Interpretation of the LHCb <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> States as Hadronic Molecules and Hints of a Narrow <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4380</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
Meng-Lin Du, V. Baru, Feng-Kun Guo, C. Hanhart, Ulf-G. Meißner, J. A. Oller, Qian Wang
Abstract
Three hidden-charm pentaquark ${P}_{c}$ states, ${P}_{c}(4312)$, ${P}_{c}(4440)$, and ${P}_{c}(4457)$ were revealed in the ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p{K}^{\ensuremath{-}}$ 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 $J/\ensuremath{\psi}p$ 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 ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{\overline{D}}^{(*)}$ molecular states in two spin multiplets, such that the ${P}_{c}(4312)$ is mainly a ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$ bound state with ${J}^{P}=1/{2}^{\ensuremath{-}}$, while ${P}_{c}(4440)$ and ${P}_{c}(4457)$ are ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ bound states with quantum numbers $3/{2}^{\ensuremath{-}}$ and $1/{2}^{\ensuremath{-}}$, respectively. We also show that there is evidence for a narrow ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}\overline{D}$ 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 ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$, ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}\overline{D}$, and ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ hadronic molecules are seen in the data, while the missing three ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}{\overline{D}}^{*}$ states are expected to be found in future runs of the LHC or in photoproduction experiments.