Study of P${}_c$(4457) , P${}_c$(4440) , and P${}_c$(4312) in a quasipotential Bethe–Salpeter equation approach

Very recently, the LHCb Collaboration reported their new results about the pentaquarks at charm energy region. Based on the new experimental results, we recalculate the molecular states composed of a Σ${}_c^{\left(\text{â}\text{ˆ}\text{—}\right)}$ baryon and a $\overline{D}$${}^{\left(\text{â}\text{ˆ}\text{—}\right)}$ meson in a quasipotential Bethe–Salpeter equation approach. The two-peak structure around 4450 MeV can be interpreted as two Σ${}_c$$\overline{D}$${}^{\text{â}}\text{ˆ}\text{—}$ bound states with spin parities 1/2${}^{-}$ and 3/2${}^{-}$. The newly observed pentaquark P${}_c$(4312) can be assigned as a Σ${}_c$$\overline{D}$ bound state with spin parity 1/2${}^{-}$. The experimental determination of spin parities will be very helpful to understand the internal structure of these pentaquarks.