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Register a new userTetraquark molecular states in the $D_sbar{D}_{s1}$ and $D_s^*bar{D}_{s0}^*$ mass spectrum
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In the present work, we construct the color-singlet-color-singlet type four-quark currents to investigate the $D_sbar{D}_{s1}$ and $D_s^*bar{D}_{s0}^*$ tetraquark molecular states with the $J^{PC}=1^{--}$ and $1^{-+}$ via the QCD sum rules, and obtain satisfactory results. We can search for the $D_sbar{D}_{s1}$ and $D_s^*bar{D}_{s0}^*$ tetraquark molecular states with the $J^{PC}=1^{--}$ and $1^{-+}$ at the BESIII and Belle II in the future.
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In this article, we assume that there exist the pseudoscalar $Dbar{D}_{s0}^*(2317)$ and $D^*bar{D}_{s1}^*(2460)$ molecular states $Z_{1,2}$ and construct the color singlet-singlet molecule-type interpolating currents to study their masses with the QCD sum rules. In calculations, we consider the contributions of the vacuum condensates up to dimension-10 and use the formula $mu=sqrt{M_{X/Y/Z}^{2}-left(2{mathbb{M}}_{c}right)^{2}}$ to determine the energy scales of the QCD spectral densities. The numerical results, $M_{Z_1}=4.61_{-0.08}^{+0.11},text{GeV}$ and $M_{Z_2}=4.60_{-0.06}^{+0.07},text{GeV}$, which lie above the $Dbar{D}_{s0}^*(2317)$ and $D^*bar{D}_{s1}^*(2460)$ thresholds respectively, indicate that the $Dbar{D}_{s0}^*(2317)$ and $D^*bar{D}_{s1}^*(2460)$ are difficult to form bound state molecular states, the $Z_{1,2}$ are probably resonance states.
In this work, we preform a systematic investigation about hidden heavy and doubly heavy molecular states from the $D^{(*)}bar{D}^{(*)}/B^{(*)}bar{B}^{(*)}$ and $D^{(*)}D^{(*)}/bar{B}^{(*)}bar{B}^{(*)}$ interactions in the quasipotential Bethe-Salpeter equation (qBSE) approach. With the help of the Lagrangians with heavy quark and chiral symmetries, interaction potentials are constructed within the one-boson-exchange model in which we include the $pi$, $eta$, $rho$, $omega$ and $sigma$ exchanges, as well as $J/psi$ or $Upsilon$ exchange. Possible bound states from the interactions considered are searched for as the pole of scattering amplitude. The results suggest that experimentally observed states, $Z_c(3900)$, $Z_c(4020)$, $Z_b(10610)$, and $Z_b(10650)$, can be related to the $Dbar{D}^{*}$, $D^*bar{D}^{*}$, $Bbar{B}^{*}$, and $B^*bar{B}^{*}$ interactions with quantum numbers $I^G(J^P)=1^+(1^{+})$, respectively. The $Dbar{D}^{*}$ interaction is also attractive enough to produce a pole with $0^+(0^+)$ which is related to the $X(3872)$. Within the same theoretical frame, the existence of $Dbar{D}$ and $Bbar{B}$ molecular states with $0(0^+)$ are predicted. The possible $D^*bar{D}^*$ molecular states with $0(0^+, 1^+, 2^+)$ and $1(0^+)$ and their bottom partners are also suggested by the calculation. In the doubly heavy sector, no bound state is produced from the $DD/bar{B}bar{B}$ interaction while a bound state is found with $0(1^+)$ from $DD^*/bar{B}bar{B}^*$ interaction. The $D^*D^*/bar{B}^*bar{B}^*$ interaction produces three molecular states with $0(1^+)$, $0(2^+)$ and $1(2^+)$.
We have calculated the mass spectra for the $bar{D}_s^{(*)}D^{(*)}$ molecular states and $scbar qbar c$ 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 two almost degenerate states, as the strange partners of the $X(3872)$ and $Z_c(3900)$. We propose to carefully examine the $Z_{cs}(3985)$ in future experiments to verify this. One may also search for more hidden-charm four-quark states with strangeness not only in the open-charm $bar{D}_s^{(*)}D^{(*)}$ channels, but also in the hidden-charm channels $eta_c K/K^ast$, $J/psi K/K^ast$.
Recently, a new structure $Y(4626)$ was reported by the Belle Colloboration in the process $e^+e^-to D_s^+D_{s1}(2536)^-$. In this work, we propose an assignment of the $Y(4626)$ as a ${D}^*_sbar{D}_{s1}(2536)$ molecular state, which decays into the $D_s^+D_{s1}(2536)^-$ channel through a coupling between ${D}^*_sbar{D}_{s1}(2536)$ and ${D}_sbar{D}_{s1}(2536)$ channels. With the help of the heavy quark symmetry, the potential of the interaction ${D}^*_sbar{D}_{s1}(2536)-{D}_sbar{D}_{s1}(2536)$ is constructed within the one-boson-exchange model, and inserted into the quasipotential Bethe-Salpeter equation. The pole of obtained scattering amplitude is searched for in the complex plane, which corresponds to a molecular state from the interaction ${D}^*_sbar{D}_{s1}(2536)-{D}_sbar{D}_{s1}(2536)$. The results suggest that a pole is produced near the ${D}^*_sbar{D}_{s1}(2536)$ threshold, which exhibits as a peak in the invariant mass spectrum of the ${D}_sbar{D}_{s1}(2536)$ channel at about 4626 MeV. It obviously favors the $Y(4265)$ as a ${D}^*_sbar{D}_{s1}(2536)$ molecular state. In the same model, other molecular states from the interaction ${D}^*_sbar{D}_{s1}(2536)-{D}_sbar{D}_{s1}(2536)$ are also predicted, which can be checked in future experiments.
The mass and coupling of the scalar tetraquark $T_{bb;overline{u}overline{d }}^{-}$ (hereafter $T_{b:overline{d}}^{-} $) are calculated in the context of the QCD two-point sum rule method. In computations we take into account effects of various quark, gluon and mixed condensates up to dimension ten. The result obtained for the mass of this state $m=(10135pm 240)~mathrm{MeV} $ demonstrates that it is stable against the strong and electromagnetic decays. We also explore the dominant semileptonic $T_{b:overline{d}}^{-} to widetilde{Z}_{bc;bar{u}bar{d}}^{0}loverline{ u }_{l}$ and nonleptonic decays $T_{b:overline{d}}^{-} to widetilde{Z}_{bc;bar{u}bar{ d}}^{0}M$, where $widetilde{Z}_{bc;bar{u}bar{d}}^{0}$ is the scalar tetraquark composed of color-sextet diquark and antidiquark, and $M$ is one of the final-state pseudoscalar mesons $pi^{-}, K^{-}, D^{-}$ and $D_s^{-}$ , respectively. The partial widths of these processes are calculated in terms of the weak form factors $G_{1(2)}(q^2)$, which are determined from the QCD three-point sum rules. Predictions for the mass, full width $Gamma _{mathrm{full}} =(10.88pm 1.88)times 10^{-10}~mathrm{MeV}$, and mean lifetime $tau=0.61_{-0.09}^{+0.13}~mathrm{ps}$ of the $T_{b:overline{d} }^{-}$ obtained in the present work can be used in theoretical and experimental studies of this exotic state.
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