Identifying the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>6100</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> as the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi></mml:math>-wave bottom baryon of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:mi>P</mml:mi></mml:mrow></mml:msup><mml:malignmark/><mml:mo>=</mml:mo><mml:mn>3</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>
H. L. Yang, Hua-Xing Chen, Er-Liang Cui, Qiang Mao
Abstract
We study the ${\mathrm{\ensuremath{\Xi}}}_{b}(6100)$ using the methods of QCD sum rules and light-cone sum rules within the framework of heavy quark effective theory. Our results suggest that the ${\mathrm{\ensuremath{\Xi}}}_{b}(6100)$ can be well interpreted as the $P$-wave bottom baryon of ${J}^{P}=3/{2}^{\ensuremath{-}}$, belonging to the $SU(3)$ flavor ${\overline{\mathbf{3}}}_{F}$ representation. It has a partner state of ${J}^{P}=1/{2}^{\ensuremath{-}}$, labeled as ${\mathrm{\ensuremath{\Xi}}}_{b}(1/{2}^{\ensuremath{-}})$, whose mass and width are predicted to be ${m}_{{\mathrm{\ensuremath{\Xi}}}_{b}(1/{2}^{\ensuremath{-}})}={6.08}_{\ensuremath{-}0.11}^{+0.13}\text{ }\text{ }\mathrm{GeV}$ and ${\mathrm{\ensuremath{\Gamma}}}_{{\mathrm{\ensuremath{\Xi}}}_{b}(1/{2}^{\ensuremath{-}})}={4}_{\ensuremath{-}4}^{+29}\text{ }\text{ }\mathrm{MeV}$, respectively, with the mass splitting $\mathrm{\ensuremath{\Delta}}M={m}_{{\mathrm{\ensuremath{\Xi}}}_{b}(6100)}\ensuremath{-}{m}_{{\mathrm{\ensuremath{\Xi}}}_{b}(1/{2}^{\ensuremath{-}})}=9\ifmmode\pm\else\textpm\fi{}3\text{ }\text{ }\mathrm{MeV}$. We propose to search for it in the ${\mathrm{\ensuremath{\Xi}}}_{c}({1/2}^{\ensuremath{-}})\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{'}}\ensuremath{\pi}$ decay channel. Our results also suggest that the ${\mathrm{\ensuremath{\Lambda}}}_{b}(5912)$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}(5920)$ are their partner states with ${J}^{P}=1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$, respectively, and, moreover, the ${\mathrm{\ensuremath{\Lambda}}}_{c}(2595)$, ${\mathrm{\ensuremath{\Lambda}}}_{c}(2625)$, ${\mathrm{\ensuremath{\Xi}}}_{c}(2790)$, and ${\mathrm{\ensuremath{\Xi}}}_{c}(2815)$ are their charmed partner states.