Revisiting the nature of the P c pentaquarks

Abstract

Abstract 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 Λ b 0 → J / ψ pK − $$ {\Lambda}_b^0\to J/\psi {pK}^{-} $$ 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 Σ c ∗ D ¯ ∗ $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ molecules, by including the Λ c D ¯ ∗ $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ 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., Σ c ∗ D ¯ ∗ $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ , and inelastic channels and without the Λ c D ¯ ∗ $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the Λ c D ¯ ∗ $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ 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 Λ c D ¯ $$ {\Lambda}_c\overline{D} $$ and Σ c D ¯ ∗ $$ {\Sigma}_c{\overline{D}}^{\ast } $$ hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, P c (4380), identified as a Σ c ∗ D ¯ $$ {\Sigma}_c^{\ast}\overline{D} $$ 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 Σ c ∗ D ¯ $$ {\Sigma}_c^{\left(\ast \right)}\overline{D} $$ and η c p mass distributions from Λ b 0 → Σ c ∗ D ¯ K − $$ {\Lambda}_b^0\to {\Sigma}_c^{\left(\ast \right)}\overline{D}{K}^{-} $$ and Λ b 0 → η c pK − $$ {\Lambda}_b^0\to {\eta}_c{pK}^{-} $$ will shed light on the quantum numbers of those states, once the data are available. We also investigate possible pentaquark signals in the Λ c D ¯ ∗ $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ final states.

Keywords

• QCD Phenomenology
• Non-perturbative renormalization