P-c(4457) -> P-c (4312)pi/gamma in the molecular picture

The three pentaquark states, P-c (4312), P-c (4440), and P-c (4457), discovered by the LHCb Collaboration in 2019, can be nicely arranged into a multiplet of (D) over bar (()*())Sigma(()(c)*()) of seven molecules dictated by heavy quark spin symmetry. In this work we employ the effective Lagrangian approach to investigate the two decay modes of P-c(4457), P-c(4457) -> P-c(4312)pi, and P-c(4457) -> P-c(4312)gamma, via the triangle mechanism, assuming that P-c(4457) and P-c(4312) are (D) over bar*Sigma(c) and (D) over bar Sigma(c) bound states but the spin of P-c(4457) can be either 1/2 or 3/2. Our results show that the spin of P-c(4457) can not be discriminated through these two decay modes. The decay widths of P-c(4457) -> P-c(4312)g and P-c(4457) -> P-c(4312)gamma are estimated to be of order of 100 keV and 1 keV, respectively. The ratio of the partial decay widths of P-c(4457) -> P-c(4312)pi to P-c(4457) -> P-c(4312)pi is similar to the ratio of D* -> D pi to D* -> D gamma, which could be used to check the molecular nature of P-c(4457) and P-c(4312) if they can be observed in the future.