Search

We conduct systematic calculations of the S-wave fully strange systems with ``normal" $\left(J^{P C}=0^{++}, 1^{+-}, 2^{++}\right)$ and ``exotic" $\left(J^{P C}=0^{+-}, 1^{++}, 2^{+-}\right)$ C-parities, which are the strange analogue of the fully charmed tetraquark state $X(6900)$. Within a constituent quark potential model, we employ the Gaussian expansion method to solve the four-body Schr\"odinger equation and the complex scaling method to identify resonant states. We obtain a series of resonant states and zero-width states in the mass range of 2.7 to 3.3 GeV, with their widths ranging from less than 1 MeV to about 50 MeV. Their rms radii strongly indicate that they are compact tetraquark states. Among these states, the $T_{4s,2^{++}}(2714)$ may be the most likely one to be observed experimentally. We urge the experimental exploration of the $2^{++}$ $s s \bar{s} \bar{s}$ state around 2.7 GeV in the $\phi\phi$ channel. Since the lowest S-wave $s s \bar{s} \bar{s}$ state is around 2.7 GeV, the compact P-wave $s s \bar{s} \bar{s}$ states are expected to be heavier. Hence, $\phi(2170)$ and $X(2370)$ are unlikely to be compact tetraquark states., Comment: 9 pages, 2 figures. Comments are welcomed

We use the quark potential model to calculate the mass spectrum of the S-wave fully heavy tetraquark systems with different flavors, including the $ bc\bar b\bar c, bb\bar c\bar c, cc\bar c\bar b $ and $ bb\bar b\bar c $ systems. We employ the Gaussian expansion method to solve the four-body Schr\"odinger equation, and the complex scaling method to identify resonant states. The $ bc\bar b\bar c, bb\bar c\bar c, cc\bar c\bar b $ and $ bb\bar b\bar c $ resonant states are obtained in the mass regions of $ (13.2,13.5) $, $ (13.3,13.6) $, $ (10.0,10.3) $, $ (16.5,16.7) $ GeV, respectively. Among these states, the $ bc\bar b\bar c $ tetraquark states are the most promising ones to be discovered in the near future. We recommend the experimental exploration of the $ 1^{++} $ and $ 2^{++} $ $ bc\bar b\bar c $ states with masses near $ 13.3 $ GeV in the $ J/\psi\Upsilon $ channel. From the root-mean-square radii, we find that all the resonant states we have identified are compact tetraquark states., Comment: 10 pages,7 figures,8 tables

The $X(3872)$, as the first and the most crucial member in the exotic charmoniumlike $XYZ$ family, has been studied for a long time. However, its dynamical origin, whether stemming from a $D\bar{D}^*$ hadronic molecule or the first excited $P$-wave charmonium $\chi_{c1}(2P)$, remains controversial. In this Letter, we demonstrate that the $X(3872)$ definitely does not result from the mass shift of the higher bare $\chi_{c1}(2P)$ resonance pole in the coupled-channel dynamics involving a short-distance $c\bar{c}$ core and the long-distance $D\bar{D}^*$ channels. Instead, it originates from either the $D\bar{D}^*$ molecular pole or the shadow pole associated with the $P$-wave charmonium, which depends on the concrete coupling mode between the $c\bar{c}$ and $D\bar{D}^*$. In order to further exploit the nature of $X(3872)$, we carefully investigate potential mechanisms that contribute to its pole width, which suggests that the coupled-channel dynamics plays a critical role in causing a noticeable discrepancy between the pole widths of $X(3872)$ and $T_{cc}^+$. Interestingly, we bridge the quantitative connection among the dynamics origin of $X(3872)$, its pole width and the properties of the predicted new resonance. The precise measurement of the pole width of $X(3872)$ and the search for the new charmoniumlike resonance become highly significant and can be anticipated in future LHCb, BESIII and Belle II experiments., Comment: 11 pages, 5 figures

We calculate the mass spectrum of the S-wave fully heavy tetraquark systems $ QQ\bar Q\bar Q~(Q=c,b) $ with both normal $ (J^{PC}=0^{++},1^{+-},2^{++}) $ and exotic $ (J^{PC}=0^{+-},1^{++},2^{+-}) $ C-parities using three different quark potential models (AL1, AP1, BGS). The exotic C-parity systems refer to the ones that cannot be composed of two S-wave ground heavy quarkonia. We incorporate the molecular dimeson and compact diquark-antidiquark spatial correlations simultaneously, thereby discerning the actual configurations of the states. We employ the Gaussian expansion method to solve the four-body Schr\"odinger equation, and the complex scaling method to identify the resonant states. The mass spectra in three different models qualitatively agree with each other. We obtain several resonant states with $ J^{PC} = 0^{++}, 1^{+-}, 2^{++}, 1^{++} $ in the mass region $(6.92,7.30)\, \mathrm{GeV}$, some of which are good candidates of the experimentally observed $X(6900)$ and $X(7200)$. We also obtain several exotic C-parity zero-width states with $ J^{PC}=0^{+-} $ and $ 2^{+-} $. These zero-width states have no corresponding S-wave diquarkonium threshold and can only decay strongly to final states with P-wave quarkonia. With the notation $T_{4Q,J(C)}(M)$, we deduce from the root mean square radii that the $ X(7200) $ candidates $ T_{4c,0(+)}(7173), T_{4c,2(+)}(7214) $ and the state $ T_{4c,1(-)}(7191) $ look like molecular states although most of the resonant and zero-width states are compact states., Comment: 16 pages, 6 figures, 10 tables. Version accepted by PRD

We calculate the mass spectrum of the $Qs\bar q \bar q$ $(Q=c, b)$ tetraquark states with $J^P=(0,1,2)^+$ using the AL1 quark potential model, which successfully describes the conventional hadron spectrum. We employ the Gaussian expansion method to solve the four-body Schr\"odinger equation, and use the complex scaling method to identify the resonances. With the notation $T_{Q s, I(J)}^{\text {Theo. }}(M)$, we find several near-threshold bound states and resonances, including $T_{cs,0(0)}^{\mathrm{Theo.}}(2350)$, $T_{cs,0(0)}^{\mathrm{Theo.}}(2906)$, $T_{bs,0(0)}^{\mathrm{Theo.}}(5781)$, $T_{bs,0(1)}^{\mathrm{Theo.}}(5840)$, and $T_{bs,0(0)}^{\mathrm{Theo.}}(6240)$ which are close to the $D\bar{K}$, $D^*\bar{K}^*$, $\bar{B}\bar{K}$, $\bar{B}^*\bar{K}$ and $\bar{B}^*\bar{K}^*$ thresholds, respectively. Furthermore, their spatial structures clearly support their molecular natures. The resonance $T_{cs,0(0)}^{\mathrm{Theo.}}(2906)$ has a mass of $2906$ MeV, a width of $20$ MeV, and quantum numbers $I(J^P)=0(0^+)$, which may serve as a good candidate for the experimental $T_{cs0}(2900)$ state. We strongly urge the experimental search of the predicted states., Comment: 9 pages, 4 figures, 3 tables. Version accepted by PRD

We investigate the tetraquark bound states that are manifestly exotic using three distinct few-body methods: Gaussian Expansion Method (GEM), Resonating Group Method (RGM), and Diffusion Monte Carlo (DMC). We refer to manifestly exotic states that do not involve a mixture with the conventional mesons through the creation and annihilation of $n\bar{n}$, where $n=u, d$. Our calculations are conducted with two types of quark models: the pure constituent quark model featuring one-gluon-exchange interactions and confinement interactions, and the chiral constituent quark model, supplemented by extra one-boson-exchange interactions. This study represents a comprehensive benchmark test of various few-body methods and quark models. Our findings reveal the superiority of GEM over RGM and DMC methods based on present implements for the tetraquark bound states. Additionally, we observe a tendency for the chiral quark model to overestimate the binding energies. We systematically explore the fully, triply, doubly, and singly heavy tetraquark states with $J^P=0^+,1^+,2^+$, encompassing over 150 states in total. We successfully identify several bound states, including $[cc\bar{n}\bar{n}]_{J^{P}=1^{+}}^{I=0}$, $[bb\bar{n}\bar{n}]_{J^{P}=1^{+}}^{I=0}$, $[bc\bar{n}\bar{n}]_{J^{P}=0^{+},1^{+},2^{+}}^{I=0}$, $[bs\bar{n}\bar{n}]_{J^{P}=0^{+},1^{+}}^{I=0}$, $[cs\bar{n}\bar{n}]_{J^{P}=0^{+}}^{I=0}$, and $[bb\bar{n}\bar{s}]_{J^{P}=1^{+}}$, all found to be bound states below the dimeson thresholds., Comment: 15 pages, 7 figures and 5 Tables. Version accepted by PRD

We use the diffusion Monte Carlo method to calculate the doubly heavy tetraquark $T_{cc}$ system in two kinds of constituent quark models, the pure constituent quark model AL1/AP1 and the chiral constituent quark model. When the discrete configurations are complete and no spatial clustering is preseted, the AL1/AP1 model gives an energy of $T_{cc}$ close to the $DD^*$ threshold, and the chiral constituent quark model yields a deeply bound state. We further calculate all doubly heavy tetraquark systems with $J^P=0^+,1^+,2^+$, and provide the binding energies of systems with bound states. The $I(J^P)=0(0^+)$ $bc\bar{n}\bar{n}$, $0(1^+)$ $bb\bar{n}\bar{n}$, $0(1^+)$ $bc\bar{n}\bar{n}$, $\frac{1}{2}(1^+)$ $bb\bar{s}\bar{n}$ systems have bound states in all three models. Since the DMC method has almost no restriction on the spatial part, the resulting bound states have greater binding energies than those obtained in previous works., Comment: 9 pages, 1 figure. Comments are welcomed

We improve the complex scaling method (CSM) to obtain virtual states, which were previously challenging in the conventional CSM. Our approach solves the Schr\"odinger equation in the momentum space as an eigenvalue problem by choosing the flexible contours. It proves to be highly effective in identifying the poles across the different Riemann sheets in the multichannel scatterings. It is more straightforward and efficient than searching for the zeros of the Fredholm determinant of the Lippmann-Schwinger equation using the root-finding algorithms. This advancement significantly extends the capabilities of the CSM in accurately characterizing the resonances and virtual states in quantum systems., Comment: 12 pages, 14 figures, 2 tables. Version accepted by PRD

In the present work, we investigate the productions of the molecular states composed of $D^{(*)}_s \bar{D}^{(*)}$ and $D^{(*)}_s \bar{D}^{(*)}_s$ in the $B$ and $B_s$ decays by using an effective Lagrangian approach. The branching ratios in terms of the model parameter $\alpha$ and the binding energy $\Delta E$ are estimated. Our estimations indicate that the branching fractions are of the order of $10^{-4}$ and the relative ratios are very weakly dependent on the model parameter $\alpha$ and the binding energy $\Delta E$. The predicted ratios are helpful for searching the hidden-charm molecular states with strange quark in the future experiments at Belle II and LHCb., Comment: 12 pages, 4 figures and 6 tables, accepted by Phys. Rev. D

We make a systematical diffusion Monte Carlo (DMC) calculation for all ground state baryons in two confinement scenarios, the pairwise confinement and the three-body flux-tube confinement. With the baryons as an example, we illustrate a feasible procedure to investigate the few-quark states with possible few-body confinement mechanisms, which can be extended to the multiquark states easily. For each baryon, we extract the mass, mean-square radius, charge radius, and the quark distributions. We use the Jackknife resampling method to estimate the statistical uncertainties of masses to be less than 1 MeV. To determine the baryon charge radii, we include the constituent quark size effect, which is fixed by the experimental and lattice QCD results. Our results show that both two-body and three-body confinement mechanisms can give a good description of the experimental data if the parameters are chosen properly. In the flux-tube confinement, introducing different tension parameters for the baryons and mesons are necessary, specifically, $\sigma_Y= 0.9204 \sigma_{Q\bar{Q}}$. The lesson from the calculation of the nucleon mass with the DMC method is that the improper pre-assignment of the channels may prevent us from obtaining the real ground state. With this experience, we obtain the real ground state (the $\eta_c \eta_c$ threshold with the di-meson configuration) of the $cc\bar{c}\bar{c}$ system with $J^{PC}=0^{++}$ starting from the diquark-antidiquark spin-color channels alone, which is hard to achieve in the variational method and was not obtained in the previous DMC calculations., Comment: 24 pages, 18 figures. The Supplement material is attached in the source code of LaTeX. Comments are welcomed

The exotic states $X_{0,1}(2900)$ with the quark flavor of $cs\bar{u}\bar{d}$ are recently observed in the mass spectrum of $D^+K^-$ in $B^-\to D^-D^+K^-$ by the LHCb collaboration. To explore the nature of $X_{0,1}(2900)$, except for analyzing their masses and decay widths as usually did in literatures, the study of their production mechanism in $B$-meson weak decays would provide another important information. The amplitude of $B^-\to D^- X_{0,1}$ is non-factorizable. We consider the final-state-interaction effects and calculate them via the rescattering mechanism. The measured branching fractions of $B^-\to D^- X_{0,1}$ are revealed. It is manifested by ${B}^-\to \Lambda_c^-\Xi_c^{(\prime)0}$ and $\Lambda_b^0\to P_c^+K^-$ that the rescattering mechanism can result in the relatively large branching fractions. The similar processes of $B^-\to \pi^-X_{0,1}$ are also analyzed. The isospins of $X_{0,1}$ can be investigated by $B\to DX_{0,1}^{\pm,0}$ decays., Comment: 12 pages, 10 figures. Version published in EPJC. Additional contributions are added in $B\to \pi X_{0,1}$ in Fig.8. Numerical results of the isospin-partner processes are changed by a factor of 2 in Eqs.(12) and (13)