We study the pair description of heavy tetraquark systems $|QQ\bar Q \bar Q\rangle$ in the frame of a non-relativistic potential model. By taking the two heavy quark pairs $(Q\bar Q)$ as colored clusters, the four-quark Schrödinger equation is reduced to a two-pair equation, when the inner motion inside the pairs can be neglected. Taking into account all the Casimir scaling potentials between two quarks and using the lattice QCD simulated mixing angle between the two color-singlet states for the tetraquark system, we extracted a detailed pair potential between the two heavy quark pairs.
A review is presented of some discussions about the fully-heavy tetraquarks made of two charmed quarks and two anticharmed antiquarks, and other multiquark states involving some heavy flavors.
Chiral Quark Soliton Model has been successfully applied to describe heavy baryon spectrum, both for charm and bottom, leading to the conclusion that the heavy quark has no effect on the soliton. This suggests that replacing a heavy quark by a heavy anti-diquark $\bar{Q}\bar{Q}$ in color triplet should give a viable description of heavy tetraquarks. We follow this strategy to compute tetraquark masses. To estimate heavy diquark masses we use Cornell potential with appropriately rescaled parameters. The lightest charm tetraquark is 70 MeV above the $DD^*$ threshold. On the contrary, both non-st…
In this article, we study the ground-state mass of full-heavy tetraquarks $cc\bar c\bar c$ and $bb\bar b \bar b$ with solving the nonrelativistic four-body systems. The flux-tube configurations, the tetraquark four-body potential butterfly, and the dimeson potential flip-flop of SU(3) lattice quantum chromodynamics have been applied to describe the tetraquark interaction. Our numerical analysis indicates that the disconnected and connected static potentials can predict the mass of tetraquark very close to experimental data.
Using an extended chromomagnetic model, we perform a systematic study of the masses of the doubly heavy tetraquarks. We find that the ground states of the doubly heavy tetraquarks are dominated by color-triplet $\ket{(qq)^{\bar{3}_{c}}(\bar{Q}\bar{Q})^{3_{c}}}$ configuration, which is opposite to that of the fully heavy tetraquarks. The combined results suggest that the color-triplet configuration becomes more important when the mass difference between the quarks and antiquarks increases. We find three stable states which lie below the thresholds of two pseudoscalar mesons. They are the $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.
The homogeneous Lippmann-Schwinger integral equation is solved in momentum space to calculate the masses of heavy tetraquarks with hidden charm and bottom. The tetraquark bound states are studied in the diquark-antidiquark picture as a two-body problem. A regularized form of the diquark-antidiquark potential is used to overcome the singularity of the confining potential at large distances or small momenta. Our numerical results indicate that the relativistic effect leads to a small reduction in the mass of heavy tetraquarks, which is less than $2\,\%$ for charm and less than $0.2\,\%$ for bott…
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.
This paper focuses on tetraquarks containing one heavy quark and one heavy antiquark in the formal limit where the heavy quark masses go to infinity. It extends the theoretical framework developed for tetraquark containing two heavy quarks based on semi-classical analysis and the Born-Oppenheimer approximation. It is shown that for sufficiently small light quark masses, parametrically narrow $q\bar{q}'Q\bar{Q}$ tetraquarks must exist in the formal limit of arbitrarily large heavy quark masses. The analysis is model-independent; it requires no assumptions about the structure of the state or the…
In this article, we construct the axialvector-diquark-scalar-antidiquark type currents to interpolate the axialvector doubly heavy tetraquark states, and study them with the QCD sum rules in details by carrying out the operator product expansion up to the vacuum condensates of dimension 10.
During recent years, the study of exotic hadrons including tetraquarks and pentaquarks has attracted a lot of interests and more studies are in progress experimentally and theoretically. It is well-known that at sufficiently large transverse momentum the dominant production mechanism for standard heavy hadrons (mesons/baryons) is actually the fragmentation so that the same mechanism is also proposed for the production of heavy exotic hadrons. This work is the first attempt to study the direct fragmentation of a heavy quark into ground state heavy tetraquarks in leading order of perturbative QC…
We give heavy quark-diquark symmetry predictions for doubly heavy baryons and tetraquarks in light of the recent discovery of the $Ξ_{cc}^{++}$ by LHCb. For five excited doubly charm baryons that are predicted to lie below the $Λ_c D$ threshold, we give predictions for their electromagnetic and strong decays using a previously developed chiral Lagrangian with heavy quark-diquark symmetry. Based on the mass of the $Ξ_{cc}^{++}$, the existence of a doubly heavy bottom $I=0$ tetraquark that is stable to the strong and electromagnetic decays has been predicted. If the mass of this state is below 1…
Assuming X(3872) is a $qc \bar q \bar c$ tetraquark and using its mass as input, we perform a schematic study of the masses of possible heavy tetraquarks using the color-magnetic interaction with the flavor symmetry breaking corrections.
In this article, we perform a systematic study of the mass spectrum of the scalar doubly charmed and doubly bottom tetraquark states using the QCD sum rules.
We study lifetimes and weak decays of the triply heavy tetraquarks ${b\bar c}{b\bar q}$. Following the heavy quark expanding(HQE), the lifetimes of tetraquarks ${b\bar c}{b\bar q}$ can be expressed as the summation of different dimension operators. Particularly, we obtain the lifetimes of ${b\bar c}{b\bar q}$ at the next-to-leading order(NLO) given as $τ(T^{\{bb\}}_{\{\bar c\bar q\}})=0.70\times 10^{-12}s$. Besides, we construct the weak decays Hamiltonian of ${b\bar c}{b\bar q}$ in hadronic level under the SU(3) flavor symmetry. The discussion of the Hamiltonian can deduce the decay amplitude…
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…
There exist heavy tetraquark states $QQ \bar q \bar q$ in the heavy quark limit. These states are stable with respect to strong interactions and hence must decay weakly. It is shown that the semileptonic decay depends on a single Isgur--Wise form factor, which can be expressed in term of the Isgur--Wise form factors which govern the semileptonic decays of the $Qqq$ and $QQq$ baryons.
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.
Previous work done in collaboration with David Brink is reviewed in the light of the recent observation of new charmonium-like resonances which can be interpreted as tetraquarks. In the framework of a schematic quark model the spectrum of $c \bar c q \bar q $ tetraquarks is presented
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.
In this article, we take the point of view that the charmed scalar meson $D_{s0}(2317)$ be a tetraquark state and devote to calculate its mass within the framework of the QCD sum rules approach in the heavy quark limit. The numerical values for the mass of the $D_{s0}(2317)$ are consistent with the experimental data, there must be some tetraquark component in the scalar meson $D_{s0}(2317)$. Detailed discussions about the threshold parameter and Borel parameter for the multiquark states are also presented.
In the light of the recent discovery of the $Ξ^{++}_{cc}$ by LHCb collaboration, we study the stable doubly heavy tetraquarks. These states are compact exotic hadrons which can be approximated as the diquark-anti-diquark correlations. In the flavor SU(3) symmetry, they form an SU(3) triplet or anti-sextet. The spectra of the stable doubly heavy tetraquark states are predicted by Sakharov-Zeldovich formula. We find that the $T^+_{cc\bar{u}\bar{d}}({\bf 3})$ is about 16MeV below the $DD^*$ threshold, while $T^{-}_{bb\bar{u}\bar{d}}({\bf 3})$ is about 73MeV below the $BB^*$ threshold. We then stu…
In the current work spectroscopy and possibility of observation at the LHC of tetraquarks composed of 4 heavy quarks is discussed. Tetraquarks concerned are T_{4c}=[cc][cc]$, T_{4b}=[bb][bb] and T_{2[bc]}=[bc][bc]. By solving nonrelativistic Schroedinger equation masses of these states are found with the hyperfine splitting accounted for. It is shown that masses of tensor tetraquarks T_{4c}(2++) and T_{2[bc]}(2++) are high enough to observe these states as peaks in the invariant mass distributions of heavy quarkonia pairs in pp -> T_{4c}+X -> 2J/ψ+X, pp -> T_{2[bc]}+X -> 2B_{c}+X and pp -> T_{…
In this work, we compute masses and magnetic moments of the heavy baryons and tetraquarks with one and two open heavy flavors in a unified framework of MIT bag model. Using the parameters of MIT bag model, we confirm that an extra binding energy, which is supposed to exist between heavy quarks ($c$ and $b$) and between heavy and strange quarks in literatures, is required to reconcile light hadrons with heavy hadrons. Numerical calculations are made for all light mesons, heavy hadrons with one and two open heavy flavors, predicting the masses of doubly charmed baryons to be $ M(Ξ_{cc})=3.604$ G…
In the present work, the triply heavy tetraquarks states $QQ\bar{Q}\bar{q}$ with $Q=(c, b)$ and $q=(u, d, s)$ with all possible quantum numbers are systematically investigated in the framework of the chiral quark model with the resonance ground method. Two kinds of structures, including the meson-meson configuration (the color-singlet channels and the hidden-color channels) and the diquark-antidiquark configuration (the color sextet-antisextet and the color triplet-antitriplet), are considered. In the considered system, several bound states are obtained for the $cc\bar{c}\bar{q^{'}}$, $bb\bar{…
Tetraquarks QQq*q* are found to be described remarkably well with the Quantum Chromodynamics version of the Hydrogen bond, as treated with the Born-Oppenheimer approximation. We show the robustness of the method by computing the mass of the observed Tcc tetraquark following two different paths. Relying on this, we provide a prediction for the mass of the expected Tbb particle. The average sizes of tetraquarks are estimated to be approximately 3 - 5 GeV**-1. As a consequence hyperfine separations are not expected to be sizeable. We discussed possible reasons why LHCb has observed only one state…
With the discovery of a doubly charmed $Ξ_{cc}$ baryon a somewhat forgotten issue of tetraquarks containing two heavy and two light (anti) quarks, ${\cal T}_{QQ}$, triggered theorist's interest. We discuss quark model estimates of ${\cal T}_{QQ}$ masses and such objects including a model where the light sector is treated as a soliton. We show that this model has different large $N_c$ limit than other approaches.
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=…
In this paper we present in greater detail previous work on the Born-Oppenheimer approximation to treat the hydrogen bond of QCD, and add a similar treatment of doubly heavy baryons. Doubly heavy exotic resonances X and Z can be described as color molecules of two-quark lumps, the analogue of the H_2 molecule, and doubly heavy baryons as the analog of the H_2^+ ion, except that the two heavy quarks attract each other. We compare our results with constituent quark model and lattice QCD calculations and find further evidence in support of this upgraded picture of compact tetraquarks and baryons.
The mass spectra of light-heavy tetraquarks $cq\bar{c}\bar{q}$ (q= u, d) are computed in a non-relativistic diquark model with one-gluon exchange plus confining potential. In the diquark model, a $cq\bar{c}\bar{q}$ state is regarded to be made of a light-heavy diquark (qc) and an antidiquark $\bar{q}\bar{c}$ in triplet and antitriplet colour configuration respectively. The masses of charm mesons were calculated in order to fit the model parameters used to create the masses of tetraquarks and therefore enhance the model's reliability. The masses of $(cq\bar{c}\bar{q})$ tetra-quark states are de…
Recently, some progresses have been made on the double-heavy tetraquarks in the experiments, such as $T_{cc}$ reported by LHCb Collaboration, and $X_{cc\bar{s}\bar{s}}$ reported by the Belle Collaboration. Coming on the heels of our previous work about $T_{cc}$ and $T_{bb}$, we present a study on the bound states and the resonant states of its companions $QQ\bar{q}\bar{s}$ ($Q=c,b; q=u, s$) tetraquarks with strange flavor in the chiral quark model. Two pictures, one with meson-meson picture, another with diquark-antidiquark picture and their couplings are considered in our calculations. Isospi…
We report on an effective field theory (EFT) description of exotic quarkonia as bound states on the spectrum of hybrid and tetraquark static energies. We provide expressions for hybrid and tetraquark static energies in terms of Wilson loops. The former have been computed in quenched lattice calculations but the latter are yet unavailable. From the few simulations with dynamical light-quarks we argue that the overall picture from hybrid static energies does not change but additional states, such as heavy meson pairs, need to be considered for a full description. In this EFT framework for quarko…
We study the weak decays of exotic tetraquark states ${b\bar c}{q\bar q}$ with two heavy quarks. Under the SU(3) symmetry for light quarks, these tetraquarks can be classified into an octet plus a singlet: $3\bigotimes\bar 3=1\bigoplus8$. We will concentrate on the octet tetraquarks with $J^{P}=0^{+}$, and study their weak decays, both semileptonic and nonleptonic. Hadron-level effective Hamiltonian is constructed according to the irreducible representations of the SU(3) group. Expanding the Hamiltonian, we obtain the decay amplitudes parameterized in terms of a few irreducible quantities. Bas…
We study the lifetime and weak decays of the full-heavy S-wave $0^+$ tetraquark $T^{\{bb\}}_{\{\bar c\bar c\}}$. Using the operator product expansion rooted in heavy quark expansion, we find a rather short lifetime, at the order $(0.1-0.3)\times 10^{-12}s$ depending on the inputs. With the flavor SU(3) symmetry, we then construct the effective Hamiltonian at the hadron level, and derive relations between decay widths of different channels. According to the electro-weak effective operators, we classify different decay modes, and make a collection of the golden channels, such as $T_{\{\bar c \ba…
We systematically investigate the stability of the doubly heavy tetraquark states $[QQ][\bar{q}\bar{q}]$ ($Q=c$ and $b$, $q=u$, $d$ and $s$) within the framework of the color flux-tube model involving a multibody confinement potential, $σ$-exchange, one-gluon-exchange and one-Goldstone-boson-exchange interactions. Our numerical analysis indicates that the states $[bb][\bar{u}\bar{d}]$ with $01^+$ and $[bb][\bar{u}\bar{s}]$ with $\frac{1}{2}1^+$ are the most promising stable states against strong interactions. The states $[cc][\bar{u}\bar{d}]$ with $01^+$, $[bc][\bar{u}\bar{d}]$ with $00^+$, $0…
Scalar tetraquark states are studied within the diquark-antidiquark picture in a non-relativistic approach. We consider two types of confining potentials, a quadratic and a linear one, to which we also add spin-spin, isospin-isospin, and spin-isospin interactions. We calculate the masses of the scalar diquarks and of the ground-state open and hidden charmed and bottom scalar tetraquarks. Our results indicate that the scalar resonances $D_{0}^{\ast}(2400)$ and $D_{s}(2632)$ have a sizable tetraquark amount in their wave function, while, on the other hand, it turns out that the scalar states $D_…
Diquarks with $J^{P}=0^{\pm}$, $1^{\pm}$ containing a heavy (charm or bottom) quark and a light quark are investigated using QCD Laplace sum rules. Masses are determined using appropriately constructed gauge invariant correlation functions, including for the first time next-to-leading order perturbative contributions. The $J^P=0^+$ and $1^+$ charm-light diquark masses are respectively found to be 1.86$\pm$0.05 GeV and 1.87$\pm$0.10 GeV, while those of the $0^+$ and $1^+$ bottom-light diquarks are both determined to be 5.08$\pm$0.04 GeV. The sum rules derived for heavy-light diquarks with negat…
A systematic study of multiquark exotics with one or $N_c-1$ heavy quarks in the large $N_c$ limit is presented. By binding a chiral soliton to a heavy meson, either a normal $N_c$-quark baryon or an exotic $(N_c+2)$-quark baryon is obtained. By replacing the heavy quark with $N_c-1$ heavy antiquarks, exotic $(2N_c-2)$-quark and $2N_c$-quark mesons are obtained. When $N_c = 3$, they are just the normal triquark baryon $Qqq$, the exotic pentaquark baryon $Q\bar q\bar q\bar q\bar q$, tetraquark di-meson $\bar Q \bar Q qq$ and the hexaquark di-baryon $\bar Q \bar Q \bar q \bar q\ bar q \bar q$ re…
Hadrons and their distributions are the most direct observables in experiment, which would shed light on the non-perturbative mystery of quantum chromodynamics (QCD). As the result, any new hadron will challenge our current knowlege on the one hand, and provide additional inputs on the other hand. The fully heavy $cc\bar{c}\bar{c}$ system observed by LHCb recently opens a new era for hadron physics. We first extract the internal structure of the fully heavy tetraquarks directly from the experimental data, within the compact tetraquark picture. By fitting to the di-$J/ψ$ lineshape, we find that…
We present a study of the isospin-violating one-pion strong decays of single heavy tetraquarks $X_Q = X(s q \bar q \bar Q)$, $Q=c, b$, and $q=u, d$ with spin-parity $J^P = 0^+$. We assume that the tetraquarks have the configuration of a color diquark and a antidiquark. Three mechanisms of isospin violation can contribute to the decay rate: (1) mixing of the $X(s u \bar u \bar Q)$ and $X(s d \bar d \bar Q)$ tetraquark currents, (2) an explicit $m_d-m_u$ quark mass difference in the quark diagrams describing the corresponding decay transitions and (3) $π^0-η$ mixing in the final state. Our main …
Masses of tetraquarks with two heavy quarks and open charm and bottom are calculated in the framework of the diquark-antidiquark picture in the relativistic quark model. All model parameters were regarded as fixed by previous considerations of various properties of mesons and baryons. The light quarks and diquarks are treated completely relativistically. The c quark is assumed to be heavy enough to make the diquark configurations dominating. The diquarks are considered not to be point-like but to have an internal structure which is taken into account by the calculated diquark form factor enter…
In the framework of a nonrelativistic chiral quark model, we continue to study the mass spectra of the fully-heavy $bb\bar{c}\bar{c}$ and $bc\bar{b}\bar{c}$ tetraquarks. In the present calculations, two structures, meson-meson [$\bar{Q}Q$][$\bar{Q}Q$] and diquark-antidiquark [$QQ$][$\bar{Q}\bar{Q}$] ($Q$ = $c$ or $b$), and their mixing, along with all possible color, spin configurations are considered. The calculations suggest that no bound state can be formed for $bb\bar{c}\bar{c}$ and $bc\bar{b}\bar{c}$ systems. However, resonances are possible because of the color structure. Several resonan…
In the framework of the color-magnetic interaction, we systematically investigate the mass splittings of the $QQ\bar{Q}\bar{q}$ tetraquark states and estimated their rough masses in this work. These systems include the explicitly exotic states $cc\bar{b}\bar{q}$ and $bb\bar{c}\bar{q}$ and the hidden exotic states $cc\bar{c}\bar{q}$, $cb\bar{b}\bar{q}$, $bc\bar{c}\bar{q}$, and $bb\bar{b}\bar{q}$. If a state around the estimated mass region could be observed, its nature as a genuine tetraquark is favored. The strong decay patterns shown here will be helpful to the experimental search for these e…
In the heavy-quark limit, the two heavy quarks in a doubly heavy baryon or a doubly heavy tetraquark are bound by their color-Coulomb potential into a compact diquark. The doubly heavy hadrons are related by the approximate heavy-quark--diquark symmetry of QCD to the heavy hadrons obtained by replacing the heavy diquark by a heavy antiquark. Effective field theories can be used to expand the masses of singly heavy hadrons and doubly heavy hadrons in inverse powers of the heavy quark masses. The coefficients in the expansions for doubly heavy tetraquarks can be determined from those for heavy m…
LHCb Collaboration has recently announced the observation of a doubly charmed tetraquark $T_{cc \bar{u} \bar{d}}^+$ state with spin parity $J^P = 1^+$. This exotic state can be explained as a molecular state with small binding energy. According to conventional quark model, both $D^+ D^{0\ast}$ and $(D^0 D^{+\ast})$ multiquark states are expected to have the same mass and flavor in the exact $SU(3)$ symmetry. However, since the quark masses are different, $SU(3) (SU(2))$ symmetry is violated, hence, the mass and flavor eigenstates do not coincide. The mass eigenstates can be represented as a li…
