Partial decay widths of $P_{c}(4312)$ as a $\bar{D}Σ_{c}$ molecular state

In the present work, the partial decay widths of $P_{c}(4312)$ to $η_{c} p$ and $J/ψp$ are investigated with the QCD sum rule method under the assumption that $P_{c}(4312)$ is a $\bar{D}Σ_{c}$ 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 $η_{c} p$ and $J/ψp$ are estimated to be $Γ(P_{c}(4312)\rightarrow η_{c} p)=5.54^{+0.75}_{-0.5}\mbox{MeV}$ and $Γ(P_{c}(4312)\rightarrow J/ψp)=1.67^{+0.92}_{-0.56}\mbox{MeV}$, 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 $\bar{D}Σ_{c}$ molecular state with $J^{P}=\frac{1}{2}^{-}$.

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