No Arabic abstract
The recently discovered fully charmed tetraquark candidate $X(6900)$ is analyzed within the frameworks of effective-range expansion, compositeness relation and width saturation, and a coupled multichannel dynamical study. By taking into account constraints from heavy-quark spin symmetry, the coupled-channel amplitude including the $J/psi J/psi,~ chi_{c0}chi_{c0}$ and $chi_{c1}chi_{c1}$ is constructed to fit the experimental di-$J/psi$ event distributions around the energy region near $6.9$ GeV. Another dynamical two-coupled-channel amplitude with the $J/psi J/psi$ and $psi(3770) J/psi$ is also considered to describe the same datasets. The three different theoretical approaches lead to similar conclusions that the two-meson components do not play dominant roles in the $X(6900)$. Our determinations of the resonance poles in the complex energy plane from the refined coupled-channel study are found to be consistent with the experimental analyses. The coupled-channel amplitudes also have another pole corresponding to a narrow resonance $X(6825)$ that we predict sitting below the $chi_{c0}chi_{c0}$ threshold and of molecular origin. We give predictions to the line shapes of the $chi_{c0}chi_{c0}$ and $chi_{c1}chi_{c1}$ channels, which could provide a useful guide for future experimental measurements.
Recently LHCb declared a new structure $X(6900)$ in the final state di-$J/psi$ which is popularly regarded as a $cc$-$bar cbar c$ tetraquark state. %popularly. Within the Bethe-Salpeter (B-S) frame we study the possible $cc$-$bar cbar c$ bound states and the interaction between diquark ($cc$) and antidiquark ($bar cbar c$). In this work $cc$ ($bar cbar c$) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of $cc$-$bar cbar c$ bound state are $0^+$, $1^+$ and $2^+$. Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for diquark and antidiquark system. Then we deduce the B-S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of $X(6900)$ when we assign appropriate values for parameter $kappa$ introduced in the interaction (kernel).We also briefly calculate the spectra of $bb$-$bar bbar b$ bound states. Future measurement of $bb$-$bar bbar b$ state will help us to determine the exact form of effective interaction.
Inspired by the observation of the fully-charm tetraquark $X(6900)$ state at LHCb, the production of $X(6900)$ in $bar{p}prightarrow J/psi J/psi $ reaction is studied within an effective Lagrangian approach and Breit-Wigner formula. The numerical results show that the cross section of $X(6900)$ at the c.m. energy of 6.9 GeV is much larger than that from the background contribution. Moreover, we estimate dozens of signal events can be detected by D0 experiment, which indicates that searching for the $X(6900)$ via antiproton-proton scattering may be a very important and promising way. Therefore, related experiments are suggested to be carried out.
The doubly charmed exotic state $T_{cc}$ recently discovered by the LHCb Collaboration could well be a $DD^{*}$ molecular state long predicted in various theoretical models, in particular, the $DD^*$ isoscalar axial vector molecular state predicted in the one-boson-exchange model. In this work, we study the $DDD^*$ system in the Gaussian Expansion Method with the $DD^*$ interaction derived from the one-boson-exchange model and constrained by the precise binding energy of $273pm63$ keV of $T_{cc}$ with respect to the $D^{*+}D^0$ threshold. We show the existence of a $DDD^*$ state with a binding energy of a few hundred keV and spin-parity $1^-$. Its main decay modes are $DDDpi$ and $DDDgamma$. The existence of such a state could in principle be confirmed with the upcoming LHC data and will unambiguously determine the nature of the $T_{cc}^+$ state and of the many exotic state of similar kind, thus deepening our understanding of the non-perturbative strong interaction.
We study the existence of fully-heavy hidden-flavor $bcbar{b}bar{c}$ tetraquark states with various $J^{PC}=0^{pm+}, 0^{--},1^{pmpm}, 2^{++}$, 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 $bcbar{b}bar{c}$ 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, such results are below the thresholds $T_{eta_ceta_b}/T_{Upsilonpsi}$ and $T_{B_cB_c}$, implying that these S-wave positive parity $bcbar{b}bar{c}$ tetraquark states are probably stable against the strong interaction. For the P-wave negative parity $bcbar{b}bar{c}$ tetraquarks, their masses in the $[mathbf{bar{3}_c}]_{bc}otimes[mathbf{3_c}]_{bar{b}bar{c}}$ channel are around $12.9-13.2$ GeV, while a bit higher in the $[mathbf{6_c}]_{bc}otimes[mathbf{bar{6}_c}]_{bar{b}bar{c}}$ channel. They can decay into the $cbar c+bbar b$ and $cbar b+bbar c$ final states via the spontaneous dissociation mechanism, including the $J/psiUpsilon$, $eta_cUpsilon$, $J/psieta_b$, $B_c^+B_c^-$ channels.
We calculate the radiative decay width of the $psi(3770)$ into the dynamically generated scalar resonance X(3700) which is predicted in a previous paper. The results show that it is possible that the upgraded BEPC-II facility will generate enough statistics in order to observe this decay and thus confirm the existence of the X(3700).