The masses of tetraquark states of all $qc\bar q \bar c$ and $cc\bar c \bar c$ quark configurations are evaluated in a constituent quark model, where the Cornell-like potential and one-gluon exchange spin-spin coupling are employed. All model parameters are predetermined by comparing the theoretical and experimental masses of light, charmed and bottom mesons. The theoretical predictions of the charmoniumlike tetraquarks are compared with the observed $XYZ$ states, and one tentative assignment is suggested. The work suggests that the $X(6900)$ observed by LHCb is likely to be the first radial excited fully-charm tetraquark state with $J^{PC} = 1^{+-}$ in the $\bar 3_c \otimes 3_c$ configuration, and the ground and second radial excited states of fully-charm tetraquark are around $6494$ and $7253$ MeV respectively.
To identify the nature of the newly observed charged resonance Zc(4200), we study its hadronic decays Zc(4200) -> J/psi pi, Zc(4200) -> eta_c rho and Zc(4200) -> D bar D* as a charmonium-like tetraquark state. In the framework of the QCD sum rules, we calculate the three-point functions and extract the coupling constants and decay widths for these interaction vertices. Including all these channels, the full decay width of the Zc(4200) state is consistent with the experimental value reported by the Belle Collaboration, supporting the tetraquark interpretation of this state.
Our hadro-charmonium and compact tetraquark model predictions, published before the BESIII and LHCb experimental data for the $Z_{\rm cs}(3985)$ and $Z_{\rm cs}(4003)$ tetraquarks were released, match surprisingly well with them. Here, we extend our results for the $P_{\rm cs}$ states to $Λ$ + charmonium configurations and also our hadro-charmonium predictions for $Z_{\rm c}$ and $X_{\rm c}$ tetraquarks to charmonium + pion/eta. We use them, in combination with our previous findings, to discuss the possible emergence of SU(3)$_{\rm f}$ pentaquark octets and tetraquark nonets in the hidden-char…
Using the QCD sum rule approach we study the X(4260) state assuming that it can be described by a mixed charmonium-tetraquark current with $J^{PC}=1^{--}$ quantum numbers. For the mixing angle around $θ=(53.0 \pm 0.5)^0$, we obtain a value for the mass which is in good agreement with the experimental mass of the X(4260). For the decay width into the channel $X \to J/ψππ$, we find the value $Γ_{X \to J/ψππ}=(4.1 \pm 0.6)$ MeV, which is much smaller than the total experimental width $Γ= (108\pm 12)$ MeV. However, considering the experimental upper limits for the decay of the X(4260) into open ch…
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 article, we perform a systematic study of the mass spectrum of the vector hidden charmed and bottomed tetraquark states using the QCD sum rules.
The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson-meson states with the four-quark states is considered. The four-quark amplitudes of the tetraquarks with hidden charm including u, d, s and charmed quarks are constructed. The poles of these amplitudes determine the masses and widths of tetraquarks.
The masses of the excited heavy tetraquarks with hidden charm are calculated within the relativistic diquark-antidiquark picture. The dynamics of the light quark in a heavy-light diquark is treated completely relativistically. The diquark structure is taken into account by calculating the diquark-gluon form factor. New experimental data on charmonium-like states above open charm threshold are discussed. The obtained results indicate that X(3872), Y(4260), Y(4360), Z(4248), Z(4433) and Y(4660) could be tetraquark states with hidden charm.
The feasibility of tetraquark detection is studied. For the cc\bar{u}\bar{d} tetraquark we show that in present (SELEX, Tevatron, RHIC) and future facilities (LHCb, ALICE) the production rate is promising and we propose some detectable decay channels.
The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson-meson states with the four-quark states is considered. The four-quark amplitudes of the negative parity tetraquarks including the quarks of three flavors (u, d, s) and the charmed quark are constructed. The poles of these amplitudes determine the masses of tetraquarks. The mass values of low-lying tetraquarks with the spin-parity JP=0-,1-,2-,3- are calculated.
In this article, we study the mass spectrum of the scalar hidden charm and hidden bottom tetraquark states which consist of the axial-axial type and the vector-vector type diquark pairs with the QCD sum rules.
The discovery in July 2020 of fully-charm tetraquark led to the need for its theoretical explanation. For investigation of such complex four-quark formation, the modern mathematical apparatus of the theory of derived categories is used. By representing diquarks as solitonic objects in terms of sheaves, one can explain the measured mass of the broad resonance of fully-charm tetraquarks consisting of di-charmonia.
The mass spectra of all-charm tetraquark states with the [cc][$\bar{c}\bar{c}$] quark configuration are investigated. The coulomb plus linear potential is used in conjunction with the relativistic mass correction term $\mathcal{O}(\frac{1}{m})$. To determine the fitting parameters for all-charm tetraquarks states [cc][$\bar{c}\bar{c}$], we first calculate the mass spectra of charmonia [c$\bar{c}$] and its decay constants ($f^{2}_{P/V}$). We estimated the masses of the tetraquark states in their ground and radially excited states. For mass spectra of tetraquark states, we also included spin-spi…
In this article, we investigate the mass spectrum of the ground state hidden-charm tetraquark molecular states without strange, with strange and with hidden-strange via the QCD sum rules in a comprehensive way and revisit the assignments of the $X$, $Y$, $Z$ states in the scenario of tetraquark molecular states consistently based on the QCD sum rules.
In two recent papers, we used the hadro-quarkonium model to study the properties of hidden-charm and bottom tetraquarks and pentaquarks. Here, we extend the previous results and calculate the masses of heavy-quarkonium-kaon/hyperon systems. We also compute the spectrum of hidden-charm and bottom tetraquarks with strangeness in the compact tetraquark (diquark-antidiquark) model. If heavy-light exotic systems with non-null strangeness content were to be observed experimentally, it might be possible to distinguish among the large variety of available theoretical pictures for tetra- and pentaquark…
Using the QCD sum rule approach we study the Y(4260) state assuming that it can be described by a mixed charmonium-tetraquark current with $J^{PC}=1^{--}$ quantum numbers. For the mixing angle around $θ\approx (53.0\pm 0.5)^{0}$, we obtain a value for the mass which is in good agreement with the experimental mass of the Y(4260). However, for the decay width we find the value $\Ga_Y \approx (1.0\pm 0.2)$ MeV which is not compatible with the experimental value $\Ga \approx (88\pm 23)$ MeV. Therefore, we conclude that, although we can explain the mass of the Y(4260), this state cannot be describe…
In this paper we present the main results of our investigation of the $cq \bar{q} \bar{q}$ single-charm scalar tetraquarks and their SU(3)$_\mathrm{F}$ representations: $\bar{15}_S$, $\bar{3}_S$, $6_A$ and $\bar{3}_A$. We use the Fermi-Breit interaction Hamiltonian with SU(3) flavor symmetry breaking to determine the masses of the single-charm tetraquarks. We also discuss mass spectra obtained from meson and baryon mass fits. The mass spectra are very similar to those obtained with Glozman-Riska hyperfine interaction, and they indicate that some of the experimentally detected states may have t…
We review the current theoretical situation with regard to the anomalously large cross section for exclusive J/psi + eta_c production in e^+ e^- annihilation, as measured by BELLE Collaboration.
We study the possible spin-1 charmonium-like states by using QCD sum rule approach. We calculate the two-point correlation functions for all the local form tetraquark interpolating currents with $J^{PC}=1^{--}, 1^{-+}, 1^{++}$ and $1^{+-}$ and extract the masses of the tetraquark charmonium-like states. The mass of the $1^{--}$ $qc\bar q\bar c$ state is $4.6\sim4.7$ GeV, which implies a possible tetraquark interpretation for Y(4660) meson. The masses for both the $1^{++}$ $qc\bar q\bar c$ and $sc\bar s\bar c$ states are $4.0\sim 4.2$ GeV, which is slightly above the mass of X(3872). For the $1…
In this article, we study the mass spectrum of the scalar hidden charm and bottom tetraquark states with the QCD sum rules. The numerical results are compared with the corresponding ones from a relativistic quark model based on a quasipotential approach in QCD. The relevant values from the constituent diquark model based on the constituent diquark masses and the spin-spin interactions are also discussed.
We investigate four-body states with only charm quarks. Working in a large but finite oscillator basis, we present a net binding analysis to determine if the resulting states are stable against breakup into a pair of c-cbar mesons. We find several close-lying bound states in the two models we examine.
The LHCb experiment at CERN has discovered a doubly charmed isoscalar tetraquark $T_{cc}$ with the quantum numbers of $c c \bar u \bar d$ and mass of about 3875 MeV/$c^2$, decaying to $D^0 D^0 π^+$ through the intermediate channel $D^{*+} D^0$. We present a study of its strange companions with the quantum numbers of $c c \bar q \bar s$, where $q = u, d$ and isospin violation is neglected.
In this article, we assume that there exist hidden charmed tetraquark states with the spin-parity $J^P=1^-$, and calculate their masses with the QCD sum rules. The numerical result indicates that the masses of the vector hidden charmed tetraquark states are about $M_{Z}=(5.12\pm0.15) \rm{GeV}$ or $M_{Z}=(5.16\pm0.16) \rm{GeV}$, which are inconsistent with the experimental data on the $π^+ χ_{c1}$ invariant mass distribution. The hidden charmed mesons $Z_1$, $Z_2$ or $Z$ may be scalar hidden charmed tetraquark states, hadro-charmonium resonances or molecular states.
In the paper we discuss contribution of the doubly intrinsic heavy mechanism into the production of $B_c$ meson, the doubly heavy baryons and the all-charm tetraquark at a future fixed-target experiment at the LHC (AFTER@LHC). The production cross sections and the mean values of Feynman-x for the finale states are presented.
Spectrum of the low-lying hidden- and double-charm tetraquark states are investigated in a nonrelativistic quark potential model, where the Instanton-induced interaction is taken as the residual spin-dependent hyperfine interaction between quarks. The model parameters are fixed by fitting the spectrum of the ground hadron states. Our numerical results show that masses of several presently studied tetraquark states are close to those of the experimentally observed candidates of exotic meson, which indicates that the corresponding compact tetraquark components may take considerable probabilities…
In this article, we study the masses and pole residues of the pseudoscalar-diquark-pseudoscalar-antidiquark type and vector-diquark-vector-antidiquark type scalar hidden-charm $cu\bar{c}\bar{d}$ ($cu\bar{c}\bar{s}$) tetraquark states with QCD sum rules by taking into account the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. The predicted masses can be confronted with the experimental data in the future. Possible decays of those tetraquark states are also discussed.
We apply the newly developed NRQCD factorization formula to analyze the exclusive production of the fully-charmed tetraquark $T_{4c}$ plus a hard photon at $B$ factory. For simplicity, in this work we have concentrated on the associated production of the $0^{++}$ and $2^{++}$ tetraquarks with a photon. With some rough estimates about the size of the unknown nonperturbative NRQCD matrix elements, we predict the production rates of these types of exclusive channels at $\sqrt{s}=10.6$ GeV and also assess their observation prospect at {\tt Belle 2} experiment.
We study all-charm tetraquarks in the front form of Hamiltonian dynamics using the many-body basis function approach known as basis light-front quantization. The model Hamiltonian contains transverse and longitudinal confining potentials and a one-gluon-exchange effective potential. We calculate masses of two-charm-two-anticharm states focusing on the lowest state. We also calculate two-quark and four-quark estimates of meson-meson breakup threshold. The results suggest that the lowest two-charm-two-anticharm state is not a tightly bound tetraquark. We discuss implications of the cluster decom…
The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson-meson states with the four-quark states 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 cryptoexotic mesons including the quarks of three flavours (u, d, s) and the charmed quark are constructed. The poles of these amplitudes determine the masses of tetraquarks. The mass values of low-lying tetraquarks are calculated.
We study the possible charmonium-like states with $J^{PC}=0^{--}, 0^{-+}$ using the tetraquark interpolating currents with the QCD sum rules approach. The extracted masses are around 4.5 GeV for the $0^{--}$ charmonium-like states and 4.6 GeV for the $0^{-+}$ charmonium-like states while their bottomonium-like analogues lie around 10.6 GeV. We also discuss the possible decay, production and the experiment search of the $0^{--}$ charmonium-like state.
We use a non-relativistic model to study the spectroscopy of a tetraquark composed of $[cc][\bar{c}\bar{c}]$ in a diquark-antidiquark configuration. By numerically solving the Schrödinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the $c\bar{c}$ spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory descript…
We present a systematic and selfconsistent analysis of four-quark charmonium states and applied it to study compact four-quark systems and meson-meson molecules. Our results are robust and should serve to clarify the situation of charmonium spectroscopy above the threshold production of charmed mesons.
The cross section value of doubly charmonium production in e+e- annihilations have been estimated at interaction energy 10.6 GeV. The quarkonium wave function shape, as well as the nonzero value of charm quark have been taken into account.
In the present work, we adopt the scalar, pseudoscalar, vector, axialvector and tensor (anti)diquark operators as the elementary building blocks to construct vector and tensor local four-quark currents without introducing explicit P-waves, and explore the mass spectrum of the vector hidden-charm tetraquark states via the QCD sum rules comprehensively, and revisit the interpretations of the existing $Y$ states in the scenario of vector tetraquark states. We resort to the energy scale formula to enhance the pole contributions and improve the convergent behaviors of the operator product expansion…
We analyze the singlet $P$--wave charmonium production at $e^+ e^-$ colliders within the framework of unconstrained supersymmetry. We show that the CP--violating transitions, dominated by the gluino exchange, are typically four orders of magnitude larger than the CP--conserving ones, and former is generated by the electric dipole moment of the charm quark. Our results can be directly tested via the charmonium searches at the CLEO--c experiment.
This contribution briefly discusses some new theoretical results for the properties of charmonium, especially the "higher charmonium" states above open-charm threshold. In particular we discuss the spectrum of states, open-flavor strong decays, and the surprisingly large effects of virtual decay loops of charmed meson pairs.
Possible experimental searches of doubly charmed baryons and tetraquarks at fixed target experiments with high energy hadron beams and a high intensity spectrometer are considered here. The baryons considered are: $Ξ_{cc}^{+}$ (ccd), $Ξ_{cc}^{++}$ (ccu), and $Ω_{cc}^{+}$ (ccs); and the tetraquark is T ($cc\bar{u}\bar{d}$). Estimates are given of masses, lifetimes, internal structure, production cross sections, decay modes, branching ratios, and yields. Experimental requirements are given for optimizing the signal and minimizing the backgrounds. This paper is designed as an experimental and the…
In this study, the properties of the $J^{PC}=1^{++}$ hidden charm poles are analyzed under the variation of the bare 2P charmonium mass within the effective field theory proposed in Ref.[1]. The main focus of the current work is on the pole trajectory of the $χ_{c1}(2P)$ charmonium dressed by the $D \bar{D}^*$ meson loops. It is shown that the trajectories of the pole change radically for values of the bare charmonium mass above a certain value and also depending on how close the pole is to the threshold.
We study the mass spectra for the $cc\bar c\bar c$ and $bb\bar b\bar b$ tetraquark states by developing a moment sum rule method. Our results show that the $bb\bar b\bar b$ tetraquarks lie below the threshold of $η_b(1S)η_b(1S)$. They are probably stable and very narrow. The masses for the doubly hidden-charm states $cc\bar c\bar c$ are higher than the spontaneous dissociation thresholds of two charmonium mesons. We suggest to search for such states in the $J/ψJ/ψ$ and $η_c(1S)η_c(1S)$ channels.
In the diquark-diantiquark composition, we study the masses of hidden charm tetraquark systems ($cq\bar{c}\bar{q}$, $cs\bar{c}\bar{s}$ and $cs\bar{c}\bar{q}$) using a linear confinement potential. In this study, we have factorized the four body system into three subsequent two body systems. To remove degeneracy in the S and P wave masses of mesons and tetraquark states, the spin-spin, spin orbit and tensor components of the confined one gluon exchange interactions are employed. In this attempt, we have been able to assign the $ψ(4230)$ as pure $cq\bar{c}\bar{q}$ tetraquark state. $ψ(4360)$ and…
This talk summarizes the status of the charmonium system, with particular emphasis on outstanding problems in QCD spectroscopy which a tau-charm factory can address.
By using QCD sum rules, the mass of the hidden charm tetraquark $[cu][\bar{c}\bar{d}]$ state with $I^{G} (J^{P}) = 1^+ (1^{+})$ (HCTV) is estimated, which presumably will turn out to be the newly observed charmonium-like resonance $Z_c^+(3900)$. In the calculation, contributions up to dimension eight in the operator product expansion(OPE) are taken into account. We find $m_{1^+}^c = (3912^{+306}_{-153}) \, \text{MeV}$, which is consistent, within the errors, with the experimental observation of $Z_c^+(3900)$. Extending to the b-quark sector, $m_{1^+}^b = (10561^{+395}_{-163}) \,\text{MeV}$ is …
Recent theoretical progress in calculations of the spectrum and decays of charmonium is reviewed. Traditionally, our understanding of charmonium was based on potential models. This is now being replaced by first principles.
We discuss the production of the exotic doubly-charmed tetraquark mesons ${\rm T}_{{\rm c}{\rm c}}({\rm c}{\rm c}\bar{\rm u}\bar{\rm d})$ from electron-positron collisions. ${\rm T}_{{\rm c}{\rm c}}({\rm c}{\rm c}\bar{\rm u}\bar{\rm d})$ is a compact exotic hadron whose binding energy is provided by the diquark correlations. We evaluate the production cross section in the electron-positron collisions using the nonrelativistic QCD framework, and investigate the difference of the production cross section for different color configurations in two charm quarks (antitriplet and sextet), where the m…
In this article, we introduce a relative P-wave to construct the doubly-charm axialvector diquark operator, then take the doubly-charm axialvector (anti)diquark operator as the basic constituent to construct the scalar and tensor tetraquark currents to study the scalar, axialvector and tensor fully-charm tetraquark states with the QCD sum rules. We observe that the ground state $\tilde{A}\tilde{A}$ type tetraquark states and the first radial excited states of the $AA$ type tetraquark states have almost degenerated masses, where the $\tilde{A}$ and $A$ stand for the diquark operators with and w…
Based on the diquark configuration, we construct the diquark-antidiquark interpolating tetraquark currents with $J^{PC}=1^{-\pm}$ and $1^{+\pm}$, which can couple to the scalar and pseudoscalar tetraquark states respectively, since they are not conserved currents. Then we investigate their two-point correlation functions including the contributions of the vacuum condensates up to dimension-10 and extract the masses and pole residues of the tetraquark states with $J^{PC}=0^{+\pm}$ and $0^{-\pm}$ through the QCD sum rule approach. The predicted masses can be confronted with the experimental data…
We discuss the interpretation of the $J\!/\!ψ\,J\!/\!ψ$ peak recently seen by the LHCb collaboration at CERN, and take the opportunity to review the experimental and theoretical state of the art for exotic hadrons. It is stressed that in constituent models, the states in the continuum require a dedicated treatment to single out resonances atop the continuum.
The chromomagnetic interaction, with full account for flavour-symmetry breaking, is applied to S-wave configurations containing two quarks and two antiquarks. Phenomenological implications are discussed for light, charmed, charmed and strange, hidden-charm and double-charm mesons, and extended to their analogues with beauty.
In this article, we take the pseudoscalar, scalar, axialvector, vector, tensor (anti)diquark operators as the basic constituents, and construct the scalar, axialvector and tensor tetraquark currents to study the mass spectrum of the ground state hidden-charm tetraquark states with the QCD sum rules in a comprehensive way. We revisit the assignments of the $X$, $Y$, $Z$ states, such as the $X(3860)$, $X(3872)$, $X(3915)$, $X(3940)$, $X(4160)$, $Z_c(3900)$, $Z_c(4020)$, $Z_c(4050)$, $Z_c(4055)$, $Z_c(4100)$, $Z_c(4200)$, $Z_c(4250)$, $Z_c(4430)$, $Z_c(4600)$, etc in the scenario of tetraquark st…
Studying the hidden-charm dipion decays of the charmoniumlike state Y(4360), we show that there exist charged charmoniumlike structures near $D\bar{D}^*$ and $D^*\bar{D}^*$ thresholds in the $J/ψπ^+$, $ψ(2S)π^+$ and $h_c(1P)π^+$ invariant mass spectra of the corresponding hidden-charm dipion decays of Y(4360) using the {\it{Initial Single Pion Emission} mechanism}. We suggest to do further experimental study on these predicted charged enhancement structures, especially by BESIII, Belle, and the forthcoming BelleII.
After constructing all the tetraquark interpolating currents with $J^{PC}=1^{-+}, 1^{--}, 1^{++}$ and $1^{+-}$ in a systematic way, we investigate the two-point correlation functions to extract the masses of the charmonium-like states with QCD sum rule. For the $1^{--}$ $qc\bar q\bar c$ charmonium-like state, $m_X=4.6\sim4.7$ GeV, which implies a possible tetraquark interpretation for the state Y(4660). The masses for both the $1^{++}$ $qc\bar q\bar c$ and $sc\bar s\bar c$ charmonium-like states are around $4.0\sim 4.2$ GeV, which are slightly above the mass of X(3872). For the $1^{-+}$ $qc\ba…
