<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi></mml:math>-wave charmed baryons from QCD sum rules

Abstract

We study the $P$-wave charmed baryons using the method of QCD sum rule in the framework of heavy quark effective theory. We consider systematically all possible baryon currents with a derivative for internal $\ensuremath{\rho}$- and $\ensuremath{\lambda}$-mode excitations. We have found a good working window for the currents corresponding to the $\ensuremath{\rho}$-mode excitations for ${\mathrm{\ensuremath{\Lambda}}}_{c}(2595)$, ${\mathrm{\ensuremath{\Lambda}}}_{c}(2625)$, ${\mathrm{\ensuremath{\Xi}}}_{c}(2790)$, and ${\mathrm{\ensuremath{\Xi}}}_{c}(2815)$ that complete two $SU(3)$ ${\overline{\mathbf{3}}}_{F}$ multiplets of ${J}^{P}=1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$, while the currents corresponding to the $\ensuremath{\lambda}$-mode excitations seem also consistent with the data. Our results also suggest that there are two ${\mathrm{\ensuremath{\Sigma}}}_{c}(2800)$ states of ${J}^{P}=1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$ whose mass splitting is $14\ifmmode\pm\else\textpm\fi{}7\text{ }\text{ }\mathrm{MeV}$, and two ${\mathrm{\ensuremath{\Xi}}}_{c}(2980)$ states whose mass splitting is $12\ifmmode\pm\else\textpm\fi{}7\text{ }\text{ }\mathrm{MeV}$. They have two ${\mathrm{\ensuremath{\Omega}}}_{c}$ partners of ${J}^{P}=1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$, whose masses are around $3.25\ifmmode\pm\else\textpm\fi{}0.20\text{ }\text{ }\mathrm{GeV}$ with mass splitting $10\ifmmode\pm\else\textpm\fi{}6\text{ }\text{ }\mathrm{MeV}$. All of them together complete two $SU(3)$ ${\mathbf{6}}_{F}$ multiplets of ${J}^{P}=1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$. They may also have ${J}^{P}=5/{2}^{\ensuremath{-}}$ partners. ${\mathrm{\ensuremath{\Xi}}}_{c}(3080)$ may be one of them, and the other two are ${\mathrm{\ensuremath{\Sigma}}}_{c}(5/{2}^{\ensuremath{-}})$ and ${\mathrm{\ensuremath{\Omega}}}_{c}(5/{2}^{\ensuremath{-}})$, whose masses are $85\ifmmode\pm\else\textpm\fi{}23\text{ }\text{ }\mathrm{MeV}$ and $50\ifmmode\pm\else\textpm\fi{}27\text{ }\text{ }\mathrm{MeV}$ larger.