Study of $P_c(4457)$, $P_c(4440)$, and $P_c(4312)$ in a quasipotential Bethe-Salpeter equation approach

Abstract: 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 $\Sigma_c^{(*)}$ baryon and a $\bar{D}^{(*)}$ meson in a quasipotential Bethe-Salpeter equation approach. The two-peak structure around 4450 MeV can be interpreted as two $\Sigma_c \bar{D}^*$ bound states with spin parities $1/2^-$ and $3/2^-$. The newly observed pentaquark $P_c(4312)$ can be assigned as a $\Sigma_c\bar{D}$ 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.