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Register a new user$P_{cs}(4459)$ and other possible molecular states from $Xi_{c}^{(*)}bar{D}^{(*)}$ and $Xi_cbar{D}^{(*)}$ interactions
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Recently, the LHCb Collaboration reported a new structure $P_{cs}(4459)$ with a mass of 19 MeV below the $Xi_c bar{D}^{*} $ threshold. It may be a candidate of molecular state from the $Xi_c bar{D}^{*} $ interaction. In the current work, we perform a coupled-channel study of the $Xi_c^*bar{D}^*$, $Xi_cbar{D}^*$, $Xi^*_cbar{D}$, $Xi_cbar{D}^*$, $Xi_cbar{D}$, and $Xi_cbar{D}$ interactions in the quasipotential Bethe-Salpeter equation approach. With the help of the heavy quark chiral effective Lagrangian, the potential is constructed by light meson exchanges. Two $Xi_c bar{D}^{*} $ molecular states are produced with spin parities $ J^P=1/2^-$ and $3/2^- $. The lower state with $3/2^-$ can be related to the observed $P_{cs}(4450)$ while two-peak structure can not be excluded. Within the same model, other strange hidden-charm pentaquarks are also predicted. Two states with spin parities $1/2^-$ and $3/2^-$ are predicted near the $Xi_cbar{D}$, $Xi_cbar{D}$, and $Xi_c^*bar{D}$ thresholds, respectively. As two states near $Xi_c bar{D}^{*}$ threshold, two states are produced with $1/2^-$ and $3/2^-$ near the $Xi_cbar{D}^*$ threshold. The couplings of the molecular states to the considered channels are also discussed. The experimental research of those states are helpful to understand the origin and internal structure of the $P_{cs}$ and $P_c$ states.
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In this work, we study the strong decay of the newly observed $P_{cs}(4459)$ assuming that it is a pure $Xi_cbar{D}^{*}$ molecular state. Considering two possible spin-parity assignments $J^P=1/2^{-}$ and $J^P=3/2^{-}$ the partial decay widths of the $Xi_cbar{D}^{*}$ molecular state into $J/psi{}Lambda$, $D_s^{-}Lambda_c^{+}$, and $DXi_c^{()}$ final states through hadronic loops are evaluated with the help of the effective Lagrangians. In comparison with the LHCb data, the spin-party $J^P=1/2^{-}$ the assignment is preferred while this of $J^P=3/2^{-}$ is disfavored. The $P_{cs}(4459)$ in spin-parity $J^P=3/2^{-}$ case maybe explained as $S$-wave coupled bound state with lager $Xi_cbar{D}^{*}$ component. In addition, the calculated partial decay widths with $J^P=1/2^{-}$ $Xi_cbar{D}^{*}$ molecular state picture indicates that allowed decay mode, $DXi_c^{}$, may have the biggest branching ratio. The experimental measurements for this strong decay process could be a crucial test for the molecule interpretation of the $P_{cs}(4459)$.
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 $1(2^+)$.
Inspired by the observation of the $P_{cs} (4459)$ state by LHCb recently, we reexamine the results of the interaction of the $J/psi Lambda$ channel with its coupled channels, exploiting the coupled channel unitary approach combined with heavy quark spin and local hidden gauge symmetries. By tuning the only free parameter, we find a pole of $(4459.07+i6.89)$ MeV below the $bar D^* Xi_c$ threshold, which was consistent well with the mass and width of the $P_{cs} (4459)$ state. Thus, we assume the $P_{cs} (4459)$ state to be a $bar D^* Xi_c$ bound state with the uncertainties on its degeneracy with $J^P = frac{1}{2}^-$ and $J^P = frac{3}{2}^-$. For the degeneracy, it would have two-poles structure, like $P_c (4450)$ before. There is another pole in the $J^P = frac{1}{2}^-$ sector, $(4310.53+i8.23)$ MeV, corresponding to a deep bound state of $bar D Xi_c$. Furthermore, the previously predicted loose bound states of $bar D Xi_c$, $bar D^* Xi_c$, $bar D^* Xi^*_c$ with $J=1/2,~I=0$ and $bar D^* Xi_c$, $bar D Xi^*_c$, $bar D^* Xi_c^*$ with $J=3/2,~I=0$ may exist as either bound states or unbound virtual states. We hope that future experiments can search for the $bar D^{(*)} Xi_c$ molecular states in their dominant decay channels of $bar D^{(*)}_s Lambda_c$, also in the $J/psi Lambda$ and $eta_c Lambda$ channels to reveal their different nature.
We study the $Z_{cs}(3985)$ state recently observed by the BESIII Collaboration in the one-boson-exchange model, assuming that it is a $bar{D}_s^{(*)}D^{(*)}$ molecule, which has the quark content $cbar{c}sbar{q}$ with $q = u$, $d$. It is shown that the one-boson-exchange potential is too weak to generate dynamcally $bar{D}_s D$, $bar{D}^*_s D$, and $bar{D}_sD^*$ states, while for the case of $bar{D}^*_s D^*$, very loosely bound states are likely, with binding energies of the order of several MeV. We conclude that, the observed $Z_{cs}(3985)$ state, if confirmed by further experiments, cannot be a pure hadronic molecular state of $bar{D}_s D^*$ and $bar{D}_s^*D$ and could consist of large components of compact nature.
Motivated by the recent discovery of the first hidden charm pentaquark state with strangeness $P_{cs}(4459)$ by the LHCb Collaboration, we study the likely existence of a three-body $Sigma_{c}bar{D}bar{K}$ bound state, which shares the same minimal quark content as $P_{cs}(4459)$. The $Sigma_{c}bar{D}$ and $DK$ interactions are determined by reproducing $P_c(4312)$ and $D_{s0}^*(2317)$ as $Sigma_cbar{D}$ and $bar{D}bar{K}$ molecules, respectively, while the $Sigma_cbar{K}$ interaction is constrained by chiral effective theory. We indeed find a three-body bound state by solving the Schrodinger equation using the Gaussian Expansion Method, which can be viewed as an excited hidden charm pentaquark state with strangeness, $P_{cs}^*(4739)$, with $I(J^P)=1(1/2^+)$ and a binding energy of $77.8^{+25}_{-10.3}$ MeV. We further study its strong decays via triangle diagrams and show that its partial decay widths into $DXi_c$ and $D_s^*Sigma_c$ are of a few tens MeV, with the former being dominant.
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