Predicting possible molecular states of nucleons with Ξc,Ξc* , and <mml:math xmlns:mml="http://…

In the framework of a one-boson-exchange model, we carry out a comprehensive investigation of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="normal">Ξ</a:mi><a:mi>c</a:mi></a:msub><a:mi>N</a:mi><a:mo>/</a:mo><a:msub><a:mi mathvariant="normal">Λ</a:mi><a:mi>c</a:mi></a:msub><a:mi mathvariant="normal">Σ</a:mi><a:mo>/</a:mo><a:msubsup><a:mi mathvariant="normal">Ξ</a:mi><a:mi>c</a:mi><a:mo>′</a:mo></a:msubsup><a:mi>N</a:mi><a:mo>/</a:mo><a:msub><a:mi mathvariant="normal">Σ</a:mi><a:mi>c</a:mi></a:msub><a:mi mathvariant="normal">Λ</a:mi><a:mo>/</a:mo><a:msubsup><a:mi mathvariant="normal">Ξ</a:mi><a:mi>c</a:mi><a:mo>*</a:mo></a:msubsup><a:mi>N</a:mi><a:mo>/</a:mo><a:msubsup><a:mi mathvariant="normal">Σ</a:mi><a:mi>c</a:mi><a:mo>*</a:mo></a:msubsup><a:mi mathvariant="normal">Λ</a:mi><a:mo>/</a:mo><a:msub><a:mi mathvariant="normal">Σ</a:mi><a:mi>c</a:mi></a:msub><a:mi mathvariant="normal">Σ</a:mi><a:mo>/</a:mo><a:msubsup><a:mi mathvariant="normal">Σ</a:mi><a:mi>c</a:mi><a:mo>*</a:mo></a:msubsup><a:mi mathvariant="normal">Σ</a:mi></a:math> interactions. We consider the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:mi>S</p:mi><p:mtext>−</p:mtext><p:mi>D</p:mi></p:mrow></p:math>-wave mixing effects and the coupled-channel effects to derive the relevant effective potentials. Our results can predict several possible charm-strange deuteronlike <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msubsup><r:mi mathvariant="normal">Ξ</r:mi><r:mi>c</r:mi><r:mrow><r:msup><r:mo stretchy="false">(</r:mo><r:mo>′</r:mo></r:msup><r:mo>,</r:mo><r:mo>*</r:mo><r:mo stretchy="false">)</r:mo></r:mrow></r:msubsup><r:mi>N</r:mi></r:math> hexaquarks, the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msubsup><w:mi mathvariant="normal">Ξ</w:mi><w:mi>c</w:mi><w:mo>′</w:mo></w:msubsup><w:mi>N</w:mi></w:math> molecules with <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>I</z:mi><z:mo stretchy="false">(</z:mo><z:msup><z:mi>I</z:mi><z:mi>P</z:mi></z:msup><z:mo stretchy="false">)</z:mo><z:mo>=</z:mo><z:mn>0</z:mn><z:mo stretchy="false">(</z:mo><z:msup><z:mn>0</z:mn><z:mo>+</z:mo></z:msup><z:mo stretchy="false">)</z:mo></z:math>, <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mn>0</fb:mn><fb:mo stretchy="false">(</fb:mo><fb:msup><fb:mn>1</fb:mn><fb:mo>+</fb:mo></fb:msup><fb:mo stretchy="false">)</fb:mo></fb:math>, <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mn>1</jb:mn><jb:mo stretchy="false">(</jb:mo><jb:msup><jb:mn>1</jb:mn><jb:mo>+</jb:mo></jb:msup><jb:mo stretchy="false">)</jb:mo></jb:math>, the <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:msubsup><nb:mi mathvariant="normal">Ξ</nb:mi><nb:mi>c</nb:mi><nb:mo>*</nb:mo></nb:msubsup><nb:mi>N</nb:mi></nb:math> molecules with <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mn>0</qb:mn><qb:mo stretchy="false">(</qb:mo><qb:msup><qb:mn>1</qb:mn><qb:mo>+</qb:mo></qb:msup><qb:mo stretchy="false">)</qb:mo></qb:math>, <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mn>0</ub:mn><ub:mo stretchy="false">(</ub:mo><ub:msup><ub:mn>2</ub:mn><ub:mo>+</ub:mo></ub:msup><ub:mo stretchy="false">)</ub:mo></ub:math>, <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mn>1</yb:mn><yb:mo stretchy="false">(</yb:mo><yb:msup><yb:mn>2</yb:mn><yb:mo>+</yb:mo></yb:msup><yb:mo stretchy="false">)</yb:mo></yb:math>, and the coupled <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:msub><cc:mi mathvariant="normal">Ξ</cc:mi><cc:mi>c</cc:mi></cc:msub><cc:mi>N</cc:mi><cc:mo>/</cc:mo><cc:msubsup><cc:mi mathvariant="normal">Ξ</cc:mi><cc:mi>c</cc:mi><cc:mo>′</cc:mo></cc:msubsup><cc:mi>N</cc:mi><cc:mo>/</cc:mo><cc:msubsup><cc:mi mathvariant="normal">Ξ</cc:mi><cc:mi>c</cc:mi><cc:mo>*</cc:mo></cc:msubsup><cc:mi>N</cc:mi><cc:mo>/</cc:mo><cc:msub><cc:mi mathvariant="normal">Σ</cc:mi><cc:mi>c</cc:mi></cc:msub><cc:mi mathvariant="normal">Σ</cc:mi><cc:mo>/</cc:mo><cc:msubsup><cc:mi mathvariant="normal">Σ</cc:mi><cc:mi>c</cc:mi><cc:mo>*</cc:mo></cc:msubsup><cc:mi mathvariant="normal">Σ</cc:mi></cc:math> molecule with <lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" display="inline"><lc:mn>0</lc:mn><lc:mo stretchy="false">(</lc:mo><lc:msup><lc:mn>1</lc:mn><lc:mo>+</lc:mo></lc:msup><lc:mo stretchy="false">)</lc:mo></lc:math>. We expect the experiments to search for our predictions of the <pc:math xmlns:pc="http://www.w3.org/1998/Math/MathML" display="inline"><pc:msubsup><pc:mi mathvariant="normal">Ξ</pc:mi><pc:mi>c</pc:mi><pc:mrow><pc:mo stretchy="false">(</pc:mo><pc:mo>′</pc:mo><pc:mo>,</pc:mo><pc:mo>*</pc:mo><pc:mo stretchy="false">)</pc:mo></pc:mrow></pc:msubsup><pc:mi>N</pc:mi></pc:math> bound states. Published by the American Physical Society 2024