Revisiting the nature of the Pc pentaquarks

A bstract The nature of the three narrow hidden-charm pentaquark P c states, i.e., P c (4312), P c (4440) and P c (4457), is under intense discussion since their discovery from the updated analysis of the process Λb⁰→ J/ψ pK⁻ Λ b 0 → J / ψ pK − by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124 , 072001 (2020)], in which the P c states are treated as Σc( )D̄( ) Σ c ∗ D ¯ ∗ molecules, by including the ΛcD̄( ) Λ c D ¯ ∗ and η c p as explicit inelastic channels in addition to the J/ψp , as required by unitarity and heavy quark spin symmetry (HQSS), respectively. Since inelastic parameters are very badly constrained by the current data, three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic, i.e., Σc( )D̄( ) Σ c ∗ D ¯ ∗ , and inelastic channels and without the ΛcD̄( ) Λ c D ¯ ∗ interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the ΛcD̄( ) Λ c D ¯ ∗ interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with S -wave-to- D -wave mixing contact terms. As a result, in line with our previous analysis, we demonstrate that the experimental data for the J/ψp invariant mass distribution are consistent with the interpretation of the P c (4312) and P c (4440)/ P c (4457) as ΛcD̄ Λ c D ¯ and ΣcD̄ Σ c D ¯ ∗ hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, P c (4380), identified as a Σc^D̄ Σ c ∗ D ¯ molecule, which should exist as a consequence of HQSS. While two statistically equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the P c (4440) and P c (4457) being J P = 3/2 − and 1/2 − , respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the P c (4440) and the P c (4457) in the Σc( )D̄ Σ c ∗ D