In present work, we systematically calculate the mass spectra of open charm and bottom tetraquarks $q q\bar q \bar Q$ within an extended relativized quark model. The four-body relativized Hamiltonians including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections are solved by using the variational method. It is found that the predicted masses of four $0^+$ $ud\bar s \bar c$ states are 2765, 3065, 3152, and 3396 MeV, which disfavor the assignment of the newly observed $X_0(2900)$ as a compact tetraquark. Moreover, the whole mass spectra of the open charm and bottom tetraquarks show quite similar patterns, which preserve the light flavor SU(3) symmetry and heavy quark symmetry well. In addition, our results suggest that the flavor exotic states $nn\bar s \bar c$, $nn\bar s \bar b$, $ss\bar n \bar c$, and $ss\bar n \bar b$ and their antiparticles can be searched in the heavy-light meson plus kaon final states by future experiments. More theoretical and experimental efforts are needed to investigate these singly heavy tetraquarks.
Inspired by recent measurement of possible fully charmed tetraquarks in LHCb Collaboration, we investigate the mass spectra of fully heavy tetraquarks $QQ \bar Q \bar Q$ in an extended relativized quark model. Our estimations indicate that the broad structure around 6.4 GeV should contain one or more ground $cc \bar c \bar c$ tetraquark states, while the narrow structure near 6.9 GeV can be categorized as the first radial excitation of $cc \bar c \bar c$ system. Moreover, with the wave functions of the tetraquarks and mesons, the strong decays of tetraquarks into heavy quarkonium pair are qual…
In this paper, we adopt an extended relativized quark model to investigate the triply-heavy tetrquarks systematically. The mass spectra are obtained by solving the four-body relativized Hamiltonian including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections. We find that all of the triply-heavy tetraquarks lie above the corresponding meson-meson thresholds, and thus no stable one exists. In particular, besides the spin-spin interactions, the Coulomb and confining potentials also contribute to the mass splittings in the $cb\bar c \bar q$ and $cb\ba…
In the present work, the mass spectra of doubly heavy tetraquarks $T_{QQ^\prime}$ are systematically investigated in a relativized quark model. The four-body systems including the Coulomb potential, confining potential, spin-spin interactions, and relativistic corrections are solved within the variational method. Our results suggest that the $IJ^P=01^+$ $bb \bar u \bar d$ state is 54 MeV below the relevant $\bar B \bar B$ and $\bar B \bar B^*$ thresholds, which indicates that both strong and electromagnetic decays are forbidden, and thus this state can be a stable one. Its large hidden color c…
The $X(4140)$, $X(4274)$, $X(4500)$ and $X(4700)$ in the relativized quark model
利用Godfrey和Isgur提出的相对化夸克模型，研究了双夸克-反双夸克图中$cs \bar c \bar s$四夸克态的质量.只计算了色空间中的反三重双夸克态。首先用相对化势求出双夸克态的质量，然后将双夸克和反双夸克分别当作通常的反夸克和夸克，用双夸克和反双夸克之间的相对化势求解薛定谔方程，得到四夸克态的质量.屏蔽效应引起的理论不确定性也被考虑在内。发现$X(4140)$的共振态可以看作是$cs \bar c \bar s$的四夸克基态，而$X(4700)$可以看作是$2S$的激发四夸克态.当考虑双夸克的内激发态时，$X(4500)$的共振可以解释为一个$2S$标量双夸克和一个标量反双夸克组成的四夸克态。在我们的方法中，$X(4274)$不能被解释为四夸克态，然而，它可以是传统的$χ_{c1}(3^3P_1)$态的一个很好的候选者。此外，还讨论了其他类粲偶素态$χ_{c0}(3915)$，$X(4350)$，$X(4630)$和$X(4660)$，作为$cs \bar c \bar s$四夸克态.
We investigate the mass spectrum of the $ss \bar s \bar s$ tetraquark states within the relativized quark model. By solving the Schrödinger-like equation with the relativized potential, the masses of the $S-$ and $P-$wave $ss \bar s \bar s$ tetraquarks are obtained. The screening effects are also taken into account. It is found that the observed resonant structure $X(2239)$ in the $e^+e^- \to K^+K^-$ process by BESIII Collaboration can be assigned as a $P-$wave $1^{--}$ $ss \bar s \bar s$ tetraquark state. Furthermore, the radiative transition and strong decay behaviors of this structure are a…
We calculate the spectrum of $q\bar q c \bar c$ and $s\bar s c \bar c$ tetraquarks, where $q$, $s$ and $c$ stand for light ($u,d$), strange and charm quarks, respectively, in a relativized diquark model, characterized by one-gluon-exchange (OGE) plus confining potential. In the diquark model, a $q\bar q c \bar c$ ($s\bar s c \bar c$) tetraquark configuration is made up of a heavy-light diquark, $q c$ ($sc$), and anti-diquark, $\bar q \bar c$ ($\bar s \bar c$). According to our results, 13 charmonium-like observed states can be accommodated in the tetraquark picture, both in the hidden-charm ($…
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.
Motivated by the LHCb's new observation of structures in the $J/ψ$-pair invariant mass spectrum, for which could be classified as possible $cc\bar{c}\bar{c}$ tetraquark candidates, we systematically study $0^{+}$ fully-charmed tetraquark states through QCD sum rules. Making the development of calculation techniques to fourfold heavy hadronic systems, four different configuration currents with $0^{+}$ are considered and vacuum condensates up to dimension $6$ are included in the operator product expansion (OPE). Finally, mass values acquired for $0^{+}$ $cc\bar{c}\bar{c}$ tetraquark states agree…
In this study, we investigate the discovery potential of double-charm tetraquarks $T^{\{cc\}}_{[\bar{q}\bar{q}']}$. We find that their production cross sections at the LHCb with $\sqrt{s} = 13$ TeV reach $\mathcal{O}(10^4)$ pb, which indicates that the LHCb has collected $\mathcal{O}(10^8)$ such particles. Through the decay channels of $T^{\{cc\}}_{[\bar{u}\bar{d}]}\to D^{+}K^{-}π^{+}$ or $D^0D^+γ$ (if stable) or $T^{\{cc\}}_{[\bar{u}\bar{d}]}\to D^0D^{*+}\to D^0D^0π^+$ (if unstable), it is highly expected that they get discovered at the LHCb in the near future. We also discuss the productions…
We investigate a nonrelativistic model of tetraquarks, which are assumed to be compact and to consist of diquark-antidiquark pairs. We fit, for the first time, basically all currently known values for the measured masses of 45 mesons, including both charmed and bottom mesons, to the model and predict masses of tetraquarks as well as diquarks. In particular, we find masses of four axial-vector diquarks, i.e., $qc$, $cc$, $qb$, and $bb$, where $q = u,d$, and 24 ground-state tetraquarks, including both heavy-light tetraquarks ($qc\overline{qc}$ and $qb\overline{qb}$) and heavy tetraquarks ($cc\ov…
We discuss the possible existence of the fully-heavy tetraquarks. We calculate the ground-state energy of the $bb \bar b \bar b$ bound state, where $b$ stands for the bottom quark, in a nonrelativistic effective field theory framework with one-gluon-exchange (OGE) color Coulomb interaction, and in a relativized diquark model characterized by OGE plus a confining potential. Our analysis advocates the existence of uni-flavor heavy four-quark bound states. The ground state $bb\bar b\bar b$ tetraquark mass is predicted to be $(18.72\pm0.02)$~GeV. Mass inequality relations among the lowest $QQ\bar{…
We study strong decays of the possible fully-charm tetraquarks recently observed by LHCb, and calculate their relative branching ratios through the Fierz rearrangement. Together with our previous QCD sum rule study [Phys. Lett. B 773, 247 (2017)], our results suggest that the broad structure around $6.2$-$6.8$ GeV can be interpreted as an $S$-wave $cc\bar c \bar c$ tetraquark state with $J^{PC} = 0^{++}$ or $2^{++}$, and the narrow structure around 6.9 GeV can be interpreted as a $P$-wave one with $J^{PC} = 0^{-+}$ or $1^{-+}$. These structures were observed in the di-$J/ψ$ invariant mass spec…
Motivated by the LHCb's very recent observation of exotic $X_{0}(2900)$ in the $B^{+}\rightarrow D^{+}D^{-}K^{+}$ process, for which could be a good open charm $ud\bar{c}\bar{s}$ tetraquark candidate, we endeavor to investigate its possibility by means of QCD sum rules. In technique, four configurations of interpolating currents with $J^{P}=0^{+}$ are studied for the $ud\bar{c}\bar{s}$ tetraquark state. In the end, mass values are calculated to be $2.76^{+0.16}_{-0.23}~\mbox{GeV}$ for the axial vector diquark-axial vector antidiquark configuration and $2.75^{+0.15}_{-0.24}~\mbox{GeV}$ for the …
We study the mass splittings of $Q_1q_2\bar{Q}_3\bar{q}_4$ ($Q=c,b$, $q=u,d,s$) tetraquark states with chromomagnetic interactions between their quark components. Assuming that $X(4140)$ is the lowest $J^{PC}=1^{++}$ $cs\bar{c}\bar{s}$ tetraquark, we estimate the masses of the other tetraquark states. From the obtained masses and defined measure reflecting effective quark interactions, we find the following assignments for several exotic states: (1) both $X(3860)$ and the newly observed $Z_c(4100)$ seem to be $0^{++}$ $cn\bar{c}\bar{n}$ tetraquarks; (2) $Z_c(4200)$ is probably a $1^{+-}$ $cn\b…
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…
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 …
The molecular assignments to the three $P_c$ states and the similar production mechanism between the $Λ_b\to P_c+K$ and $B\to XYZ+K$ convince us the $B$ decaying to a charmonium state plus light mesons could be the appropriate production process to search for the charmoniumlike molecular tetraquarks. In this work, we systematically study the interactions between a charmed (charmed-strange) meson and an anti-charmed (anti-charm-strange) meson, which include the $D^{(*)}\bar{D}^{(*)}$, $\bar{D}^{(*)}\bar{D}_1$, $D^{(*)}\bar{D}_2^*$, $D_s^{(*)}\bar{D}_s^{(*)}$, ${D}_s^{(*)}\bar{D}_{s0}^*$, $D_s^{…
Using a relativized diquark model Hamiltonian, we calculate the masses of $J^{PC}=0^{++}$ ground-state tetraquarks in the following systems: $b s \bar b \bar s$, $bb \bar n \bar n$ ($n=u, d$), $bb \bar s \bar s$, $cc\bar c \bar c$, $b b \bar b \bar b$, $b c\bar b \bar c$ and $b b \bar c \bar c$. We also compute extensive spectra for the fully-heavy quark flavour combinations. Finally, as a test of the diquark model approach, we compute the masses of fully-heavy baryons in the diquark model. Our results may be compared soon to the forthcoming experimental data for fully-heavy three-quark system…
The hidden-charm tetraquarks with strangeness, $c\bar{c}s\bar{q}$ $(q=u,\,d)$, in $J^P=0^+$, $1^+$ and $2^+$ are systematically investigated in the framework of real- and complex-scaling range of a chiral quark model, whose parameters have been fixed in advance describing hadron, hadron-hadron and multiquark phenomenology. Each tetraquark configuration, compatible with the quantum numbers studied, is taken into account; this includes meson-meson, diquark-antidiquark and K-type arrangements of quarks with all possible color wave functions in four-body sector. Among the different numerical techn…
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 purpose of the present study is to explore the mass spectrum of the hidden charm tetraquark states within a diquark model. Proposing that a tetraquark state is composed of a diquark and an antidiquark, the masses of all possible $[qc][\bar{q}\bar{c}]$, $[sc][\bar{s}\bar{c}]$, and $[qc][\bar{s}\bar{c}]$ $\left([sc][\bar{q}\bar{c}]\right)$ hidden charm tetraquark states are systematically calculated by use of an effective Hamiltonian, which contains color, spin, and flavor dependent interactions. Apart from the $X(3872)$, $Z(3900)$, $χ_{c2}(3930)$, and $X(4350)$ which are taken as input to f…
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…
We study the decay behaviors of the fully-bottom tetraquark states within the diquark-antidiquark picture, and calculate their relative branching ratios through the Fierz rearrangement. Our results suggest that the $C=+$ states can be searched for in the $μ^+ μ^- Υ(1S)$ and $μ^+ μ^- Υ(2S)$ channels with the relative branching ratio $\mathcal{B}(X \to μμΥ(2S)) / \mathcal{B}(X \to μμΥ(1S)) \approx 0.4$. Our results also suggest that the $C=-$ states can be searched for in the $μ^+ μ^- η_b(1S)$ and $μ^+ μ^- η_b(2S)$ channels with the similar relative branching ratio $\mathcal{B}(X \to μμη_b(2S)) …
We calculate the mass spectrum of the $S$-wave fully-charmed tetraquark resonant states $cc\bar c\bar c $ in the nonrelativistic quark model, which successfully describes the charmonium spectrum. The four-body system is solved with the Gaussian expansion method. The complex scaling technique is used to identify the genuine resonances. With the nonrelativistic quark model, our results show the existence of two $cc\bar c\bar c$ resonances in each of the $J^{PC}=$ $0^{++}$, $1^{+-}$ and $2^{++}$ sectors, respectively. In the $S$-wave sector, no resonance is found at the energy region of the $X(62…
