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Register a new userCoupled Channel Effects of the $Sigma_c^{(*)}bar{D}^{(*)}$-$Lambda_c(2595)bar{D}$ System and Molecular Nature of the $P_c$ Pentaquark States from One-Boson Exchange Model
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The effects of the $Sigma_cbar{D}^*$-$Lambda_{c}(2595)bar{D}$ coupled-channel dynamics and various one-boson-exchange (OBE) forces for the LHCb pentaquark states, $P_c(4440)$ and $P_c(4457)$, are reinvestigated. Both the pion and $rho$-meson exchanges are considered for the $Sigma_cbar{D}^*$-$Lambda_{c}(2595)bar{D}$ coupled-channel dynamics. It is found that the role of the $Lambda_{c}(2595)bar{D}$ channel in the descriptions of the $P_c(4440)$ and $P_c(4457)$ states is not significant with the OBE parameters constrained by other experimental sources. The naive OBE models with the short-distance $delta(vec{r})$ term of the one-pion exchange (OPE) kept fail to reproduce the $P_c(4440)$ and $P_c(4457)$ states simultaneously. The OPE potential with the full $delta(vec{r})$ term results in a too large mass splitting for the $J^P=1/2^-$ and $3/2^-$ $Sigma_cbar{D}^*$ bound states with total isospin $I=1/2$. The OBE model with only the OPE $delta(vec{r})$ term dropped may fit the splitting much better, but somewhat underestimates the splitting. Since the $delta(vec r)$ potential is from short-distance physics, which also contains contributions from the exchange of mesons heavier than those considered explicitly, we vary the strength of the $delta(vec r)$ potential and find that the masses of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ can be reproduced simultaneously with the $delta(vec r)$ term in the OBE model reduced by about 80%. While two different spin assignments are possible to produce their masses, in the preferred description the spin-parities of the $P_c(4440)$ and $P_c(4457)$ are $3/2^-$ and $1/2^-$, respectively.
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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 evaluate the partial decay widths for the semileptonic $Lambda_b to bar u_l l Lambda_c(2595)$ and $Lambda_b to bar u_l l Lambda_c(2625)$ decays from the perspective that these two $Lambda^*_c$ resonances are dynamically generated from the $DN$ and $D^*N$ interaction with coupled channels. We find that the ratio of the rates obtained for these two reactions is compatible with present experimental data and is very sensitive to the $D^* N$ coupling, which becomes essential to obtain agreement with experiment. Together with the results obtained for the $Lambda_b to pi^- Lambda^*_c$ reactions, it gives strong support to the molecular picture of the two $Lambda^*_c$ resonances and the important role of the $D^*N$ component neglected in prior studies of the $Lambda_c(2595)$ from the molecular perspective.
We consider the ${bar D}^{(*)}Sigma_c^{(*)}$ states, together with $J/psi N$ and other coupled channels, and take an interaction consistent with heavy quark spin symmetry, with the dynamical input obtained from an extension of the local hidden gauge approach. By fitting only one parameter to the recent three pentaquark states reported by the LHCb collaboration, we can reproduce the three of them in base to the mass and the width, providing for them the quantum numbers and approximate molecular structure as $1/2^-$ $bar{D} Sigma_c$, $1/2^-$ $bar{D}^* Sigma_c$, and $3/2^-$ $bar{D}^* Sigma_c$, and isospin $I=1/2$. We find another state around 4374 MeV, of $3/2^-$ $bar{D} Sigma_c^*$ structure, for which indications appear in the experimental spectrum. Two other near degenerate states of $1/2^-$ $bar{D}^* Sigma_c^*$ and $3/2^-$ $bar{D}^* Sigma_c^*$ nature are also found around 4520 MeV, which although less clear, are not incompatible with the observed spectrum. In addition, a $5/2^-$ $bar D^* Sigma_c^*$ state at the same energy appears, which however does not couple to $J/psi p$ in $S-$wave, and hence it is not expected to show up in the LHCb experiment.
We evaluate the s-wave interaction of pseudoscalar and vector mesons with both charm and beauty to investigate the possible existence of molecular $BD$, $B^*D$, $BD^*$, $B^*D^*$, $Bbar D$, $B^*bar D$, $Bbar D^*$ or $B^* bar D^*$ meson states. The scattering amplitude is obtained implementing unitarity starting from a tree level potential accounting for the dominant vector meson exchange. The diagrams are evaluated using suitable extensions to the heavy flavor sector of the hidden gauge symmetry Lagrangians involving vector and pseudoscalar mesons{, respecting heavy quark spin symmetry}. We obtain bound states at energies above 7 GeV for $BD$ ($J^P=0^+$), $B^*D$ ($1^+$), $BD^*$ ($1^+$) and $B^*D^*$ ($0^+$, $1^+$, $2^+$), all in isospin 0. For $Bbar D$ ($0^+$), $B^*bar D$ ($1^+$), $Bbar D^*$ ($1^+$) and $B^*bar D^*$ ($0^+$, $1^+$, $2^+$) we also find similar bound states in $I=0$, but much less bound, which would correspond to exotic meson states with $bar b$ and $bar c$ quarks, and for the $I=1$ we find a repulsive interaction. We also evaluate the scattering lengths in all cases, which can be tested in current investigations of lattice QCD.
In this talk we address two topics: The first one is an empirical explanation in terms of a new state $h_1$ of the peak in the $K^{*0}bar{K}^{*0}$ invariant mass distribution close to threshold of this channel in the $J/psi to eta K^{*0}bar{K}^{*0}$ decay. The second one is a theoretical description of the isospin $I=1$ $Z_c(3900)$ and $Z_c(4020)$ states in terms of molecular states of $D bar D^*+ cc$ and $D^* bar D^*$.
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