We have systematically calculated the mass spectra for S-wave and P-wave fully-charm $c\bar{c}c\bar{c}$ and fully-bottom $b\bar{b}b\bar{b}$ tetraquark states in the $\mathbf{8}_{[Q\bar{Q}]}\otimes \mathbf{8}_{[Q\bar{Q}]}$ color configuration, by using the moment QCD sum rule method. The masses for the fully-charm $c\bar cc\bar c$ tetraquark states are predicted about $6.3-6.5$ GeV for S-wave channels and $7.0-7.2$ GeV for P-wave channels. These results suggest the possibility that there are some $\mathbf{8}_{[c\bar{c}]}\otimes \mathbf{8}_{[c\bar{c}]}$ components in LHCb's di-$J/ψ$ structures. For the fully-bottom $b\bar{b}b\bar{b}$ system, their masses are calculated around 18.2 GeV for S-wave tetraquark states while 18.4-18.8 GeV for P-wave ones, which are below the $η_bη_b$ and $Υ(1S)Υ(1S)$ two-meson decay thresholds.
In this article, we take the $Y(4260/4220)$ as the vector tetraquark state with $J^{PC}=1^{--}$, and construct the $Cγ_5\otimes\stackrel{\leftrightarrow}{\partial}_μ\otimes γ_5C$ type diquark-antidiquark current to study its mass and pole residue with the QCD sum rules in details by taking into account the vacuum condensates up to dimension 10 in a consistent way. The predicted mass $M_{Y}=4.24\pm0.10\,\rm{GeV}$ is in excellent agreement with experimental data and supports assigning the $Y(4260/4220)$ to be the $Cγ_5\otimes\stackrel{\leftrightarrow}{\partial}_μ\otimes γ_5C$ type vector tetraqu…
We study the existence of fully-heavy hidden-flavor $bc\bar{b}\bar{c}$ tetraquark states with various $J^{PC}=0^{\pm+}, 0^{--},1^{\pm\pm}, 2^{++}$, by using the moment QCD sum rule method augmented by fundamental inequalities. Using the moment sum rule analyses, our calculation shows that the masses for the S-wave positive parity $bc\bar{b}\bar{c}$ tetraquark states are about $12.2-12.4$ GeV in both $[\mathbf{\bar{3}_c}]_{bc}\otimes[\mathbf{3_c}]_{\bar{b}\bar{c}}$ and $[\mathbf{6_c}]_{bc}\otimes[\mathbf{\bar{6}_c}]_{\bar{b}\bar{c}}$ color configuration channels. Except for two $0^{++}$ states,…
In this article, we study the $Cγ_5\otimes γ_5C$ type and $C\otimes C$ type scalar $cs\bar{c}\bar{s}$ tetraquark states with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in a consistent way. The ground state masses $M_{Cγ_5\otimes γ_5C}=3.89\pm 0.05\,\rm{GeV}$ and $M_{C\otimes C}=5.48\pm0.10\,\rm{GeV}$ support assigning the $X(3915)$ to be the ground state $Cγ_5\otimes γ_5C$ type tetraquark state with $J^{PC}=0^{++}$, but do not support assigning the $X(4700)$ to be the ground state $C\otimes C$ type $cs\bar{c}\bar{s}$ tetraquark state with $J…
We have calculated the mass spectra for the $\bar{D}_s^{(*)}D^{(*)}$ molecular states and $sc\bar q\bar c$ tetraquark states with $J^P=0^+, 1^+, 2^+$. The masses of the axial-vector $\bar{D}_sD^{*}$, $\bar{D}_s^{*}D$ molecular states and $\mathbf{1}_{[sc]} \oplus \mathbf{0}_{[\bar q \bar{c}]}$, $\mathbf{0}_{[sc]} \oplus \mathbf{1}_{[\bar q \bar{c}]}$ tetraquark states are predicted to be around 3.98 GeV, which are in good agreement with the mass of $Z_{cs}(3985)^-$ from BESIII \cite{besiii2020Zcs}. In both the molecular and diquark-antidiquark pictures, our results suggest that there may exist…
In this article, we construct the $C \otimes γ_μC$ and $Cγ_5 \otimes γ_5γ_μC$ type currents to interpolate the vector tetraquark states, then carry out the operator product expansion up to the vacuum condensates of dimension-10 in a consistent way, and obtain four QCD sum rules. In calculations, we use the formula $μ=\sqrt{M^2_{Y}-(2{\mathbb{M}}_c)^2}$ to determine the optimal energy scales of the QCD spectral densities, moreover, we take the experimental values of the masses of the $Y(4260/4220)$, $Y(4360/4320)$, $Y(4390)$ and $Y(4660/4630)$ as input parameters and fit the pole residues to re…
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.
The low-lying $sQ\bar{q}\bar{q}$ $(q=u,\,d,\, Q=c,\,b)$ tetraquark states with $J^P=0^+$, $1^+$ and $2^+$, and in the isoscalar and isovector sectors, 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, and thus all results presented here are pure predictions. Each tetraquark configuration, compatible with the quantum numbers studied, is taken into account; this includes meson-meson, diquark-antidiquark and K-type arrangements of qu…
We systematically construct tetraquark currents of $I^GJ^{PC}=1^-1^{++}$ and classify them into types $\mathbf{A}$ (antisymmetric), $\mathbf{S}$ (symmetric) and $\mathbf{M}$ (mixed), based on flavor symmetries of diquarks and antidiquarks composing the tetra quark currents. We use tetraquark currents of type $\mathbf{M}$ to perform QCD sum rule analyses, and find a tetraquark current $η^M_{5μ}$ with quark contents $q s\bar q \bar s$($q=u$ or $d$) leading to a mass of $1.44 \pm 0.08$ GeV consistent with the $a_1(1420)$ state recently observed by the COMPASS collaboration. Our results support te…
We study the mass spectra of D-wave excited $cs\bar{c}\bar{s}$ tetraquark states with $J^{PC}=1^{++}$ and $1^{+-}$ in both symmetric $\mathbf{6}_{cs}\otimes\bar{\mathbf{6}}_{\bar{c}\bar{s}}$ and antisymmetric $\bar{\mathbf{3}}_{cs}\otimes\mathbf{3}_{\bar{c}\bar{s}}$ color configurations by using the QCD sum rule method. We construct the D-wave diquark-antidiquark type of $cs\bar{c}\bar{s}$ tetraquark interpolating currents in various excitation structures with $(L_λ,L_ρ\{l_{ρ_1},l_{ρ_2}\})=(2,0\{0,0\}),(1,1\{1,0\}),(1,1\{0,1\}),(0,2\{1,1\}),(0,2\{2,0\}),(0,2\{0,2\})$. Our results support to in…
In this work, we estimate the masses of tetraquark states with four different flavors by virtue of QCD sum rules, in both $b$ and $c$ sectors. We construct four $[8_c]_{\bar{b} s} \otimes [8_c]_{\bar{d} u}$ tetraquark currents with $J^P = 0^+$, and then perform analytic calculation up to dimension eight in the Operator Product Expansion (OPE). We keep terms which are linear in the strange quark mass $m_s$, and in the end find two possible tetraquark states with masses $(5.57 \pm 0.15)$ and $(5.58 \pm 0.15)$ GeV. We find that their charmed-partner masses lie in $(2.54 \pm 0.13)$ and $(2.55 \pm …
Stimulated by the state $Y(4626)$ recently reported by Belle Collaboration, we utilize a multiquark color flux-tube model with a multibody confinement potential and one-glue-exchange interaction to make an exhaustive investigation on the diquark-antidiquark state $[cs][\bar{c}\bar{s}]$. Numerical results indicate that the appearance of the states $[cs][\bar{c}\bar{s}]$ like a dumb-bell, the larger the orbital excitation $L$, the more distinguished the shape. The mixing of the color configurations $\left[[cs]_{\bar{\mathbf{3}}_c}[\bar{c}\bar{s}]_{\mathbf{3}_c}\right]_{\mathbf{1}}$ and $\left[[c…
We use a color-magnetic interaction model (CMIM), a traditional constituent quark model (CQM) and a multiquark color flux-tube model (MCFTM) to systematically investigate the properties of the states $[Q_1Q_2][\bar{Q}_3\bar{Q}_4]$ ($Q=c,b$). The dynamical investigation indicates that the CMIM can not completely absorb QCD dynamical effects through the effective constituent quark mass and overestimates the color-magnetic interaction in the states under the assumption of the same spatial configurations. The Coulomb interaction plays a critical role in the dynamical model calculations on the heav…
In this article, we tentatively assign the $X^*(3860)$ to be the $Cγ_5\otimes γ_5C$ type scalar tetraquark state, study its mass and width with the QCD sum rules, special attention is paid to calculating the hadronic coupling constants $G_{Xη_cπ}$ and $G_{XDD}$ concerning the tetraquark state. We obtain the values $M_{X}=3.86 \pm 0.09\,\rm{GeV}$ and $Γ_{X}= 202\pm 146 \,\rm{MeV}$, which are consistent with the experimental data. The numerical result supports assigning the $X^*(3860)$ to be the $Cγ_5\otimes γ_5C$ type scalar tetraquark state.
In the framework of QCD Sum Rules we investigate the $q q^\prime \bar{Q} \bar{Q}$ tetraquark structure with quantum number $J^P = 1^+$, which are embedded in two types of configurations, the $[8_c]_{q \bar{Q}} \otimes [8_c]_{q^\prime \bar{Q}}$ and $[1_c]_{q \bar{Q}} \otimes [1_c]_{q^\prime \bar{Q}}$ with $Q = b, c$, $q = u$, and $q^\prime = d, s$. Our finding confirms the Lattice QCD result that the bottom tetraquark states could exist and their masses are evaluated. In the calculation, the non-perturbative condensate contributions up to dimension eight in operator product expansion are consid…
Compact $cs\bar{s}\bar{s}$ Tetraquarks in the Charm--Strange Sector: Mass Spectra, Rearrangement Decays and Regge Trajectories with $D_s$ Threshold Inputs
Sardar Vallabhbhai National Institute of Technology（萨达尔·瓦拉巴伊国家技术学院）
The lepton sector is studied within a flavored non-renormalizable model where the $\mathbf{S}_{3}\otimes \mathbf{Z}_{2}$ flavor symmetry drives the Yukawa couplings. In this framework, the effective neutrino mass, that comes from the type II see-saw mechanism, as well as the charged lepton mass matrices are hierarchical and possessed (under a benchmark in the charged sector) a kind of Fritzsch textures that achieve to accommodate the mixing angles in good agreement with the last experimental data. The model predicts a CP-violating phase consistent with the experimental data and the branching r…
We investigate the recent evidence for a charged $X(5568)$ meson as an exotic open-flavor tetraquark state $su\bar b\bar d$ with $J^P=0^+/1^+$ in the framework of QCD sum rules. We use the color antisymmetric $[\mathbf{\bar 3_c}]_{su} \otimes [\mathbf{3_c}]_{\bar{b}\bar d}$ tetraquark currents in both scalar and axial-vector channels to perform evaluations and numerical analyses. Our results imply that the $X(5568)$ can be interpreted as both the scalar $su\bar b\bar d$ tetraquark state and the axial-vector one, which are in good agreement with the experimental measurement. We also discuss the…
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…
Inspired by the recent observation of exotic resonances $X(4140)$, $X(4274)$, $X(4350)$, $X(4500)$ and $X(4700)$ reported by several experiment collaborations, we investigated the four-quark system $cs\bar c\bar s$ with quantum numbers $J^{PC}=1^{++}$ and $0^{++}$ in the framework of the chiral quark model. Two configurations, diquark-antidiquark and meson-meson, with all possible color structures are considered. The results show that no molecular state can be formed, but the resonance may exist if the color structure of meson-meson configuration is $8\otimes8$. In the present calculation, the…
Recently, a hadronic state named $η_1(1855)$, about 1.86 GeV, was observed in the BESIII experiment. This finding has a peculiar interest due to its exotic quantum number $J^{PC}=1^{-+}$. In this paper, we examine the tetraquark interpretation for the structure of $η_1(1855)$ in the configurations of $[1_c]_{\bar{s}s}\otimes[1_c]_{\bar{q}q}$ and $[1_c]_{\bar{s}q}\otimes[1_c]_{\bar{s}q}$, and perform a mass spectrum calculation in the framework of QCD sum rules. The results show that the observed $η_1(1855)$ could be embedded into the $[1_c]_{\bar{s}s}\otimes[1_c]_{\bar{q}q}$ configuration. The…
Very recently, the LHCb Collaboration observed distinct structures with the $cc\bar{c}\bar{c}$ in the $J/Ψ$-pair mass spectrum. In this work, we construct four scalar ($J^{PC} = 0^{++}$) $[8_c]_{Q\bar{Q^\prime}}\otimes [8_c]_{Q^\prime \bar{Q}}$ type currents to investigate the fully-heavy tetraquark state $Q Q^\prime \bar{Q} \bar{Q^\prime}$ in the framework of QCD sum rules, where $Q=c, b$ and $Q^\prime = c, b$. Our results suggest that the broad structure around 6.2-6.8 GeV can be interpreted as the $0^{++}$ octet-octet tetraquark states with masses $6.44\pm 0.11$ GeV and $6.52\pm 0.10$ GeV, …
Systematic study of fully heavy-flavored tetraquarks $Q_1Q_2\bar{Q}_1\bar{Q}_2\,(Q_{1;2} \in \left\{b;c\right\})$: Mass spectra, threshold analysis, and confrontation with LHC data
University of Geneva（日内瓦大学）；University of Yaounde I（雅温得第一大学）
The LHCb collaboration has found that the production rate of $X(3872)$ in proton-proton collisions decreases as final state particle multiplicity increases. Moreover, the ALICE experiment at CERN has observed that the number of deuterons produced increases with multiplicity, a behavior that is qualitatively different from that of the $X(3872)$. These experimental findings may point to a compact structure for the $X(3872)$ or, at least, that its hadronization could proceed through a charm-anticharm core. We have recently used a diffusion Monte Carlo method to solve the many-body Schrödinger equ…
