We review our investigations devoted to the analysis of the resonances $ Z_{c}(3900)$, $Z_{c}(4430)$, $Z_{c}(4100)$, $X(4140)$, $X(4274)$, $a_1(1420)$ , $Y(4660)$, $X(2100)$, $X(2239)$ and $Y(2175)$ discovered in various processes by Belle, BaBar, BESIII, D0, CDF, CMS, LHCb and COMPASS collaborations. These resonances are considered as serious candidates to four-quark (tetraquark) exotic mesons. We treat all of them as diquark-antidiquark states with relevant spin-parities, find their masses and couplings, as well as explore their dominant strong decay channels. Calculations are performed in the context of the QCD sum rule method. Thus, the spectroscopic parameters of the tetraquarks are evaluated using the two-point sum rules. For computations of the strong couplings $G_{TM_1M_2}$, corresponding to the vertices $TM_1M_2$ and necessary to find the partial widths of the strong decays $T \to M_1M_2$, we employ either the three-point or full/approximate versions of the QCD light-cone sum rules methods. Obtained results are compared with available experimental data, and with predictions of other theoretical studies.
Tetra-quark mesons with exotic quantum numbers, their production rates and decay properties are studied, because they are useful to establish existence of tetra-quark mesons.
Recent results on meson spectroscopy from lattice QCD are reviewed. The emphasis is on interesting states near thresholds like $Z_c^+(3900)$, $X(3872)$ and $D_{s0}^*(2317)$. Another focus is on the meson resonances in light, strange and charm sector, where the resonance masses as well as the strong decay widths are extracted from the lattice.
Some of the currently most popular conjectures for the structure of the recently discovered heavy mesons that do not find a place in the quark model quarkonium spectrum are sketched. Furthermore, some observables are identified that should allow one to identify the most prominent components of individual states.
Meson states with exotic quantum numbers arise naturally in a covariant bound-state framework in QCD. We investigate the consequences of shifting quark masses such that the states are no longer restricted to certain C-parities, but only by J^P. Then, a priori, one can no longer distinguish exotic or conventional states. In order to identify signatures of the different states to look for experimentally, we provide the behavior of masses, leptonic decay constants, and orbital-angular-momentum decomposition of such mesons, as well as the constellations in which they could be found. Most prominent…
We first construct the effective chiral Lagrangians for the $1^{-+}$ exotic mesons. With the infrared regularization scheme, we derive the one-loop infrared singular chiral corrections to the $π_1(1600)$ mass explicitly. We investigate the variation of the different chiral corrections with the pion mass under two schemes. Hopefully, the explicit non-analytical chiral structures will be helpful to the chiral extrapolation of the lattice data from the dynamical lattice QCD simulation of either the exotic light hybrid meson or tetraquark state.
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).
Exotic and higher spin (> 1) mesons are still not throughly investigated in lattice QCD. Using a set of derivative based operators we report our exploratory study of these mesons in charmonium region. We use a 12^3 X 48 anisotropic (xi = 3) clover lattice with inverse temporal lattice spacing a^-1 = 6.05 GeV. Techniques developed in this exploratory study will be utilized in our future comprehensive study of light hybrid mesons that are to be explored in the 12 GeV GlueX experiment at Jefferson Laboratory.
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.
Hybrid mesons, made from a quark, an antiquark and gluons, can have quantum numbers inaccessible to conventional quark-antiquark states. Confirmation of such states would give information on the role of "dynamical" color in low energy QCD. We present preliminary results for hybrid meson masses using light Wilson valence quarks.
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 s…
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). We also discuss string breaking as a mixing between colour flux states and $B \bar{B}$ states.
Non-exotic scalar-meson resonances in S-wave meson-meson scattering are studied in the light of a unitarised Schroedinger model. The resulting poles in the scattering matrices, by analytical continuation into the complex-energy plane, are grouped into nonets of isoscalar, isodoublet, and isotriplet resonances. All singularities can be related to quark-antiquark confinement states, the light-quark nonet of which has ground states at 1.3 to 1.4 GeV and level spacings of some 300-400 MeV, except for a nonet of light scalar mesons below 1 GeV. All non-exotic S-wave resonances reported by experimen…
A surprising number of new c c-bar mesons with masses above the D D-bar threshold have been discovered at the B factories. Some of them are ordinary charmonium states, but others are definitely exotic mesons. The current theoretical status of the new c c-bar mesons is summarized.
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.
We present highly-excited charmonium, $D_s$ and $D$ meson spectra from dynamical lattice QCD calculations with light quarks corresponding to $M_π \sim 240$ MeV and compare these to previous results with $M_π \sim 400$ MeV. Utilising the distillation framework, large bases of carefully constructed interpolating operators and a variational procedure, we extract and reliably identify the continuum spin of an extensive set of excited mesons. These include states with exotic quantum numbers which, along with a number with non-exotic quantum numbers, we identify as having excited gluonic degrees of …
We examine the chiral corrections to exotic meson masses calculated in lattice QCD. In particular, we ask whether the non-linear chiral behavior at small quark masses, which has been found in other hadronic systems, could lead to large corrections to the predictions of exotic meson masses based on linear extrapolations to the chiral limit. We find that our present understanding of exotic meson decay dynamics suggests that open channels may not make a significant contribution to such non-linearities whereas the virtual, closed channels may be important.
We evaluate the leading order amplitude for the deep exclusive electroproduction of an exotic hybrid meson in the Bjorken regime. We show that, contrary to naive expectation, this amplitude factorizes at the twist 2 level and thus scales like usual meson electroproduction when the virtual photon and the hybrid meson are longitidinally polarized. Exotic hybrid mesons may thus be studied in electroproduction experiments at JLAB, HERA (HERMES) or CERN (COMPASS).
Using a new quark-field construction algorithm and a large variational basis of operators, we extract a highly excited isovector meson spectrum on dynamical anisotropic lattices. We show how carefully constructed operators can be used to reliably identify the continuum spin of extracted states, overcoming the reduced cubic symmetry of the lattice. Using this method we extract, with confidence, excited states, states with exotic quantum numbers (0+-, 1-+ and 2+-) and states of high spin, including for the first time in lattice QCD, spin-four states.
In this talk I summarize the status of exotic mesons, including both theoretical expectations and experimental candidates. The current experimental candidates are ``spin-parity exotics''; since these are most often considered possible hybrid mesons, the theoretical discussion will be mainly concerned with hybrids. The exotic meson candidates discussed are the surprisingly light pi_1(1400) and pi_1(1600).
We analyze the process $\vec γ+p\to ρ^0 π^{+}n$ 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.
We describe a four-parameter model for non-exotic meson-meson scattering, which accommodates all non-exotic mesons, hence also the light scalar mesons, as resonances and bound states characterised by complex singularities of the scattering amplitude as a function of the total invariant mass. The majority of the full $S$-matrix mesonic poles stem from an underlying confinement spectrum. However, the light scalar mesons K0*(830), a0(980), f0(400-1200), and f0(980) do not, but instead originate in 3P0-barrier semi-bound states. In the case of bound states, wave functions can be determined. For cc…
This is a conference mostly devoted to diquarks. Although an exotic meson can in principle be composed of a diquark and an antidiquark, such an exotic is unlikely to be experimentally observable in the near future. The reason, according to the model, is that diquark-antidiquark exotics have masses well above the threshold for decay into two mesons, and are likely to have widths too large to make them observable. A possible exception is a $ u d \bar b \bar b$ exotic, but it will be a long time before such a state can be observed even if it is stable against strong decay.
Charmonium, the spectroscopy of c\bar{c} mesons, has recently enjoyed a renaissance with the discovery of several missing states and a number of unexpected charmonium-like resonances. The discovery of these new states has been made possible by the extremely large data samples made available by the B-factories at the Stanford Linear Accelerator Center and at KEK in Japan, and at the CESR e^+e^- collider at Cornell. Conventional c\bar{c} states are well described by quark potential models. However, many of these newly discovered charmonium-like mesons do not seem to fit into the conventional c\b…
If the exotic baryon $Θ^+(1540)$ is a correlated $udud\bar{s}$ with $J^P = {1/2}^+$, then there should exist an exotic meson, $J^P = 1^-$ $\vartheta^+ (S=+2)$ $\to K^+K^0$ $\sim 1.6$GeV with width $O(10-100)$MeV. The $π_1(1400;1600)$ may be broad members of {\bf 10} $\pm$ \10bar in such a picture. Vector mesons in the 1.4 - 1.7GeV mass range are also compared with this picture.
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…
The search for mesons with non-quark-antiquark (exotic) quantum numbers has gone on for nearly thirty years. There currently is experimental evidence of three isospin one states, the $π_{1}(1400)$, the $π_{1}(1600)$ and the $π_{1}(2015)$. For all of these states, there are questions about the identification of these state, and even if some of them exist. In this article, we will review both the theoretical work and the experimental evidence associated with these exotic quantum number states. We find that the $π_{1}(1600)$ could be the lightest exotic quantum number hybrid meson, but observatio…
We propose stable exotic nuclei bound with $\bar{D}$ and $B$ mesons with respecting heavy quark symmetry. We indicate that an approximate degeneracy of $\bar{D}$($B$) and $\bar{D}^{*}$($B^{*}$) mesons plays an important role, and discuss the stability of $\bar{D}N$ and $BN$ bound states. We find the binding energies 1.4 MeV and 9.4 MeV for each state in the $J^{P}=1/2^{-}$ with I=0 channel. We discuss also possible existence of exotic nuclei $\bar{D}NN$ and $BNN$.
The relativistic four-quark equations are found in the framework of the dispersion relation technique. The dynamical mixing of the four-quark amplitudes and the glueball amplitudes is considered. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The four-quark amplitudes of exotic mesons including the quarks of three flavors (u, d, s) are calculated. The poles of these amplitudes determine the masses of the exotic mesons.
The exotic J^{PC}= 1^{-+} resonance π_{1}(1600)is examined in the framework of the Quark Model with Constituent Gluon (QMCG). We report the possibility of interpreting that resonance as quark-antiquark-gluon hybrid meson, with a masse = 1.65+0.05-0.04 GeV and a rho-pi decay width = 0.28+0.14-0.09 GeV.
We discuss a coupled channel analysis of the $ηπ$ and $η'π$ systems produced in $π^-p$ interactions at 18 GeV/$c$. We show that known $Q\bar Q$ resonances, together with residual soft meson-meson rescattering, saturate the spectra including the exotic $J^{PC}=1^{-+}$ channel. A possibility of a narrow exotic resonance at a mass near 1.6 GeV/$c^2$ cannot, however, be ruled out.
We reconsider the discrepancy between theory and data in the momentum distribution of slow J/psi in B decays. Beside an update of the standard color singlet and color octet QCD components, we include the contribution from XY Z exotic mesons, and show that the residual discrepancy could be accommodated considering new XYZ mesons still unobserved.
Masses for vector 1--, axialvector 1+-, 1++, and exotic-vector 1-+ mesons are calculated within a quantum field theoretic framework based on the Dyson-Schwinger equations using a model form of the quark-antiquark interaction that is separable. The model provides an excellent description of pion and K-meson observables and the flavor-octet ground-state meson spectrum. With no adjustments to model parameters, a numerical solution of the Bethe-Salpeter equation yields two exotic 1-+ mesons with masses of 1439 and 1498 MeV.
We show that hard electroproduction is a promising way to study exotic hybrid mesons, in particular through the hybrid decay channel $H \to πη$. We discuss the $πη$ generalized distribution amplitude, calculate the production amplitude and propose a forward-backward asymmetry as a signal for the hybrid meson production.
Two-ordinary-meson scattering in large-$N_c$ QCD implies consistency criteria for intermediate-tetraquark contributions. Their fulfilment at $N_c$-leading order constrains the nature of the spectrum of genuinely exotic tetraquark states.
We investigate the hybrid exotic meson with $J^{PC}=1^{-+}$ within the framework of an AdS/QCD model. Introducing a holographic field dual to the operator for hybrid exotic meson, we obtain the eigen-value equation for its mass. Fixing all free parameters by QCD observables such as the $ρ$-meson mass, we predict the masses of the hybrid exotic meson. The results turn out to be $1476 \mathrm{MeV}$ for the ground state, and $2611 \mathrm{MeV}$ for the first excited one. Being compared with the existing experimental data for the $π_1(1400)$, which is known to be $m_{π_1} = 1351\pm30 \mathrm{MeV}$…
We predict several new exotic doubly-heavy hadronic resonances, inferring from the observed exotic bottomonium-like and charmonium-like narrow states $X(3872)$, $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$, and $Z_c(4020/4025)$. We interpret the binding mechanism as mostly molecular-like isospin-exchange attraction between two heavy-light mesons in a relative S-wave state. We then generalize it to other systems containing two heavy hadrons which can couple through isospin exchange. The new predicted states include resonances in meson-meson, meson-baryon, baryon-baryon, and baryon-antibaryon channel…
Discussing four-point Green functions of bilinear quark currents in large-$N_c$ QCD, we formulate rigorous criteria for selecting diagrams appropriate for the analysis of potential tetraquark poles. We find that both flavor-exotic and cryptoexotic (i.e., flavor-nonexotic) tetraquarks, if such poles exist, have a width of order $O(1/N_c^2)$, so they are parametrically narrower compared to the ordinary $\bar qq$ mesons, which have a width of order $O(1/N_c)$. Moreover, for flavor-exotic states, the consistency of the large-$N_c$ behavior of "direct" and "recombination" Green functions requires t…
To obtain an exact solution of a four-body system containing two quarks and two antiquarks interacting through two-body terms is a cumbersome task that has been tackled with more or less success during the last decades. We present an exact method for the study of four-quark systems based on the hyperspherical harmonics formalism that allows us to solve it without resorting to further approximations, like for instance the existence of diquark components. We apply it to systems containing two heavy and two light quarks using different quark-quark potentials. While $QQ\bar n \bar n$ states may be…
Exotic mesons are striking predictions of quantum chromodynamics that go beyond the quark model. They can provide great insight into understanding phenomena such as asymptotic freedom, confinement, and dynamical symmetry breaking. This work analyzes hadronic decays of exotic mesons, with a focus on the lightest one, the $J^{PC}=1^{-+}$ $π_{1}$, in a fully relativistic formalism. The relativistic spin wave functions of normal and exotic mesons are constructed based on unitary representations of the Poincare group. The radial wave functions are obtained from phenomenological considerations of th…
The potential of decays of mesons containing heavy quarks [including $B$ mesons and the $Υ(1S)$] for producing final states of matter with unusual quark configurations, such as $q q \bar q \bar q$ or $q q q q \bar q$, is investigated. The usefulness of antineutron detection in such searches is stressed.
We study heavy hadron spectroscopy near heavy meson thresholds. We employ heavy pseudoscalar meson P and heavy vector meson P* as effective degrees of freedom and consider meson exchange potentials between them. All possible composite states which can be constructed from the P and P* mesons are studied up to the total angular momentum J <= 2. We consider, as exotic states, isosinglet states with exotic J^{PC} quantum numbers and isotriplet states. We solve numerically the Schrödinger equation with channel-couplings for each state. We found B(*)barB(*) molecule states for I^G(J^{PC}) = 1^+(1^{+…
Exotic mesons with quantum numbers of a hybrid ($\bar{q} q g$) such as $J^{PC} = 1^{-+}$are shown to exist as narrow resonant states in the large $N_c$ limit of QCD. The width of these states is proportional to $1/N_c$. Possible phenomenological implications for the world of $N_c=3$ are discussed.
The CMS phase II track trigger may allow for a displaced dimuon vertex trigger with qualitatively lower $p_T$ thresholds than existing dimuon triggers. With this technique, we show that the CMS reach for exotic $B$-meson decays involving a displaced dimuon resonance, such as a light, Higgs-mixed scalar, can be competitive with that of LHCb and Belle II.
Exotic mesons with hidden strange ($s\bar s$) and heavy quark pairs ($Q\bar Q$), where $Q=c,b$, are considered as diquark-antidiquark systems, $(Qs)(\bar Q\bar s)$. Taking into account that these states can recombinate into two-meson ones, we study the interplay of these states in terms of the dispersion relation D-function technique. The classification of exotic mesons is discussed, coefficients for decay modes are given, predictions for new states are presented. The nonet structure for $((Qq)(\bar Q \bar q)$, ($(Qs)(\bar Q\bar s$)), ($(Qq)(\bar Q\bar s))$- states ($q=u,d$) is suggested.
The QCD analysis of the recent experimental data (L3@LEP) of the hard exclusive $ρρ$ production in two photon collisions shows that these data can be understood as a signal for the existence of an exotic isotensor resonance with a mass around $1.5 {\rm GeV}$. We also argue that hard exclusive reactions are a powerful tool for an experimental study of exotic hybrid mesons with $J^{PC}=1^{-+}$.
We study heavy baryons with an exotic flavor quantum number formed by a heavy meson and a nucleon (Dbar-N and B-N) through a long range one pion exchange interaction. The bound state found previously in the (I,JP) =(0,1/2-) channel survives when short range interaction is included. In addition, we find a resonant state with (I,JP)=(0,3/2-) as a Feshbach resonance predominated by a heavy vector meson and a nucleon (Dbar*-N and B*-N). We find that these exotic states exist for the charm and heavier flavor region.
We present a theoretical estimate for the cross-section of exclusive $ρ^+ρ^-$ and $ρ^0ρ^0$-meson production in two photon collisions when one of the initial photons is highly virtual. We focus on the discussion of the twist 4 contributions which are related to the production of an exotic isospin 2 resonance of two $ρ$ mesons. Our analysis shows that the recent experimental data obtained by the L3 Collaboration at LEP can be understood as a signal for the existence of an exotic isotensor resonance with a mass around $1.5 {\rm GeV}$.
We present an exact calculation of $S$ and $P$ wave $QQ\bar n\bar n$ states using different standard nonrelativistic quark--quark potentials. We explore in detail the charm and bottom sectors looking for bound states that could be measured within existing facilities. Against the proliferation of four--quark states sometimes predicted in the literature, we found a small number of candidates to be stable. We analyze their properties in a trial to distinguish between compact and molecular states. Possible decay modes are discussed.
Exotic hybrid mesons H, with quantum numbers J^{PC}= 1^{- +} may be copiously produced in the hard exclusive processes gamma^*(Q^2) gamma -> H and gamma^*(Q^2) P(p) -> H P(p') because they have a leading twist distribution amplitude with a sizable coupling constant f_H, which may be estimated through QCD sum rules. The reaction rates scale in the same way as the corresponding rates for usual mesons.
We study heavy hadron spectroscopy near open bottom thresholds. We employ B and B* mesons as effective degrees of freedom near the thresholds, and consider meson exchange potentials between them. All possible composite states which can be constructed from the B and B* mesons are studied up to the total angular momentum J = 0, 1, 2. We consider, as exotic states, isosinglet states with exotic (J,PC) quantum numbers and isotriplet states. We solve numerically the Schrodinger equation with channel-couplings for each state. The masses of twin resonances Zb(10608) and Zb(10653) recently found by Be…
The meson $X(3872)$ and several related states appear to be, at least in part, hadronic molecules in which a heavy flavored meson (such as $D^0$) is bound to another heavy meson (such as $\bar D^{*0}$). Although not the only effect contributing to the binding, pion exchange seems to play a crucial role in generating the longest-range force between constituents. Mesons without $u$ and $d$ light quarks (such as $D_s$) cannot exchange pions, but under suitable circumstances can bind as a result of $η$ exchange. Channels in which this mechanism is possible are identified, and suggestions are made …
We demonstrate that the azimuthal dependence of central meson production in hadronic collisions, when suitably binned, provides unambiguous tests of whether the Pomeron couples like a conserved vector-current to protons. We discuss the possibility of discriminating between q-qbar and glueball production in such processes. Our predictions apply also to meson production in tagged two-photon events at electron--positron colliders and to vector-meson production in ep collisions at HERA.
The infinite chain of transitions of one pair of mesons (channel I) into another pair of mesons (channel II) can produce bound states and resonances in both channels even if no interactions inside channels exist. These resonances which can occur also in meson-baryon channels are called channel-coupling (CC) resonances. A new mechanism of CC resonances is proposed where transitions occur due to a rearrangement of confining strings inside each channel -- the recoupling mechanism. The amplitude of this recoupling mechanism is expressed via overlap integrals of the wave functions of participating …
In this work, we study the interaction between a nucleon and a $P$-wave charmed meson in the $T$ doublet by exchanging a pion. Our calculations indicate that a nucleon and a $P$-wave charmed meson with $J^P=0^+$ or $J^P=1^+$ in the $T$ doublet can form bound states. We propose the experimental search for these exotic molecular states near the $D_1(2420)N$ and $D_2^*(2460)N$ thresholds, where Belle, LHCb and the forthcoming Belle II have the discovery potential for them.
Hybrid mesons with exotic quantum numbers $J^{PC}=1^{-+}$ are examined in soft-wall AdS/QCD. The predicted mass spectrum is compared to the measured values of the candidates $π_1(1400)$, $π_1(1600)$ and $π_1(2015)$. Thermal effects are analysed through the spectral function in the AdS-Black Hole model, and the differences with the Hawking-Page description are discussed.
I briefly review the history of exotic meson (4-quark) and baryon (5-quark) states, which is rooted in the formalism of Regge pole and duality. There are robust model-independent predictions for the exchange of 4-quark (Baryonium) Regge trajectories in several processes, which are strongly supported by experiment. On the other hand the predictions for the spectroscopy of 4-quark resonances are based on specific QCD inspired models, with some experimental support. The corresponding predictions for the recently discovered exotic baryon (Pentaquark) state are briefly discussed.
We discuss charmed mesons in the covariant Dyson-Schwinger-Bethe-Salpeter-equation approach. In particular we computed masses, leptonic decay constants, and an orbital-angular-momentum decomposition for a basic set of states. We also report an efficient way to treat the two coupled quark propagator dressing functions via a single function.
We study exotic mesons with double charm and bottom flavor, whose quark configuration is \bar{Q}\bar{Q}qq. This quark configuration has no annihilation process of quark and antiquark, and hence is a genuinely exotic states. We take a hadronic picture by considering the molecular states composed of a pair of heavy mesons, such as DD, DD* and D*D* for charm flavor, and BB, BB* and B*B* for bottom flavor. The interactions between heavy mesons are derived from the heavy quark effective theory. All molecular states are classified by I(J^P) quantum numbers, and are systematically studied up to the t…
