Abstract
Three hidden-charm pentaquark P_{c} states, P_{c}(4312), P_{c}(4440), and P_{c}(4457) were revealed in the Λ_{b}^{0}→J/ψpK^{-} process measured by LHCb using both run I and run II data. Their nature is under lively discussion, and their quantum numbers have not been determined. We analyze the J/ψp invariant mass distributions under the assumption that the crossed-channel effects provide a smooth background. For the first time, such an analysis is performed employing a coupled-channel formalism with the scattering potential involving both one-pion exchange as well as short-range operators constrained by heavy quark spin symmetry. We find that the data can be well described in the hadronic molecular picture, which predicts seven Σ_{c}^{(*)}D[over ¯]^{(*)} molecular states in two spin multiplets, such that the P_{c}(4312) is mainly a Σ_{c}D[over ¯] bound state with J^{P}=1/2^{-}, while P_{c}(4440) and P_{c}(4457) are Σ_{c}D[over ¯]^{*} bound states with quantum numbers 3/2^{-} and 1/2^{-}, respectively. We also show that there is evidence for a narrow Σ_{c}^{*}D[over ¯] bound state in the data which we call P_{c}(4380), different from the broad one reported by LHCb in 2015. With this state included, all predicted Σ_{c}D[over ¯], Σ_{c}^{*}D[over ¯], and Σ_{c}D[over ¯]^{*} hadronic molecules are seen in the data, while the missing three Σ_{c}^{*}D[over ¯]^{*} states are expected to be found in future runs of the LHC or in photoproduction experiments.
Highlights
We find that the data can be well described in the hadronic molecular picture, which predicts seven ΣðcÃÞDðÃÞ molecular states in two spin multiplets, such that the Pcð4312Þ is mainly a ΣcDbound state with JP 1⁄4 1=2−, while Pcð4440Þ and Pcð4457Þ are ΣcD à bound states with quantum numbers 3=2− and 1=2−, respectively
While only three of the states correspond to the ones reported by LHCb, it is crucial to check whether the existence of the whole two multiplets is consistent with the J=ψp distribution measured by LHCb. This is the question addressed in this Letter: by constructing coupledchannel amplitudes analogous to those used in the analysis of the Zb states [48,49,50,51], we show that the observed J=ψp invariant mass distribution can be well described in the hadronic molecular scenario with seven ΣðcÃÞDðÃÞ molecules, where the Pcð4312Þ and Pcð4440Þ=Pcð4457Þ are ΣcDand ΣcD à bound states, respectively
We only consider the elastic ΣðcÃÞDðÃÞ channels produced in an S wave, since the energy region of interest is close to the ΣðcÃÞDðÃÞ thresholds
Summary
The model predicts in addition four more states, including one ΣÃcDstate at around 4.37 to 4.38 GeV and three states slightly below the ΣÃcD Ã threshold These seven Pc states are contained in two heavy quark spin multiplets, labeled as jPl , with jl and P the total angular momentum of the light degrees of freedom and parity, respectively: three with jPl. 1− 2 and four with jmPlix1⁄4b32e−c.auSstaetethseinΣcthðDesÞe two multiplets with the same spin is not degenerate with the ΣÃcðD ÃÞ. We allow for additional inelastic channels not included explicitly in the amplitudes To this end, we expand the two-particle states in the basis of HQSS eigenstates jsQ ⊗ jli, with sQ and jl representing the total spin of the heavy quarks and total angular momentum of light degrees of freedom, respectively.
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