in f0 pi+, f2 pi+, omega rho+ and (rho pi)+; a1 in f1 pi+ and f2 pi+; and omega in (rho pi)o, omega eta and (K1 K)o.

The pionic coupling constants in the decays of the $1^{-+}$ hybrid meson are calculated. The double Borel transformation is invoked and continuum contribution is subtracted. The decay widths of the processes $1^{-+}\to \rho\pi, f_1 \pi, \pi \gamma$ are around $40, 100, 0.3$ MeV respectively.

The current state of analysis of e+e- annihilation below 2.0 GeV and of the vector component of tau decay is reviewed. The evidence for and against the presence of hybrid vectors is discussed. It is concluded that the data strongly favour their inclusion, and the consequences of this are outlined.

We study the production of charmonium hybrids in B decays. We use the operator product expansion and nonrelativistic QCD to organize the various contributions to this process. We express the decay rate in terms of a few matrix elements which eventually will be fixed by experimental measurements or calculated on the lattice. While the Fock state expansion is problematic for hybrids, in that there is no perturbative large mass limit, the operator product expansion still provides a model independent framework for phenomenological calculations of hybrid production and decay. We then use a simple flux tube model to estimate the branching ratio B -> psi_g + X, where psi_g is a J^{PC}=0^{+-} hybrid, the large production of which could help resolve the low charm multiplicity and semileptonic branching ratio observed in B decays. We also investigate the possible contributions of tensor charmonium production. We observe that it is unlikely for either effect to be large enough to play a significant role in resolving these problems.

Hybrid $ c \bar c g$ of quantum numbers $1^{--}$ are considered in a quark model with constituant quarks and gluon. The lowest $J^P=1^-$ states may be built in two ways, $l_g=1$ (gluon excited) corresponding to an angular momentum between the gluon and the $c \bar c$ system, while $l_{c\bar c}=1$ (quark excited) corresponds to an angular momentum between the $c$ and the $\bar c$. The lowest lying hybrid $J^P=1^-$ state in the flux tube model is similar to the $l_g=1$ in the quark-gluon model. In particular it verifies the selection rule that it cannot decay into two fundamental mesons. The $l_{q\bar q}=1$ hybrid may decay into two fundamental mesons, but with decay widths larger than 1 GeV, which tells that they do not really exist as resonant states. Using a chromoharmonic potential, we find no mixing between the $l_g=1$ and $l_{c\bar c}=1$. More realistic potentials might induce a strong mixing between them, implying that no hybrid meson exist. If, on the contrary, such a strong mixing does not occur, we find, in agreement with the flux tube model, that only the $l_g=1$ appears as a real resonant state. In such a case, hybrid mesons may exist as resonances only if they are decoupled from the ground state channels, which explains the difficulty to observe them experimentally. We reconsider accordingly the Ono-Close-Page scenario of mixing between charmonium and charmed-hybrid to explain the anomalies around 4.1 GeV. We find a very small mixing between radially excited charmonium and hybrid mesons, which forbids considering the $\psi(4.040)$ and $\psi(4.160)$ as combinations of 3S charmonium and $l_g=1$ hybrid meson with a large mixing.

We develop an ansatze of the sigma enhancement of the I=0, L=0 $\pi$-$\pi$ scattering amplitude as arising from a low-energy glueball pole. Using this picture we estimate the $\pi^0\pi^0$ to $\pi^0$ branching ratio for the decays of the Roper resonance, which we previously found to be a hybrid in our QCD sum rule calculation. We find that the sigma decay might be a good signal for gluonic components of hadrons.

The models for hybrid mesons are discussed, in which the gluonic excitations manifest themselves as the vibrations of the quark- antiquark QCD string. The predictions for the spectra, decays and mixing with hadronic channels are presented.

It has become traditional to assume that the Dirac structure of the phenomenological quark confinement potential is scalar $\otimes$ scalar. We use the heavy quark expansion of the Coulomb gauge QCD Hamiltonian and the Flux Tube model to demonstrate that this is true but in the effective sense only. The demonstration contains some surprises: confinement is actually vector $\otimes$ vector and it is nonperturbative mixing between ordinary and hybrid $Q \bar Q$ states which generates the scalar-like spin dependent potential at order $1/m_q^2$. Thus the existence of hybrids is crucial to establishing well-known spin splitting phenomenology. Finally, the resolution also indicates that the gluonic degrees of freedom in a hybrid must be of a collective nature.

We present arguments that reinforce the hybrid interpretation of pi(1800) and we establish that the rho(1450) and the omega(1420) can be interpreted as radial-hybrid mixtures. Some questions for future experiments are raised.

We suggest that $\psi$ (4040) and $\psi$ (4160) are strong mixtures of ground state hybrid charmonium at $\sim 4.1$ GeV and the $\psi (3S)$ of conventional charmonium. The $\Gamma^{e^+e^-}$, masses and total widths of the $\psi(4040)$ and $\psi(4160)$ are in accord with this hypothesis. Their hadronic decays are predicted to be dominated by the $\psi (3S)$ component and hence are correlated. In particular we find a spin counting relation $\Gamma (4160 \rightarrow D_sD_s^*) \sim 4 \Gamma (4040 \rightarrow D_sD_s)$ due to their common $\psi(3S)$ component. For $D$ and $D^*$ production, using $\psi(4040)$ branching ratios as input, we predict that the decay pattern of the $\psi(4160)$ will be very different from that of the $\psi(4040)$. These predictions may be tested in historical data from SPEAR, BES or at future Tau-Charm Factories.

Decay widths, branching ratios and production dynamics of some recently discovered $J^{PC} = 1^{-+}, 0^{-+}$,$1^{--}$ and $2^{-+}$ mesons are found to be in remarkable agreement with the predicted properties of hybrid mesons. We propose tests for this new dynamics, emphasise the critical role of $\pi b_1$ or $\pi h_1$ decay channels in discriminating hybrids from conventional states, and suggest that photoproduction may offer special opportunities for isolation and confirmation of hybrids.

We introduce general selection rules arizing from flux-tube dynamics with non-relativistic and adiabatic quark motion, without employing model-dependent assumptions. Specifically, we indicate under which circumstances hybrids with an arbitrary degree of flux-tube excitation can disguise themselves by not decaying to S--wave states.

We introduce strong interaction selection rules for the two-body decay and production of hybrid and conventional mesons coupling to two S-wave hybrid or conventional mesons. The rules arise from symmetrization in states in the limit of non-relativistically moving quarks. The conditions under which hybrid coupling to S-wave states is suppressed are determined by the rules, and the nature of their breaking is indicated.

New experimental information on the non--exotic J^{PC} = 0^{-+} isovector seen at 1.8 GeV by VES yields convincing evidence of its excited gluonic (hybrid) nature when a critical study of alternative quarkonium assignments is made in the context of ^3 P_0 decay by flux--tube breaking. Production of this gluonic excitation via meson exchange is promising, although its two photon production vanishes.

The status of non-perturbative QCD calculations for mesons with gluonic excitation is presented. Lattice results for the glueball spectrum are reviewed. For hybrid mesons, the heavy quark results are summarised and new results are presented for light quarks. Preliminary results for the spectrum of light-quark hybrid mesons indicate substantial mixing with quark model states for non-exotic $J^{PC}$. For the exotic $J^{PC}$ hybrid mesons, the $J^{PC}=1^{-+}$, $0^{+-}$ and $2^{+-}$ states are explored.

Lectures at VII Jorge Andre Swieca Summer School in Nuclear Physics; Brasil; Jan 22 - Feb 4 1995. To be published by Plenum Press (C.A.Amaral Nunes ed.)

The lightest scalar glueball and ground state hybrids may have been found. I compare signals reported at this conference with theoretical expectations and highlight the questions that need to be addressed in forthcoming experiments.

In this review talk I summarize theoretical expectations for properties of hybrid mesons and baryons, and discuss the prospects for identifying these states experimentally. This is an expanded version of an Invited Contribution to the Conference on Exclusive Reactions at High Momentum Transfers, Marciana Marina, Elba, Italy, 24-26 June 1993.

I will review the current status of exotic hadrons in the meson sector. There is currently strong evidence that a scalar glueball mixed into the normal scalar mesons has been found. There is also an interesting candidate for the tensor glueball state. Finally, I will discuss hybrid mesons with explicitly exotic quantum numbers.

The experimental information on the search for non $q \bar q$ mesons as glueballs, hybrids and multiquark states is reviewed. Candidate states which are particularly amenable to detailed study by accumulating large samples of $J/\psi$, $\eta_c$, $\chi$ decays at a $\tau$-charm factory are discussed