Hidden charm pentaquarks and the nature of $P_{c}$ states observed at LHCb

Abstract: 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 $P_c (4312)<sup>+$, $P_c (4440)<sup>+$, and $P_c (4457)<sup>+$ observed by the LHCb Collaboration in 2019 can be well explained by the hadronic molecules of $[Σ<em>c\bar{D}]</em>{1/2<sup>-}<sup>{1/2}(4318)$, $$[Σ<em>c\bar{D}^*]</em>{1/2<sup>-}<sup>{1/2}(4437)$$, and $$[Σ<em>c\bar{D}^*]</em>{3/2<sup>-}<sup>{1/2}(4458)$$, respectively. Meanwhile, $P_c(4380)<sup>+$ reported by LHCb in 2015 may be assigned as the molecule $$[Σ<em>c^*\bar{D}]</em>{3/2<sup>-}<sup>{1/2}(4382)$$, 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 $Σ_c<sup>{(<em>)}\bar{D}^{(</em>)}$ bound states with isospin $I=1/2$. Depending on the potential strength of the $σ$ exchange, there may exist very shallow bound states of $Λ_c\bar{D}<sup>{(*)}$ with isospin $I=1/2$ and $Σ_c<sup>{(<em>)}\bar{D}^{(</em>)}$ with isospin $I=3/2$. Our study may provide useful information for further exploring the hidden-charm pentaquarks in future experiments.