Recently observed Pc as molecular states and possible mixture of Pc (4457)

Abstract

A recently observed spectrum of Pc states exhibits a strong link to ςcD(∗) thresholds. In spite of successful molecular interpretations, we still push forward to wonder whether there exist finer structures. Utilizing the effecitve Lagrangians respecting heavy quark symmetry and chiral symmetry, as well as instantaneous Bethe-Salpeter equations, we investigate the ςcD(∗) interactions and three Pc states. We confirm that Pc(4312) and Pc(4440) are good candidates of ςcD and ςcD∗ molecules with spin-12, respectively. Unlike other molecular calculations, our results indicate the Pc(4457) signal might be a mixture of spin-32 and spin-12 ςcD∗ molecules, where the latter one appears to be an excitation of Pc(4440). Therefore we conclude that, confronting three LHCb Pc signals, there may exist not three, but four molecular states.