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Register a new userHeavy quark spin multiplet structure of $P_c$-like pentaquark as P-wave hadronic molecular state
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We study the heavy quark spin (HQS) multiplet structure of P-wave $Qbar{Q}qqq$-type pentaquarks treated as molecules of a heavy meson and a heavy baryon. We define the light-cloud spin (LCS) basis decomposing the meson-baryon spin wavefunction into the LCS and HQS parts. Introducing the LCS basis, we find HQS multiplets classified by the LCS; five HQS singlets, two HQS doublets, and three HQS triplets. We construct the one-pion exchange potential respecting the heavy quark spin and chiral symmetries to demonstrate which HQS multiplets are realized as a bound state. By solving the coupled channel Schrodinger equations, we study the heavy meson-baryon systems with $I=1/2$ and $J^P=(1/2^+, 3/2^+, 5/2^+, 7/2^+)$. The bound states which have same LCS structure are degenerate at the heavy quark limit, and the degeneracy is resolved for finite mass. This HQS multiplet structure will be measured in the future experiments.
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Very recently, the LHCb collaboration has reported the new result about the hidden-charm pentaquarks: $P_c(4312)$ near the $bar{D}Sigma_c$ threshold, and $P_c(4440)$ and $P_c(4457)$ near $bar{D}^*Sigma_c$ threshold. We study the heavy quark spin (HQS) multiplet structures of these newly $P_c$ pentaquarks under the heavy quark spin symmetry based on the hadronic molecular picture. We point out that $P_c(4312)$ is the $J^P = 1/2^-$ member of an HQS triplet, and $P_c(4440)$ and $P_c(4457)$ are the $J^P = 3/2^-$ member of the HQS triplet and an HQS singlet with $J^P = 3/2^-$. Namely, the $P_c(4312)$ and one of $P_c(4440)$ and $P_c(4457)$ belong to an HQS triplet. The HQS multiplet structure predicts the existence of $J^P = 5/2^-$ state near $bar{D}^astSigma_c^ast$ threshold.
We propose to describe the heavy and exotic tetraquark state as a holographic molecule by binding the lightest heavy-light meson $(0^-, 1^-)$ multiplet to a flavored sphaleron in the bulk of the Witten-Sakai-Sugimoto model. The strongly bound tetraquark state emerges as an Efimov state with a binding energy that is comparable to that reported in recent lattice simulations and standard quark model estimates for bottom. Our construction finds charm and mixed charm-bottom tetraquark states to be also bound. The unique feature of these states stems from the fact that they are perhaps the first manifestation of the Efimov bound state mechanism in the hadronic world.
A narrow pentaquark state, $P_c(4312)^+$, decaying to $J/psi p$ is discovered with a statistical significance of $7.3sigma$ in a data sample of ${Lambda_b^0to J/psi p K^-}$ decays which is an order of magnitude larger than that previously analyzed by the LHCb collaboration. The $P_c(4450)^+$ pentaquark structure formerly reported by LHCb is confirmed and observed to consist of two narrow overlapping peaks, $P_c(4440)^+$ and $P_c(4457)^+$, where the statistical significance of this two-peak interpretation is $5.4sigma$. Proximity of the $Sigma_c^+bar{D}^{0}$ and $Sigma_c^+bar{D}^{*0}$ thresholds to the observed narrow peaks suggests that they play an important role in the dynamics of these states.
Recently observed spectrum of $P_c$ states exhibits a strong link to $Sigma_c bar{D}^{(*)}$ thresholds. In spite of successful molecular interpretations, we still push forward to wonder whether there exist finer structures. Utilizing the effecitve lagrangians respecting heavy quark symmetry and chiral symmetry, as well as instantaneous Bethe-Salpeter equations, we investigate the $Sigma_c bar{D}^{(*)}$ interactions and three $P_c$ states. We confirm that $P_c(4312)$ and $P_c(4440)$ are good candidates of $Sigma_c bar{D}$ and $Sigma_c bar{D}^{*}$ molecules with spin-$frac12$, respectively. Unlike other molecular calculations, our results indicate $P_c(4457)$ signal might be a mixture of spin-$frac32$ and spin-$frac12$ $Sigma_c bar{D}^{*}$ molecules, where the latter one appears to be an excitation of $P_c(4440)$. Therefore we conclude that, confronting three LHCb $P_c$ signals, there may exist not three, but four molecular states.
We investigate the observed pentaquark candidates $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ from the latest LHCb measurement, as well as four possible spin partners in the $bar{D}^{(*)}Sigma_c^*$ system predicted from the heavy quark spin symmetry with the hadronic molecule scenarios. Similar to the previous calculation on $P_c(4380)$ and $P_c(4450)$, the partial widths of all the allowed decay channels for these $P_c$ states are estimated with the effective Lagrangian method. The cutoff dependence of our numerical results are also presented. Comparing with the experimental widths, our results show that $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ can be described well with the spin-parity-$1/2^-$-$bar{D}Sigma_c$, $1/2^-$-$bar{D}^*Sigma_c$ and $3/2^-$-$bar{D}^*Sigma_c$ molecule pictures, respectively.
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