Revisiting heavy-flavor conserving weak decays of charmed baryons within the nonrelativistic quark model

In this work, we investigate the heavy-flavor conserving weak decays of charmed baryons, specifically the processes <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi mathvariant="normal">Ξ</a:mi></a:mrow><a:mrow><a:mi>c</a:mi></a:mrow></a:msub><a:mo stretchy="false">→</a:mo><a:msub><a:mrow><a:mi mathvariant="normal">Λ</a:mi></a:mrow><a:mrow><a:mi>c</a:mi></a:mrow></a:msub><a:mi>π</a:mi></a:mrow></a:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi mathvariant="normal">Ω</f:mi><f:mi>c</f:mi></f:msub><f:mo stretchy="false">→</f:mo><f:msub><f:mi mathvariant="normal">Ξ</f:mi><f:mi>c</f:mi></f:msub><f:mi>π</f:mi></f:math>, where the pole model is employed to account for the nonfactorizable contributions. Additionally, the nonperturbative parameters involved are determined within the framework of the nonrelativistic quark model, utilizing exact baryon wave functions obtained by solving the Schrödinger equation with a nonrelativistic potential. By considering the mixing angle <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mi>θ</k:mi><k:mo>∈</k:mo><k:mo stretchy="false">(</k:mo><k:mn>24.4</k:mn><k:mi>°</k:mi><k:mo>,</k:mo><k:mn>32.4</k:mn><k:mi>°</k:mi><k:mo stretchy="false">)</k:mo></k:mrow></k:math> for <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi mathvariant="normal">Ξ</o:mi><o:mi>c</o:mi></o:msub><o:mo>−</o:mo><o:msubsup><o:mi mathvariant="normal">Ξ</o:mi><o:mi>c</o:mi><o:mo>′</o:mo></o:msubsup></o:math> mixing, we find that the experimental data can be effectively reproduced. Furthermore, we estimate the branching ratios: <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mi mathvariant="script">B</s:mi><s:mo stretchy="false">(</s:mo><s:msubsup><s:mrow><s:mi mathvariant="normal">Ξ</s:mi></s:mrow><s:mrow><s:mi>c</s:mi></s:mrow><s:mrow><s:mo>+</s:mo></s:mrow></s:msubsup><s:mo stretchy="false">→</s:mo><s:msubsup><s:mrow><s:mi mathvariant="normal">Λ</s:mi></s:mrow><s:mrow><s:mi>c</s:mi></s:mrow><s:mrow><s:mo>+</s:mo></s:mrow></s:msubsup><s:msup><s:mrow><s:mi>π</s:mi></s:mrow><s:mrow><s:mn>0</s:mn></s:mrow></s:msup><s:mo stretchy="false">)</s:mo><s:mo>=</s:mo><s:mo stretchy="false">(</s:mo><s:mn>8.69</s:mn><s:mi>–</s:mi><s:mn>9.79</s:mn><s:mo stretchy="false">)</s:mo><s:mo>×</s:mo><s:msup><s:mrow><s:mn>10</s:mn></s:mrow><s:mrow><s:mo>−</s:mo><s:mn>3</s:mn></s:mrow></s:msup></s:mrow></s:math>, <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mrow><cb:mi mathvariant="script">B</cb:mi><cb:mo stretchy="false">(</cb:mo><cb:msubsup><cb:mrow><cb:mi mathvariant="normal">Ω</cb:mi></cb:mrow><cb:mrow><cb:mi>c</cb:mi></cb:mrow><cb:mrow><cb:mn>0</cb:mn></cb:mrow></cb:msubsup><cb:mo stretchy="false">→</cb:mo><cb:msubsup><cb:mrow><cb:mi mathvariant="normal">Ξ</cb:mi></cb:mrow><cb:mrow><cb:mi>c</cb:mi></cb:mrow><cb:mrow><cb:mo>+</cb:mo></cb:mrow></cb:msubsup><cb:msup><cb:mrow><cb:mi>π</cb:mi></cb:mrow><cb:mrow><cb:mo>−</cb:mo></cb:mrow></cb:msup><cb:mo stretchy="false">)</cb:mo><cb:mo>=</cb:mo><cb:mo stretchy="false">(</cb:mo><cb:mn>11.3</cb:mn><cb:mi>–</cb:mi><cb:mn>12.1</cb:mn><cb:mo stretchy="false">)</cb:mo><cb:mo>×</cb:mo><cb:msup><cb:mrow><cb:mn>10</cb:mn></cb:mrow><cb:mrow><cb:mo>−</cb:mo><cb:mn>3</cb:mn></cb:mrow></cb:msup></cb:mrow></cb:math>, and <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mrow><mb:mi mathvariant="script">B</mb:mi><mb:mo stretchy="false">(</mb:mo><mb:msubsup><mb:mrow><mb:mi mathvariant="normal">Ω</mb:mi></mb:mrow><mb:mrow><mb:mi>c</mb:mi></mb:mrow><mb:mrow><mb:mn>0</mb:mn></mb:mrow></mb:msubsup><mb:mo stretchy="false">→</mb:mo><mb:msubsup><mb:mrow><mb:mi mathvariant="normal">Ξ</mb:mi></mb:mrow><mb:mrow><mb:mi>c</mb:mi></mb:mrow><mb:mrow><mb:mn>0</mb:mn></mb:mrow></mb:msubsup><mb:msup><mb:mrow><mb:mi>π</mb:mi></mb:mrow><mb:mrow><mb:mn>0</mb:mn></mb:mrow></mb:msup><mb:mo stretchy="false">)</mb:mo><mb:mo>=</mb:mo><mb:mo stretchy="false">(</mb:mo><mb:mn>4.67</mb:mn><mb:mi>–</mb:mi><mb:mn>5.23</mb:mn><mb:mo stretchy="false">)</mb:mo><mb:mo>×</mb:mo><mb:msup><mb:mrow><mb:mn>10</mb:mn></mb:mrow><mb:mrow><mb:mo>−</mb:mo><mb:mn>3</mb:mn></mb:mrow></mb:msup></mb:mrow></mb:math>. These predictions can be tested in ongoing experiments at LHCb, Belle II, and BESIII.