Inspired by the observation of the fully-charm tetraquark $X(6900)$ state at LHCb, the production of $X(6900)$ in $\bar{p}p\rightarrow J/ψJ/ψ$ reaction is studied within an effective Lagrangian approach and Breit-Wigner formula. The numerical results show that the cross section of $X(6900)$ at the c.m. energy of 6.9 GeV is much larger than that from the background contribution. Moreover, we estimate dozens of signal events can be detected by D0 experiment, which indicates that searching for the $X(6900)$ via antiproton-proton scattering may be a very important and promising way. Therefore, related experiments are suggested to be carried out.
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.
In this article, we study the first radial excited states of the scalar, axialvector, vector and tensor diquark-antidiquark type $cc\bar{c}\bar{c}$ tetraquark states with the QCD sum rules and obtain the masses and pole residues, then we use the Regge trajectory to obtain the masses of the second radial excited states. The predicted masses support assigning the broad structure from 6.2 to 6.8 GeV in the di-$J/ψ$ mass spectrum to be the first radial excited state of the scalar, axialvector, vector or tensor $cc\bar{c}\bar{c}$ tetraquark state, and assigning the narrow structure at about 6.9 GeV…
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 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 e…
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…
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…
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.
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…
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…
We describe a heavy and exotic tetraquark state as a holographic molecule, by binding the lightest heavy-light meson $(0^-, 1^-)$ multiplet to a flavored sphaleron, in the bulk of the Witten-Sakai-Sugimoto model. Bound tetraquark states emerge as Efimov states in the heavy quark limit, with a binding energy for charm tetraquark comparable to the $T_{cc}^+$ recently reported by the LHCb, but a substantially smaller width, for a large but finite $^\prime$t Hooft coupling. Fixing the parameters of the model at the empirical mass of $T_{cc}^+$ allows us to predict the bindings of the undiscovered …
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.
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…
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…
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…
We perform a quantitative analysis of the $bb\bar{b}\bar{b}$ tetraquark decays into hidden- and open-bottom mesons and calculate, for the first time, the $bb\bar{b}\bar{b}$ tetraquark total decay width. On the basis of our results, we propose the $bb\bar{b}\bar{b} \to B^{+} B^{-} (B^0 \bar{B}^0) (B_s^0 \bar{B}_s^0) \to l^{+} l^{-}+\text{X}$ decays as the most suitable channels to observe the $bb\bar{b}\bar{b}$ tetraquark states, since the calculated two-lepton cross section upper limit, $\simeq 39 $ fb, is so large as to be potentially detectable with the 2018 LHCb sensitivity, paving the way …
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 …
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…
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…
The masses of the ground state and excited heavy tetraquarks with hidden charm and bottom 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 the open charm threshold are discussed. The obtained results indicate that X(3872), Y(4260), Y(4360), Z(4433) and Y(4660) can be tetraquark states with hidden charm.
The masses of heavy tetraquarks with hidden charm and bottom are calculated in the framework of the relativistic quark model. The tetraquark is considered as the bound state of a heavy-light diquark and antidiquark. The light quark in a heavy-light diquark is treated completely relativistically. The internal structure of the diquark is taken into account by calculating the diquark-gluon form factor in terms of the diquark wave functions. New experimental data on charmonium-like states above open charm threshold are discussed. The obtained results indicate that the X(3872) can be the tetraquark…
We provide comprehensive investigations for the mass spectrum of exotic open-flavor charmed/bottom $sq\bar q\bar c$, $qq\bar q\bar c$, $sq\bar q\bar b$, $qq\bar q\bar b$ tetraquark states with various spin-parity assignments $J^P=0^+, 1^+, 2^+$ and $0^-, 1^-$ in the framework of QCD sum rules. In the diquark configuration, we construct the diquark-antidiquark interpolating tetraquark currents using the color-antisymmetric scalar and axial-vector diquark fields. The stable mass sum rules are established in reasonable parameter working ranges, which are used to give reliable mass predictions for…
In this work, we take all the color-antitriplet diquarks, such as the scalar, pseudoscalar, vector, axialvector and tensor diquarks, as the basic constituents to construct the local pseudoscalar four-quark currents without importing the explicit P-waves to implement the negative-parity, and investigate the mass spectroscopy of the pseudoscalar hidden-charm tetraquark states without strange, with strange and with hidden-strange in the framework of the QCD sum rules in a consistent and comprehensive way. We obtain the lowest mass $4.56\pm0.08\,\rm{GeV}$ for the pseudoscalar tetraquark state with…
We perform a quantitative analysis of the decays of $cc\bar c\bar c$ tetraquarks with $J^{PC}=0^{++}, 2^{++}$ into 4 muons and into hidden- and open-charm mesons and estimate, for the first time, the fully charmed tetraquark decay width. The calculated cross section upper limit is $\sim 40$ fb for the 4 muons channel, and $\sim 28$ nb for the $D^{(*)} \bar D^{(*)} \to eμ$ channel. On the basis of our results, with the present sensitivity LHCb should detect both signals, for $0^{++}$ and $2^{++}$ fully-charmed tetraquarks.
We study the spectra of the doubly charmed tetraquark states in a diquark-antidiquark model. The doubly charmed tetraquark states form an antitriplet and a sextet configurations according to flavor SU(3) symmetry. For the tetraquark state $[qq'][\bar c\bar c]$, we show the mass for both bound and excited states. The two-body decays of tetraquark states $T^{cc}[0^+]$ and $T^{cc}[1^{--}]$ to charmed mesons have also been studied. In the end,the doubly charmed tetraquarks decays to a charmed baryon and a light baryon have been studied in the SU(3) flavor symmetry.
In the framework of the chiral quark model along with complex scaling range, we perform a dynamical study on the low-lying $S$-wave doubly-heavy tetraquark states ($QQ\bar{q}\bar{q}$, $Q=c, b$ and $q=u, d$) with an accurate computing approach, Gaussian expansion method. The meson-meson and diquark-antidiquark configurations within all possible color structures for spin-parity quantum numbers $J^P=0^+$, $1^+$ and $2^+$, and in the $0$ and $1$ isospin sectors are considered. Possible tightly bound and narrow resonance states are obtained for doubly-charm and doubly-bottom tetraquarks with $IJ^P=…
We analyse the deuteron-like $T^+_{cc}$ state observed by the LHCb Collaboration from the perspective of the quark clustering. The $T^+_{cc}$ state implies the possible existence of other compact doubly heavy tetraquark states.
In this article, we study the $S\bar{S}$ type scalar tetraquark state $cq\bar{c}\bar{q}$ in details with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and obtain the value $M_{Z_c}=\left(3.82^{+0.08}_{-0.08}\right)\,\rm{GeV}$, which is the lowest mass for the hidden charmed tetraquark states from the QCD sum rules. Furthermore, we calculate the hadronic coupling constants $G_{Z_cη_cπ}$ and $G_{Z_cDD}$ with the three-point QCD sum rules, then study the strong decays $ Z_c\to η_cπ\, ,\, DD$, and observe that the…
The three pentaquark states, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, discovered by the LHCb Collaboration in 2019, can be arranged into a complete heavy quark spin symmetry multiplet of hadronic molecules of $\bar{D}^{(\ast)}Σ_{c}^{(\ast)}$. In the heavy quark mass limit, the $Σ_{c}^{(\ast)}$ baryons can be related to the doubly charmed tetraquark states of isospin 1, i.e., $T_{\bar{c}\bar{c}}^{(\ast)}$( $T_{\bar{c}\bar{c}}^{0}$, $T_{\bar{c}\bar{c}}^{1}$, $T_{\bar{c}\bar{c}}^{2}$), via heavy antiquark diquark symmetry, which dictates that the $\bar{D}^{(\ast)}Σ_{c}^{(\ast)}$ interactions are…
The spectrum of tetraquark states with hidden charm is studied within an effective QCD Coulomb gauge Hamiltonian approach. Of the four independent color schemes, two are investigated, the $(q\bar{c})_1(c\bar{q})_1$ singlet-singlet (molecule) and the $(qc)_3(\bar{q}\bar{c})_3$ triplet-triplet (diquark), for selected $J^{PC}$ states using a variational method. The predicted masses of triplet-triplet tetraquarks are roughly a GeV heavier than the singlet-singlet states. There is also an interesting flavor dependence with $(q\bar{q})_1(c\bar{c}_1)$ states about half a GeV lighter than $(q\bar{c})_…
