Partial decay widths of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4312</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> as a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:msub><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> molecular state
Y. C. Xu, Chun-Yu Cui, Yong-Lu Liu, Ming-Qiu Huang
Abstract
In the present work, the partial decay widths of ${P}_{c}(4312)$ to ${\ensuremath{\eta}}_{c}p$ and $J/\ensuremath{\psi}p$ are investigated with the QCD sum rule method under the assumption that ${P}_{c}(4312)$ is a $\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}$ molecular state with ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$. 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 ${\ensuremath{\eta}}_{c}p$ and $J/\ensuremath{\psi}p$ are estimated to be $\mathrm{\ensuremath{\Gamma}}({P}_{c}(4312)\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}p)=5.5{4}_{\ensuremath{-}0.5}^{+0.75}\text{ }\text{ }\mathrm{MeV}$ and $\mathrm{\ensuremath{\Gamma}}({P}_{c}(4312)\ensuremath{\rightarrow}J/\ensuremath{\psi}p)=1.6{7}_{\ensuremath{-}0.56}^{+0.92}\text{ }\text{ }\mathrm{MeV}$, 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 $\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}$ molecular state with ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$.