Abstract
The pentaquark states, $P_{c}(4312)$, $P_{c}(4440)$ and $P_{c}(4457)$, could be nicely arranged into a multiplet of seven molecules of $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$ dictated by heavy quark spin symmetry. However, the spins of $P_c(4440)$ and $P_c(4457)$ are not yet fully determined. In this work we employ the contact-range effective field theory to investigate the $SU(3)$-flavor counterparts of $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$, and study the possibility whether their discovery can help determine the spins of $P_c(4457)$ and $P_c(4440)$. We find the existence of a complete hidden charm strange multiplet of $\bar{D}^{(\ast)}\Xi_{c}^{(\prime\ast)}$ molecules irrespective of the spins of $P_c(4440)$ and $P_c(4457)$. On the other hand, we find that although molecules of $\bar{D}^{(\ast)}\Xi_{c}$ are also likely, depending on the realization of the underlying dynamics, their discovery can be more useful to determine the spins of $P_{c}(4440)$ and $P_{c}(4457)$ and to tell how the heavy quark and light quark interaction depends on the spin of the light quark pair.
Highlights
In 2015, the LHCb Collaboration reported two reasonance states, Pcð4380Þ and Pcð4450Þ, in the J=ψp invariant mass spectrum of the Λb → J=ψpK decay [1], whose mass and decay width are MP4380 1⁄4 4380 Æ 8 Æ 29 MeVΓP4380 1⁄4 205 Æ 18 Æ 86 MeV; MP4450 1⁄4 4449.8 Æ 1.7 Æ 2.5 MeVΓP4450 1⁄4 39 Æ 5 Æ 19 MeV; ð1Þ respectively
In our previous work we showed that these states can be understood as hadronic molecules in both an effective field theory (EFT) approach and the one boson exchange (OBE) model [15,16]
II we present the details of the contact-range potential of DðÃÞΞc and DðÃÞΞðc0Þà according to heavy quark spin symmetry and SU(3)-flavor symmetry
Summary
In 2015, the LHCb Collaboration reported two reasonance states, Pcð4380Þ and Pcð4450Þ, in the J=ψp invariant mass spectrum of the Λb → J=ψpK decay [1], whose mass and decay width are MP4380 1⁄4 4380 Æ 8 Æ 29 MeV. We pointed out that the splittings of ΞccΣc states are correlated with the spins of Pcð4440Þ and Pcð4457Þ, which, given the fact that the former can be much more simulated on the lattice [44], provides the possibility of determining the spins of the latter in a model independent way Along these lines, in this work, we explore whether one can relate the pentaquark states Pcð4440Þ and Pcð4457Þ to other states via symmetries such that their discovery could shed light on the nature of the Pc states, their spin in the molecular picture. We focus on the correlation between hidden charm and hidden charm strange molecules, which can help check the molecular interpretation of Pcð4440Þ and Pcð4457Þ and help determine their spin ordering if the hidden charm strange pentaquark states are discovered by either experiments or lattice QCD calculations, which is analogous to the correlation dictated by HADS as shown in Refs.
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