Production of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>ψ</mml:mi><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mn>4338</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> from <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:mrow></mml:math> decay

Abstract

In the present work, we investigate the production of the newly observed <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>P</a:mi><a:mrow><a:mi>ψ</a:mi><a:mi>s</a:mi></a:mrow><a:mi mathvariant="normal">Λ</a:mi></a:msubsup><a:mo stretchy="false">(</a:mo><a:mn>4338</a:mn><a:mo stretchy="false">)</a:mo></a:math> state in <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msubsup><f:mi mathvariant="normal">Ξ</f:mi><f:mi>b</f:mi><f:mo>−</f:mo></f:msubsup></f:math> decay, where the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msubsup><i:mi>P</i:mi><i:mrow><i:mi>ψ</i:mi><i:mi>s</i:mi></i:mrow><i:mi mathvariant="normal">Λ</i:mi></i:msubsup><i:mo stretchy="false">(</i:mo><i:mn>4338</i:mn><i:mo stretchy="false">)</i:mo></i:math> is assigned as a <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi mathvariant="normal">Ξ</n:mi><n:mi>c</n:mi></n:msub><n:mover accent="true"><n:mi>D</n:mi><n:mo stretchy="false">¯</n:mo></n:mover></n:math> molecular state. By using an effective Lagrangian approach, we evaluate the branching fractions of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msubsup><s:mi mathvariant="normal">Ξ</s:mi><s:mi>b</s:mi><s:mo>−</s:mo></s:msubsup><s:mo stretchy="false">→</s:mo><s:msubsup><s:mi>P</s:mi><s:mrow><s:mi>ψ</s:mi><s:mi>s</s:mi></s:mrow><s:mi mathvariant="normal">Λ</s:mi></s:msubsup><s:mo stretchy="false">(</s:mo><s:mn>4338</s:mn><s:mo stretchy="false">)</s:mo><s:msup><s:mi>K</s:mi><s:mo>−</s:mo></s:msup></s:math> via the triangle loop mechanism. The branching fractions of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msubsup><z:mi mathvariant="normal">Ξ</z:mi><z:mi>b</z:mi><z:mo>−</z:mo></z:msubsup><z:mo stretchy="false">→</z:mo><z:msubsup><z:mi>P</z:mi><z:mrow><z:mi>ψ</z:mi><z:mi>s</z:mi></z:mrow><z:mi mathvariant="normal">Λ</z:mi></z:msubsup><z:mo stretchy="false">(</z:mo><z:mn>4338</z:mn><z:mo stretchy="false">)</z:mo><z:msup><z:mi>K</z:mi><z:mo>−</z:mo></z:msup></z:math> are in the order of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msup><gb:mn>10</gb:mn><gb:mrow><gb:mo>−</gb:mo><gb:mn>4</gb:mn></gb:mrow></gb:msup></gb:math>; the result is compared with our previous work of <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msubsup><ib:mi mathvariant="normal">Ξ</ib:mi><ib:mi>b</ib:mi><ib:mo>−</ib:mo></ib:msubsup><ib:mo stretchy="false">→</ib:mo><ib:msubsup><ib:mi>P</ib:mi><ib:mrow><ib:mi>ψ</ib:mi><ib:mi>s</ib:mi></ib:mrow><ib:mi mathvariant="normal">Λ</ib:mi></ib:msubsup><ib:mo stretchy="false">(</ib:mo><ib:mn>4459</ib:mn><ib:mo stretchy="false">)</ib:mo><ib:msup><ib:mi>K</ib:mi><ib:mo>−</ib:mo></ib:msup></ib:math>. We also predict the ratio of <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:msubsup><pb:mi>P</pb:mi><pb:mrow><pb:mi>ψ</pb:mi><pb:mi>s</pb:mi></pb:mrow><pb:mi mathvariant="normal">Λ</pb:mi></pb:msubsup><pb:mo stretchy="false">(</pb:mo><pb:mn>4459</pb:mn><pb:mo stretchy="false">)</pb:mo></pb:math> and <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msubsup><ub:mi>P</ub:mi><ub:mrow><ub:mi>ψ</ub:mi><ub:mi>s</ub:mi></ub:mrow><ub:mi mathvariant="normal">Λ</ub:mi></ub:msubsup><ub:mo stretchy="false">(</ub:mo><ub:mn>4338</ub:mn><ub:mo stretchy="false">)</ub:mo></ub:math> productions in the decay <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:msubsup><zb:mi mathvariant="normal">Ξ</zb:mi><zb:mi>b</zb:mi><zb:mo>−</zb:mo></zb:msubsup><zb:mo stretchy="false">→</zb:mo><zb:msubsup><zb:mi>P</zb:mi><zb:mrow><zb:mi>ψ</zb:mi><zb:mi>s</zb:mi></zb:mrow><zb:mi mathvariant="normal">Λ</zb:mi></zb:msubsup><zb:msup><zb:mi>K</zb:mi><zb:mo>−</zb:mo></zb:msup><zb:mo stretchy="false">→</zb:mo><zb:mi>J</zb:mi><zb:mo>/</zb:mo><zb:mi>ψ</zb:mi><zb:mi mathvariant="normal">Λ</zb:mi><zb:msup><zb:mi>K</zb:mi><zb:mo>−</zb:mo></zb:msup></zb:math>. The predicted branching fractions and their ratios could be tested experimentally, which may be helpful for understanding the molecular picture of <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:msubsup><gc:mi>P</gc:mi><gc:mrow><gc:mi>ψ</gc:mi><gc:mi>s</gc:mi></gc:mrow><gc:mi mathvariant="normal">Λ</gc:mi></gc:msubsup><gc:mo stretchy="false">(</gc:mo><gc:mn>4338</gc:mn><gc:mo stretchy="false">)</gc:mo></gc:math> as well as other hidden-charm pentaquark states with strangeness. Moreover, the experimental potential of observing <lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" display="inline"><lc:msubsup><lc:mi>P</lc:mi><lc:mrow><lc:mi>ψ</lc:mi><lc:mi>s</lc:mi></lc:mrow><lc:mi mathvariant="normal">Λ</lc:mi></lc:msubsup><lc:mo stretchy="false">(</lc:mo><lc:mn>4338</lc:mn><lc:mo stretchy="false">)</lc:mo></lc:math> in the <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:msubsup><qc:mi mathvariant="normal">Ξ</qc:mi><qc:mi>b</qc:mi><qc:mo>−</qc:mo></qc:msubsup><qc:mo stretchy="false">→</qc:mo><qc:msup><qc:mi>K</qc:mi><qc:mo>−</qc:mo></qc:msup><qc:mi>J</qc:mi><qc:mo>/</qc:mo><qc:mi>ψ</qc:mi><qc:mi mathvariant="normal">Λ</qc:mi></qc:math> is discussed. Published by the American Physical Society 2024

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