Branching fraction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup> <mml:mi mathvariant="normal">Ξ</mml:mi> <mml:mrow> <mml:mi>b</mml:mi> <mml:mi>c</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msubsup> <mml

The process of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msubsup> <a:mi mathvariant="normal">Ξ</a:mi> <a:mrow> <a:mi>b</a:mi> <a:mi>c</a:mi> </a:mrow> <a:mo>+</a:mo> </a:msubsup> <a:mo stretchy="false">→</a:mo> <a:msubsup> <a:mi mathvariant="normal">Ξ</a:mi> <a:mi>c</a:mi> <a:mo>+</a:mo> </a:msubsup> <a:mi>J</a:mi> <a:mo>/</a:mo> <a:mi>ψ</a:mi> </a:math> is among the most favored modes for searching for bottom-charm baryons. However, its branching fraction has never been studied in theory. In this work, we investigate the branching fraction of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msubsup> <f:mi mathvariant="normal">Ξ</f:mi> <f:mrow> <f:mi>b</f:mi> <f:mi>c</f:mi> </f:mrow> <f:mo>+</f:mo> </f:msubsup> <f:mo stretchy="false">→</f:mo> <f:msubsup> <f:mi mathvariant="normal">Ξ</f:mi> <f:mi>c</f:mi> <f:mo>+</f:mo> </f:msubsup> <f:mi>J</f:mi> <f:mo>/</f:mo> <f:mi>ψ</f:mi> </f:math> in the final-state-interaction approach, as it is dominated by the color-suppressed nonfactorizable contributions. A similar process, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msubsup> <k:mi mathvariant="normal">Λ</k:mi> <k:mi>b</k:mi> <k:mn>0</k:mn> </k:msubsup> <k:mo stretchy="false">→</k:mo> <k:msup> <k:mi mathvariant="normal">Λ</k:mi> <k:mn>0</k:mn> </k:msup> <k:mi>J</k:mi> <k:mo>/</k:mo> <k:mi>ψ</k:mi> </k:math> , is used as a control mode to fix the model parameter. Consequently, the branching fraction of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msubsup> <p:mi mathvariant="normal">Ξ</p:mi> <p:mrow> <p:mi>b</p:mi> <p:mi>c</p:mi> </p:mrow> <p:mo>+</p:mo> </p:msubsup> <p:mo stretchy="false">→</p:mo> <p:msubsup> <p:mi mathvariant="normal">Ξ</p:mi> <p:mi>c</p:mi> <p:mo>+</p:mo> </p:msubsup> <p:mi>J</p:mi> <p:mo>/</p:mo> <p:mi>ψ</p:mi> </p:math> is predicted to be <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mo stretchy="false">(</u:mo> <u:mn>1.5</u:mn> <u:msubsup> <u:mn>5</u:mn> <u:mrow> <u:mo>−</u:mo> <u:mn>0.42</u:mn> </u:mrow> <u:mrow> <u:mo>+</u:mo> <u:mn>0.50</u:mn> </u:mrow> </u:msubsup> <u:mo stretchy="false">)</u:mo> <u:mo>×</u:mo> <u:msup> <u:mn>10</u:mn> <u:mrow> <u:mo>−</u:mo> <u:mn>4</u:mn> </u:mrow> </u:msup> </u:math> . With the production rate of bottom-charm baryons and the detection efficiencies of the final states, it is expected for considerable signal events to observe <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msubsup> <y:mi mathvariant="normal">Ξ</y:mi> <y:mrow> <y:mi>b</y:mi> <y:mi>c</y:mi> </y:mrow> <y:mo>+</y:mo> </y:msubsup> </y:math> in the near future.