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Register a new userHeavy quark spin multiplet structure of $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$
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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.
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In a chromomagnetic model, we analyse the properties of the newly observed $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ states. We estimate the masses of the $(uud)_{8_c}(cbar{c})_{8_c}$ and $(uds)_{8_c}(cbar{c})_{8_c}$ pentaquark states by considering the isospin breaking effects. Their values are determined by calculating mass distances from the $Sigma_c^{++}D^-$ and $Xi_c^{prime+}D^-$ thresholds, respectively. It is found that the isospin breaking effects on the spectrum are small. From the uncertainty consideration and the rearrangement decay properties in a simple model, we find that it is possible to assign the $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ as $J^P=3/2^-$, $1/2^-$, and $3/2^-$ pentaquark states, respectively. The assignment in the molecule picture can be different, in particular for the $P_c(4312)^+$. The information from open-charm channels, e.g. ${cal B}[P_ctoSigma_c^{++}D^-]/{cal B}[P_cto J/psi p]$, will play an important role in distinguishing the inner structures of the $P_c$ states. Discussions and predictions based on the calculations are also given.
We study the newly reported hidden-charm pentaquark candidates $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ from the LHCb Collaboration, in the framework of the effective-range expansion and resonance compositeness relations. The scattering lengths and effective ranges from the $S$-wave $Sigma_cbar{D}$ and $Sigma_cbar{D}^*$ scattering are calculated by using the experimental results of the masses and widths of the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$. Then we calculate the couplings between the $J/psi p,,Sigma_cbar{D}$ channels and the pentaquark candidate $P_c(4312)$, with which we further estimate the probabilities of finding the $J/psi p$ and $Sigma_cbar{D}$ components inside $P_c(4312)$. The partial decay widths and compositeness coefficients are calculated for the $P_c(4440)$ and $P_c(4457)$ states by including the $J/psi p$ and $Sigma_cbar{D}^*$ channels. Similar studies are also carried out for the three $P_c$ states by including the $Lambda_cbar{D}^{*}$ and $Sigma_cbar{D}^{(*)}$ channels.
Understanding the nature of the hidden charm pentaquark(like) signals in the LHCb data for $Lambda_b^0to J/psi p K^-$ is a central problem of hadron spectroscopy. We propose a scenario completely different from previous ones such as hadron molecules and compact pentaquarks. We identify relevant double triangle mechanisms with leading or lower-order singularities. The associated anomalous threshold cusps at the $Sigma_c^{(*)}bar{D}^{(*)}$ thresholds are significantly more singular than the ordinary ones. Then we demonstrate that the double triangle amplitudes reproduce the peak structures of $P_c(4312)^+$, $P_c(4380)^+$, and $P_c(4457)^+$ in the LHCb data, through an interference with other common mechanisms. Only the $P_c(4440)^+$ peak is due to a resonance with width and strength significantly smaller than previously estimated. $P_c^+$ signals are expected in other processes and the proposed model (partly) explains the current data such as: the GlueX $J/psi$ photoproduction data with no $P_c^+$ signals; the LHCb $Lambda_b^0to J/psi p pi^-$ data with a possible signal only from $P_c(4440)^+$. The double triangle singularity is now a possible option to interpret resonancelike structures near thresholds in general.
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.
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.
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