Abstract
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 $\bar{D}\Sigma_{c}$ 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 $J/\psi p$ are estimated to be $\Gamma(P_{c}(4312)\rightarrow \eta_{c} p)=5.54^{+0.75}_{-0.5}\mbox{MeV}$ and $\Gamma(P_{c}(4312)\rightarrow J/\psi p)=1.67^{+0.92}_{-0.56}\mbox{MeV}$, 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 $\bar{D}\Sigma_{c}$ molecular state with $J^{P}=\frac{1}{2}^{-}$.
Highlights
Multiquark states with quark substructures qqqq ̄, qqqqq, and so on, are allowed both in the conventional quark model and quantum chromodynamics (QCD), the correct theory of the strong interaction
Many physicists have focused on this topic since the observation of Xð3872Þ in 2003 by the Belle Collaboration [1], and there have been many theoretical and experimental progresses on the theme in the last decade
Pcð4312Þ → ηcp and Pcð4312Þ → J=ψp are studied via the method of QCD sum rule
Summary
The pole residue of Pcð4312Þ, 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 ηcp and J=ψp are estimated to be ΓðPcð4312Þ → ηcpÞ 1⁄4 5.54þ−00..575. MeV and ΓðPcð4312Þ → J=ψ pÞ 1⁄4 1.67þ−00..5962. MeV, respectively, which are compatible with the measured total width of Pcð4312Þ.
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