The relativistic model of the ground state and excited heavy tetraquarks with hidden bottom is formulated within the diquark-antidiquark picture. The diquark structure is taken into account by calculating the diquark-gluon vertex in terms of the diquark wave functions. Predictions for the masses of bottom counterparts to the charm tetraquark candidates are given.
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 bottom, including u, d, s and bottom quarks, are constructed. The poles of these amplitudes determine the masses and widths of tetraquarks.
In this article, we perform a systematic study of the mass spectrum of the axial-vector hidden charmed and hidden bottom tetraquark states using the QCD sum rules, and identify the $Z^+(4430)$ as an axial-vector tetraquark state tentatively.
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, including $u$, $d$, $s$ and bottom quarks, are constructed. The poles of these amplitudes determine the masses and widths of $S$-wave bottom tetraquarks.
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.
In this article, we extend our previous work to study the mass spectrum of the ground state hidden-bottom tetraquark states with the QCD sum rules in a systematic way. The predicted hidden-bottom tetraquark masses can be confronted to the experimental data in the future to diagnose the nature of the $Z_b$ states. In calculations, we observe that the scalar diquark states, the axialvector diquark states and the axialvector components of the tensor diquark state are all good diquarks in building the lowest tetraquark states.
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 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.
In this article, we take the scalar diquark and antidiquark operators as the basic constituents, construct the $Cγ_5\otimes\stackrel{\leftrightarrow}{\partial}_μ\otimes γ_5C$ type tetraquark current to study the $Y(10750)$ with the QCD sum rules. The predicted mass $M_{Y}=10.75\pm0.10\,\rm{GeV}$ and width $Γ_Y= 33.60^{+16.64}_{-9.45}\,{\rm{MeV}}$ support assigning the $Y(10750)$ to be the diquark-antidiquark type vector hidden-bottom tetraquark state, which has a relative P-wave between the diquark and antidiquark constituents.
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 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=…
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.
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.
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.
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…
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.
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.
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…
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 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…
Background: A resonance has been observed by the ANDY Collaboration at the Relativistic Heavy-Ion Collider at Brookhaven National Laboratory in Cu+Au collisions at center-of-mass energy $\sqrt{s} = 200$ GeV and at forward rapidity with an average mass of 18.15 GeV. The Collaboration suggests that it is a $b \overline b b \overline b$ tetraquark state decaying to two $Υ$(1S) states, each measured through the $Υ\rightarrow ggg$ channel. Purpose: Their suggestion is investigated assuming that the two $Υ$ states are produced through the materialization of a $|uud b\overline b b \overline b \rangle…
The charged axial-vector $J^{P}=1^{+}$ tetraquarks $Z_{q}=[cq][\bar {b} \bar q ]$ and $Z_{s}=[cs][\bar {b} \bar s]$ with the open charm-bottom contents are studied in the diquark-antidiquark model. The masses and meson-current couplings of these states are calculated by employing QCD two-point sum rule approach, where the quark, gluon and mixed condensates up to eight dimensions are taken into account. These parameters of the tetraquark states $ Z_{q}$ and $Z_{s}$ are used to analyze the vertices $Z_q B_c ρ$ and $Z_s B_c ϕ$ to determine the strong $g_{Z_qB_c ρ}$ and $g_{Z_sB_c ϕ}$ couplings. F…
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 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 have done the exploratory study of bottom tetraquarks ($[bq\bar b \bar q];{q\in u,d}$) in the diquark-antidiquark framework with the inclusion of spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction. Our focus here is on the $Y_b$(10890) and other exotic states in the bottom sector. We have predicted some of the bottom counterparts to the charm tetraquark candidates. Our present study shows that if $Z_b(10610)$ and $Z_b(10650)$ are diquark-diantiquark states then they have to be first radial excitations only and we have predicted $Z_b(10650)$ state as first…
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…
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…
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…
The masses of the heavy tetraquarks with open charm and bottom are calculated within the diquark-antidiquark picture in the framework of the relativistic quark model. The dynamics of the light quarks and diquarks is treated completely relativistically. The diquark structure is taken into account by calculating the diquark-gluon form factor. New experimental data on charmed and charmed-strange mesons are discussed. Our results indicate that the anomalous scalar D_{s0}^*(2317) and axial vector D_{s1}(2460) mesons could not be considered as diquark-antidiquark bound states. On the other hand, D_s…
The exotic state $X(5568)$ which was observed by D0 Collaboration is very likely to be a tetraquark state with four different valence quark flavors, though the existence was not confirmed by other collaborations. The possibility of such state still generate lots of interests in theory. In the paper, we will study the properties of the state under the SU(3) flavor symmetry. This four quark state with a heavy bottom quark and three light quarks(anti-quark) can form a $6$ or $\overline {15}$ representation. The weak decays can be dominant and should be discussed carefully while such state is stab…
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 …
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…
The mass and meson-current coupling of the diquark-antidiquark states with the quantum numbers $J^{P}=0^{+}$ and quark contents $Z_{q}=[cq][\bar {b} \bar q ]$ and $Z_{s}=[cs][\bar {b} \bar s]$ are calculated using two-point QCD sum rule approach. In calculations the quark, gluon and mixing condensates up to eight dimensions are taken into account. The parameters of the scalar tetraquarks extracted from this analysis are employed to explore the strong vertices $Z_q B_c π$, $Z_q B_c η$ and $Z_s B_c η$ and compute the couplings $g_{Z_qB_c π}$, $g_{Z_qB_c η}$ and $g_{Z_sB_c η}$. The strong couplin…
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.
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 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 $(q\bar{c})_…
In this article, we utilise the non-relativistic potential model to calculate the mass-spectra of all bottom [$bb][\bar{b}\bar{b}$] and heavy-light bottom [$bq][\bar{b}\bar{q}$] (q=u,d) tetraquark states in diquark-antidiquark approximation. The four-body problem is reduced into two-body problems by numerically solving the $Schr\ddot{o}dinger$ equation using a cornell-inspired potential along with relativistic correction term. The splitting structure of the tetraquark spectrum is described using spin-dependent terms (spin-spin, spin-orbit, and tensor). We have successfully calculated and predi…
Motivated by the LHCb observation of exotic states $X_{0,1}(2900)$ with four open quark flavors in the $D^- K^+$ invariant mass distribution in the decay channel $B^\pm \to D^+ D^- K^\pm$, we study the spectrum and decay properties of the open charm tetraquarks. Using the two-body chromomagnetic interactions, we find that the two newly observed states can be interpreted as a radial excited tetraquark with $J^P=0^+$ and an orbitally excited tetraquark with $J^P=1^-$, respectively. We then explore the mass and decays of the other flavor-open tetraquarks made of $su \bar d \bar c$ and $ d s \bar …
We study the masses of open charm and bottom tetraquark states within the diquark-antidiquark scenario in the relativized quark model proposed by Godfrey and Isgur. The diquark and antidiquark masses are firstly solved by relativized quark potential, and then treated as the usual antiquark and quark, respectively. The masses of tetraquark states are obtained by solving the Schrödinger-type equation between the new diquark and antidiquark. We find the masses of $sq\bar b\bar q$ tetraquark configuration are much higher than that of $X(5568)$. This conclusion disfavors the possibility of $X(5568)…
We investigate four-quark systems consisting of two heavy anti-bottom quarks and two light up/down quarks. We propose to solve a coupled Schrödinger equation for the anti-bottom-anti-bottom separation using potentials computed via lattice QCD in the limit of static anti-bottom quarks. This coupled Schrödinger equation allows to incorporate effects due to the heavy anti-bottom spins. First exploratory numerical tests are discussed.
Utilizing lattice QCD results for the potential of two static antiquarks and two dynamical quarks as well as quark model techniques for the dynamics of two heavy antiquarks in a cloud of two light quarks, we are provided with an accurate framework for the study of possibly existing heavy-heavy-light-light tetraquarks. Among the possible quantum numbers of such a system, we find binding in only one channel, the scalar isosinglet. Solving the Schroedinger equation for the displacement of the heavy antiquarks and taking systematic errors into account, we find an antibottom-antibottom-light-light …
Inspired by the newly $Z_{cs}(3985)^-$ reported by the BESIII Collaboration in the $K^+$ recoil-mass spectrum of the of $e^+e^-\to (D^{*0}D_s^-/D^0D_s^{*-})K^+$ processes, we perform a dynamical study on the $D^{(*)0}D_s^{*-}$ interactions by adopting a one-boson-exchange model and considering the coupled channel effect. After producing the phase shifts for all the discussed channels, our results exclude the newly $Z_{cs}(3985)^-$ as a $D^{*0}D_s^{-}/D^{0}D_s^{*-}/D^{*0}D_s^{*-}$ resonance with $I(J^P)=1/2(1^+, 0^-, 1^-, 2^-)$.
In the hadrocharmonium picture a $\bar cc$ state and a light hadron form a bound state. The effective interaction is described in terms of the chromoelectric polarizability of the $\bar cc$ state and energy-momentum-tensor densities of the light hadron. This picture is justified in the heavy quark limit, and may successfully account for a hidden-charm pentaquark state recently observed by LHCb. In this work we extend the formalism to the description of hidden-charm tetraquarks, and address the question of whether the resonant states observed by LHCb in the $J/ψ$-$ϕ$ spectrum can be described a…