In the framework of coupled-channel formalism the relativistic four-quark equations are found. The dynamical mixing of the meson-meson states with the four-quark states is considered. The four-quark amplitudes of the tetraquarks with open charm, including u, d, s, c quarks, are constructed. The poles of these amplitudes determine the masses and widths of tetraquarks.
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…
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 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 …
By using QCD Sum Rules, we found that the charged hidden charm tetraquark $[c u][\bar{c} \bar{d}]$ states with $ J^P = 1^-$ and $ 2^+$, which are possible quantum numbers of the newly observed charmonium-like resonance $Z_c(4025)$, have masses of $m_{1^-}^c = (4.54 \pm 0.20) \, \text{GeV}$ and $m_{2^+}^c = (4.04 \pm 0.19) \, \text{GeV}$. The contributions up to dimension eight in the Operator Product Expansion (OPE) were taken into account in the calculation. The tetraquark mass of $J^{P} = 2^{+}$ state was consistent with the experimental data of $Z_c(4025)$, suggesting the $Z_c(4025)$ state …
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^{…
Stimulated by the newly reported doubly-charmed tetraquark state $T_{cc}^+$ by LHCb, we carry out a systematic investigation of the $S$-wave interactions between the charmed meson ($D,\,D^{*}$) in $H$-doublet and the charmed meson ($D_{1},\,D_{2}^{*}$) in $T$-doublet by adopting the one-boson-exchange model. Both the $S$-$D$ wave mixing effect and the coupled channel effect are taken into account. By performing a quantitative calculation, we suggest that the $S$-wave $D^{*} D_{1}$ states with $I(J^{P})=0(0^{-},\,1^{-})$ and the $S$-wave $D^{*}D_{2}^{*}$ state with $I(J^{P})=0(1^{-})$ should be…
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…
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 ($…
Hadronic states composed of multi-quark flavors may exist in reality since they are not prohibited by QCD. Compact four quark systems of color singlet are classified as tetraquarks. To understand the properties of these states, more theoretical and experimental efforts are needed. In this work, we study charmed tetraquarks with three light flavors using flavor $SU(3)$ symmetry. States with three different light quarks must be in a ${\bf \bar 6 }$ or a ${\bf 15}$ multiplet. We investigate the production of charmed tetraquarks $X_c$ in $B\to X_c (\overline {X}_c) P$ and $B_c \to X_c P$ decays. W…
With the spin rearrangement, we have performed a comprehensive investigation of the decay patterns of the S-wave tetraquarks and P-wave tetraquarks where the P-wave excitation exists either between the diquark and anti-diquark pair or inside the diquark. Especially, we compare the decay patterns of $Y(4260)$ with different inner structures such as the conventional charmonium, the molecule, the P-wave tetraquark and the hybrid charmonium. We notice the $J/ψππ$ mode is suppressed in the heavy quark symmetry limit if $Y(4260)$ is a molecular state. Moreover the hybrid charmonium and hidden-charm …
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.
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…
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)…
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.
Fully charmed tetraquark production in forward rapidity $pp$ collisions at LHC and FCC energies
Universidad de Alcalá (UAH)（阿尔卡拉大学）；Federal University of Grande Dourados（大杜拉多联邦大学）；Universidade do Estado de Santa Catarina（圣卡塔琳娜州立大学）；Federal University of Pelotas（佩洛塔斯联邦大学）；Universidade de São Paulo（圣保罗大学）
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.
For very heavy quarks, relations derived from heavy-quark symmetry imply novel narrow doubly heavy tetraquark states containing two heavy quarks and two light antiquarks. We predict that double-beauty states will be stable against strong decays, whereas the double-charm states and mixed beauty+charm states will dissociate into pairs of heavy-light mesons. Observing a new double-beauty state through its weak decays would establish the existence of tetraquarks and illuminate the role of heavy color-antitriplet diquarks as hadron constituents.
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…
Experimentally several charged axial-vector hidden-charm states were reported. Within the framework of the color-magnetic interaction, we have systematically considered the mass spectrum of the hidden-charm and hidden-bottom tetraquark states. It is impossible to accommodate all the three charged states $Z_c(3900)$, $Z_c(4025)$ and $Z_c(4200)$ within the axial vector tetraquark spectrum simultaneously. Not all these three states are tetraquark candidates. Moreover, the eigenvector of the chromomagnetic interaction contains valuable information of the decay pattern of the tetraquark states. The…
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.
In the framework of the quark delocalization color screening model (QDCSM), we systematically investigate the double-charm and double-strange tetraquark systems $cc\bar{s}\bar{s}$ with two structures: meson-meson and diquark-antidiquark. The bound-state calculation shows that there is no any bound state in present work. However, by applying a stabilization calculation and coupling all channels of both two structures, two new resonance states with $IJ^{P}=00^{+}$ are obtained. One is more possible to be a molecular resonance state with a mass and width around $4256$ MeV and $60$ MeV, respective…
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.
Four exotic charmonium-like states, i.e. $X(4140)$, $X(4274)$, $X(4500)$, and $X(4700)$, have been observed very recently by LHCb Collaboration in the decay process $B^+\to J/ψϕK^+$ using the 3${\rm fb}^{-1}$ data of $p\bar p$ collision at $\sqrt s= 7$ and $8$ TeV. In this paper, we investigate systematically the properties of hidden charm tetraquark states. The hidden charm tetraquarks form an octet configuration and a singlet configuration according to flavor $SU(3)$ symmetry. Based on a diquark-antidiquark model, the hidden charm tetraquarks spectra are given. The previous XYZ exotic states…
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 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…
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 c…
We develop a moment QCD sum rule method augmented by fundamental inequalities to study the existence of exotic doubly hidden-charm/bottom tetraquark states made of four heavy quarks. Using the compact diquark-antidiquark configuration, we calculate the mass spectra of these tetraquark states. There are 18 hidden-charm $cc\bar c\bar c$ tetraquark currents with $J^{PC} = 0^{++}$, $0^{-+}$, $0^{--}$, $1^{++}$, $1^{+-}$, $1^{-+}$, $1^{--}$, and $2^{++}$. We use them to perform QCD sum rule analyses, and the obtained masses are all higher than the spontaneous dissociation thresholds of two charmoni…
The newly observed hidden-charm tetraquark state $Z_{cs}(3985)$, together with $Z_c(3900)$ and $X(4020)$, are studied in the combined theoretical framework of the effective range expansion, compositeness relation and the decay width saturation. The elastic effective-range-expansion approach leads to sensible results for the scattering lengths, effective ranges and the compositeness coefficients, $i.e.$, the probabilities to find the two-charm-meson molecule components in the tetraquark states. The coupled-channel formalism by including the $J/ψπ$ and $D\bar{D}^*/\bar{D}D^*$ to fulfill the cons…
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…
Masses of the ground and excited (1P, 2S, 1D, 2P, 3S) states of the fully-heavy tetraquarks, composed of charm ($c$) and bottom ($b$) quarks and antiquarks, are calculated in the diquark-antidiquark picture within the relativistic quark model based on the quasipotential approach and quantum chromodynamics. The quasipotentials of the quark-quark and diquark-antidiquark interactions are constructed similarly to the previous consideration of mesons and baryons. Relativistic effects are consistently taken into account. A tetraquark is considered as a bound state of a diquark and an antidiquark. Th…
The phenomenology of the so-called X, Y and Z hadronic resonances is hard to reconcile with standard charmonium or bottomonium interpretations. It has been suggested that some of these new hadrons can possibly be described as tightly bound tetraquark states and/or as loosely bound two-meson molecules. In the present paper we focus on the hypothetical existence of flavored, doubly charmed, tetraquarks. Such states might also carry double electric charge, and in this case, if discovered, they could univocally be interpreted in terms of compact tetraquarks. Flavored tetraquarks are also amenable …
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.
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…
The doubly charm tetraquark with flavor $cc\bar u\bar d$ and isospin $I\!=\!0$ is investigated by calculating the $DD^*$ scattering amplitude with lattice QCD. The simulation is done on CLS ensembles with dynamical $u/d,s$ quarks and $m_π\simeq 280~$MeV for two charm quark masses, one slightly larger and one slightly lower than the physical value. The scattering amplitudes for partial waves $l=0,1$ are extracted near-threshold via the Lüscher's method by considering systems with total momenta $PL/(2π)=0,1,\sqrt{2},2$ on two spatial volumes. A virtual bound state pole in the $DD^*$ scattering a…
