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Register a new user$P_c$ Resonances in the Compact Pentaquark Picture
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$P_c$ resonances are studied in the approach of quark model and group theory. It is found that there are totally 17 possible pentaquark states with the quark contents $q^3Q bar Q$ ($q$ are $u$ and $d$ quarks; $Q$ is $c$ quark) in the compact pentaquark picture, where the hidden heavy pentaquark states may take the color singlet-singlet ($[111]_{{qqq}}otimes [111]_{{c bar c}}$) and color octet-octet ($[21]_{{qqq}}otimes [21]_{{c bar c}}$) configurations. The partial decay widths of hidden heavy pentaquark states are calculated for all possible decay channels. The results show that the $pJ/psi$ is the dominant decay channel for both the spin $3/2$ and $1/2$ pentaquark states, and indicate that the $P_c(4440)$ may not be a compact pentaquark state while $P_c(4312)$ and $P_c(4457)$ could be the spin-$frac{1}{2}$ and spin-$frac{3}{2}$ pentaquark states, respectively.
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We study hidden-charm pentaquarks in the baryon-meson molecule picture within the framework of the constituent quark model, considering all the possible quark configurations for the ground state. The strong decays of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ resonances are investigated. It is found that pentaquark states of all quark configurations in the model can decay through the $N J/psi$ channel, but only five pentaquark states may decay dominantly in open-charm modes. The partial decay widths in the $peta_c$ channel are in the same order as in the $p J/psi$ channel for $J^P=1/2^-$ baryon-meson pentaquark states, but the $peta_c$ channel is forbidden for $J^P=3/2^-$ states. For $P_c(4440)$ and $P_c(4457)$, the $p eta_c$, $Sigma_cbar{D}$ and $Lambda_c^+bar{D}$ channels are open only for $J^P=1/2^-$ and the $Sigma_c^*bar{D}$ channel is open only for $J^P=3/2^-$ while for $P_c(4312)$, due to the mass threshold of $Sigma_cbar{D}$ and $Sigma_c^*bar{D}$ higher than 4312 MeV, the $p eta_c$ and $Lambda_c^+bar{D}$ channels are open for $J^P=1/2^-$ but no open-charm cannel open for $J^P=3/2^-$. We strongly suggest that the spin of the $P_c$ resonances may be determined in experiments by investigating the $p eta_c$ and open-charm channels.
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.
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 investigate the quantum numbers of the pentaquark states $textrm{P}_{textrm{c}}^{+}$, which are composed of four (three flavors) quarks and an antiquark, by analyzing their inherent nodal structure in this paper. Assuming that the four quarks form a tetrahedron or a square, and the antiquark locates at the center of the four quark cluster, we determine the nodeless structure of the states with orbital angular moment $L leq 3$, and in turn, the accessible low-lying states. Since the inherent nodal structure depends only on the inherent geometric symmetry, we propose the quantum numbers $J^{P}$ of the low-lying pentaquark states $textrm{P}_{c}^{+}$ may be ${frac{3}{2}}^{-}$, ${frac{5}{2}}^{-} $, ${frac{3}{2}}^{+}$, ${frac{5}{2}}^{+} $, independent of dynamical models.
We study pentaquark states of both light $q^4bar q$ and hidden heavy $q^3 Qbar Q$ (q = u,d,s quark in SU(3) flavor symmetry; Q = c, b quark) systems with a general group theory approach in the constituent quark model, and the spectrum of light baryon resonances in the ansatz that the $l=1$ baryon states may consist of the $q^3$ as well as $q^4bar q$ pentaquark component. The model is fitted to ground state baryons and light baryon resonances which are believed to be normal three-quark states. The work reveals that the $N(1535)1/2^{-}$ and $N(1520)3/2^-$ may consist of a large $q^4bar q$ component while the $N(1895)1/2^{-}$ and $N(1875)3/2^-$ are respectively their partners, and the $N^+(1685)$ might be a $q^4bar q$ state. By the way, a new set of color-spin-flavor-spatial wave function for $q^3 Qbar Q$ systems in the compact pentaquark picture are constructed systematically for studying hidden charm pentaquark states.
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