Hidden charm pentaquarks and the nature of $P_{c}$ states observed at LHCb
We carry out a unified study of the low-lying $1S$-wave compact states and hadronic molecules composed of hidden charm pentaquarks $qqqc\bar{c}$ ($q=u,d$) within a semirelativistic potential quark model. Apart from the linear confinement and one-gluon exchange potential between quarks and/or antiquarks, one-boson exchange potential is also included for baryon and meson clusters within the pentaquark system. We also evaluate the fall-apart decays by combining the obtained spectra within the quark exchange model. It is found that the $P_c (4312)^+$, $P_c (4440)^+$, and $P_c (4457)^+$ observed by the LHCb Collaboration in 2019 can be well explained by the hadronic molecules of $[Σ_c\bar{D}]_{1/2^-}^{1/2}(4318)$, $[Σ_c\bar{D}^*]_{1/2^-}^{1/2}(4437)$, and $[Σ_c\bar{D}^*]_{3/2^-}^{1/2}(4458)$, respectively. Meanwhile, $P_c(4380)^+$ reported by LHCb in 2015 may be assigned as the molecule $[Σ_c^*\bar{D}]_{3/2^-}^{1/2}(4382)$, except that it turns to be a narrow state other than a broad one shown by the experimental data. Our study shows that the $σ$- and $ρ$-meson exchanges are crucial for the formation of $Σ_c^{(*)}\bar{D}^{(*)}$ bound states with isospin $I=1/2$. Depending on the potential strength of the $σ$ exchange, there may exist very shallow bound states of $Λ_c\bar{D}^{(*)}$ with isospin $I=1/2$ and $Σ_c^{(*)}\bar{D}^{(*)}$ with isospin $I=3/2$. Our study may provide useful information for further exploring the hidden-charm pentaquarks in future experiments.