Partial decay widths of $P_c(4312)$ as a $\bar{D}{\mathrm{\Sigma }}_c$ molecular state

In the present work, the partial decay widths of $P_c(4312)$ to $\eta_{c} p$and$J/\psi p$ are investigated with the QCD sum rule method under the assumption that $P_c(4312)$ is a $\bar{D}{\mathrm{\Sigma }}_c$ molecular state with $J^P={\frac{1}{2}}^{-}$. In the analysis, the pole residue of $P_c(4312)$, one of the input parameters for the calculations of the strong decay constants, is calculated first. With the numerical values of the strong decay constants, the partial decay widths to ${\eta }_{c}p$ and $J\mathrm{/}\psi p$ are estimated to be $\mathrm{\Gamma }(P_c(4312)\to {\eta }_{c}p)=5.54_{-0.5}^{+0.75}MeV$ and $\mathrm{\Gamma }(P_c(4312)\to J\mathrm{/}\psi p)=1.67_{-0.56}^{+0.92}MeV$, respectively, which are compatible with the measured total width of $P_c(4312)$. The results suggest that it is reasonable to assign $P_c(4312)$ to be a $\bar{D}{\mathrm{\Sigma }}_c$ molecular state with $J^P={\frac{1}{2}}^{-}$.