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Register a new userQuantum Numbers of the Pentaquark States $P_c^+$ via Symmetry Analysis
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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.
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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.
$P_c$ 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.
The QCD sum rule technique is employed to investigate pentaquark states with strangeness S = +1 and IJ^P = 0,1/2^pm, 1,1/2^pm, 0,3/2^pm, 1,3/2^pm. Throughout the calculation, emphasis is laid on the establishment of a valid Borel window, which corresponds to a region of the Borel mass, where the operator product expansion converges and the presumed ground state pole dominates the sum rules. Such a Borel window is achieved by constructing the sum rules from the difference of two independent correlators and by calculating the operator product expansion up to dimension 14. Furthermore, we discuss the possibility of the contamination of the sum rules by possible KN scattering states. As a result, we conclude that the 0,3/2^+ state seems to be the most probable candidate for the experimentally observed Theta^+(1540), while we also obtain states with 0,1/2^-, 1,1/2^-, 1,3/2^+ at somewhat higher mass regions.
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.
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