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Register a new userAnatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
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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.
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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.
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.
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.
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.
Recently, the LHCb Collaboration reported three $P_c$ states in the ${J/psi}p$ channel. We systematically study the mass spectrum of the hidden charm pentaquark in the framework of an extended chromomagnetic model. For the $nnncbar{c}$ pentaquark with $I=1/2$, we find that (i) the lowest state is $P_{c}(4327.0,1/2,1/2^{-})$ [We use $P_{c}(m,I,J^{P})$ to denote the $nnncbar{c}$ pentaquark], which corresponds to the $P_{c}(4312)$. Its dominant decay mode is $Lambda_{c}bar{D}^{*}$. (ii) We find two states in the vicinity of $P_{c}(4380)$. The first one is $P_{c}(4367.4,1/2,3/2^{-})$ and decays dominantly to $N{J/psi}$ and $Lambda_{c}bar{D}^{*}$. The other one is $P_{c}(4372.4,1/2,1/2^{-})$. Its dominant decay mode is $Lambda_{c}bar{D}$, and its partial decay width of $Neta_{c}$ channel is comparable to that of $N{J/psi}$. (iii) In higher mass region, we find $P_{c}(4476.3,1/2,3/2^{-})$ and $P_{c}(4480.9,1/2,1/2^{-})$, which correspond to $P_{c}(4440)$ and $P_{c}(4457)$. In the open charm channels, both of them decay dominantly to the $Lambda_{c}bar{D}^{*}$. (iv) We predict two states above $4.5~text{GeV}$, namely $P_{c}(4524.5,1/2,3/2^{-})$ and $P_{c}(4546.0,1/2,5/2^{-})$. The masses of the $nnncbar{c}$ state with $I=3/2$ are all over $4.6~text{GeV}$. Moreover, we use the model to explore the $nnscbar{c}$, $ssncbar{c}$ and $ssscbar{c}$ pentaquark states.
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