Surveying the mass spectra and the electromagnetic properties of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi mathvariant="normal">Ξ</mml:mi><mml:mi>c</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>′</mml:mo><mml:mo>,</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:math> molecular pentaquarks

Abstract

Motivated by the 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>4459</a:mn><a:mo stretchy="false">)</a:mo><a:mo>/</a:mo><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> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>T</i:mi><i:mrow><i:mi>c</i:mi><i:mi>c</i:mi></i:mrow></i:msub><i:mo stretchy="false">(</i:mo><i:mn>3875</i:mn><i:msup><i:mo stretchy="false">)</i:mo><i:mo>+</i:mo></i:msup></i:math> states as the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi mathvariant="normal">Ξ</m:mi><m:mi>c</m:mi></m:msub><m:msup><m:mover accent="true"><m:mi>D</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mo>*</m:mo></m:msup><m:mo>/</m:mo><m:msub><m:mi mathvariant="normal">Ξ</m:mi><m:mi>c</m:mi></m:msub><m:mover accent="true"><m:mi>D</m:mi><m:mo stretchy="false">¯</m:mo></m:mover></m:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>D</u:mi><u:msup><u:mi>D</u:mi><u:mo>*</u:mo></u:msup></u:math> molecular candidates, respectively, in this work we investigate 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:mrow><w:mo stretchy="false">(</w:mo><w:mo>′</w:mo><w:mo>,</w:mo><w:mo>*</w:mo><w:mo stretchy="false">)</w:mo></w:mrow></w:msubsup><w:msup><w:mi>D</w:mi><w:mrow><w:mo stretchy="false">(</w:mo><w:mo>*</w:mo><w:mo stretchy="false">)</w:mo></w:mrow></w:msup></w:math> molecular systems. We obtain the mass spectra and the corresponding spatial wave functions of the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msubsup><db:mi mathvariant="normal">Ξ</db:mi><db:mi>c</db:mi><db:mrow><db:mo stretchy="false">(</db:mo><db:mo>′</db:mo><db:mo>,</db:mo><db:mo>*</db:mo><db:mo stretchy="false">)</db:mo></db:mrow></db:msubsup><db:msup><db:mi>D</db:mi><db:mrow><db:mo stretchy="false">(</db:mo><db:mo>*</db:mo><db:mo stretchy="false">)</db:mo></db:mrow></db:msup></db:math>-type double-charm molecular pentaquark candidates with single strangeness, where we utilize the one-boson-exchange model and take into account both the <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mrow><kb:mi>S</kb:mi><kb:mtext>−</kb:mtext><kb:mi>D</kb:mi></kb:mrow></kb:math> wave-mixing effect and the coupled-channel effect. Our results show that the most promising candidates of the double-charm molecular pentaquarks with single strangeness include the <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi mathvariant="normal">Ξ</mb:mi><mb:mi>c</mb:mi></mb:msub><mb:mi>D</mb:mi></mb:math> state with <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:mi>I</pb:mi><pb:mo stretchy="false">(</pb:mo><pb:msup><pb:mi>J</pb:mi><pb:mi>P</pb:mi></pb:msup><pb:mo stretchy="false">)</pb:mo><pb:mo>=</pb:mo><pb:mn>0</pb:mn><pb:mo stretchy="false">(</pb:mo><pb:mn>1</pb:mn><pb:mo>/</pb:mo><pb:msup><pb:mn>2</pb:mn><pb:mo>−</pb:mo></pb:msup><pb:mo stretchy="false">)</pb:mo></pb:math>, the <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:msubsup><vb:mi mathvariant="normal">Ξ</vb:mi><vb:mi>c</vb:mi><vb:mo>′</vb:mo></vb:msubsup><vb:mi>D</vb:mi></vb:math> state with <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mi>I</yb:mi><yb:mo stretchy="false">(</yb:mo><yb:msup><yb:mi>J</yb:mi><yb:mi>P</yb:mi></yb:msup><yb:mo stretchy="false">)</yb:mo><yb:mo>=</yb:mo><yb:mn>0</yb:mn><yb:mo stretchy="false">(</yb:mo><yb:mn>1</yb:mn><yb:mo>/</yb:mo><yb:msup><yb:mn>2</yb:mn><yb:mo>−</yb:mo></yb:msup><yb:mo stretchy="false">)</yb:mo></yb:math>, the <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:msub><ec:mi mathvariant="normal">Ξ</ec:mi><ec:mi>c</ec:mi></ec:msub><ec:msup><ec:mi>D</ec:mi><ec:mo>*</ec:mo></ec:msup></ec:math> states with <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"><hc:mi>I</hc:mi><hc:mo stretchy="false">(</hc:mo><hc:msup><hc:mi>J</hc:mi><hc:mi>P</hc:mi></hc:msup><hc:mo stretchy="false">)</hc:mo><hc:mo>=</hc:mo><hc:mn>0</hc:mn><hc:mo stretchy="false">(</hc:mo><hc:mn>1</hc:mn><hc:mo>/</hc:mo><hc:msup><hc:mn>2</hc:mn><hc:mo>−</hc:mo></hc:msup><hc:mo>,</hc:mo><hc:mn>3</hc:mn><hc:mo>/</hc:mo><hc:msup><hc:mn>2</hc:mn><hc:mo>−</hc:mo></hc:msup><hc:mo stretchy="false">)</hc:mo></hc:math>, the <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:msubsup><nc:mi mathvariant="normal">Ξ</nc:mi><nc:mi>c</nc:mi><nc:mo>*</nc:mo></nc:msubsup><nc:mi>D</nc:mi></nc:math> state with <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:mi>I</qc:mi><qc:mo stretchy="false">(</qc:mo><qc:msup><qc:mi>J</qc:mi><qc:mi>P</qc:mi></qc:msup><qc:mo stretchy="false">)</qc:mo><qc:mo>=</qc:mo><qc:mn>0</qc:mn><qc:mo stretchy="false">(</qc:mo><qc:mn>3</qc:mn><qc:mo>/</qc:mo><qc:msup><qc:mn>2</qc:mn><qc:mo>−</qc:mo></qc:msup><qc:mo stretchy="false">)</qc:mo></qc:math>, the <wc:math xmlns:wc="http://www.w3.org/1998/Math/MathML" display="inline"><wc:msubsup><wc:mi mathvariant="normal">Ξ</wc:mi><wc:mi>c</wc:mi><wc:mo>′</wc:mo></wc:msubsup><wc:msup><wc:mi>D</wc:mi><wc:mo>*</wc:mo></wc:msup></wc:math> states with <zc:math xmlns:zc="http://www.w3.org/1998/Math/MathML" display="inline"><zc:mi>I</zc:mi><zc:mo stretchy="false">(</zc:mo><zc:msup><zc:mi>J</zc:mi><zc:mi>P</zc:mi></zc:msup><zc:mo stretchy="false">)</zc:mo><zc:mo>=</zc:mo><zc:mn>0</zc:mn><zc:mo stretchy="false">(</zc:mo><zc:mn>1</zc:mn><zc:mo>/</zc:mo><zc:msup><zc:mn>2</zc:mn><zc:mo>−</zc:mo></zc:msup><zc:mo>,</zc:mo><zc:mn>3</zc:mn><zc:mo>/</zc:mo><zc:msup><zc:mn>2</zc:mn><zc:mo>−</zc:mo></zc:msup><zc:mo stretchy="false">)</zc:mo></zc:math>, and the <fd:math xmlns:fd="http://www.w3.org/1998/Math/MathML" display="inline"><fd:msubsup><fd:mi mathvariant="normal">Ξ</fd:mi><fd:mi>c</fd:mi><fd:mo>*</fd:mo></fd:msubsup><fd:msup><fd:mi>D</fd:mi><fd:mo>*</fd:mo></fd:msup></fd:math> states with <id:math xmlns:id="http://www.w3.org/1998/Math/MathML" display="inline"><id:mi>I</id:mi><id:mo stretchy="false">(</id:mo><id:msup><id:mi>J</id:mi><id:mi>P</id:mi></id:msup><id:mo stretchy="false">)</id:mo><id:mo>=</id:mo><id:mn>0</id:mn><id:mo stretchy="false">(</id:mo><id:mn>1</id:mn><id:mo>/</id:mo><id:msup><id:mn>2</id:mn><id:mo>−</id:mo></id:msup><id:mo>,</id:mo><id:mn>3</id:mn><id:mo>/</id:mo><id:msup><id:mn>2</id:mn><id:mo>−</id:mo></id:msup><id:mo>,</id:mo><id:mn>5</id:mn><id:mo>/</id:mo><id:msup><id:mn>2</id:mn><id:mo>−</id:mo></id:msup><id:mo stretchy="false">)</id:mo></id:math>. To gain further insight into the inner structures and the properties of the isoscalar <od:math xmlns:od="http://www.w3.org/1998/Math/MathML" display="inline"><od:msubsup><od:mi mathvariant="normal">Ξ</od:mi><od:mi>c</od:mi><od:mrow><od:mo stretchy="false">(</od:mo><od:mo>′</od:mo><od:mo>,</od:mo><od:mo>*</od:mo><od:mo stretchy="false">)</od:mo></od:mrow></od:msubsup><od:msup><od:mi>D</od:mi><od:mrow><od:mo stretchy="false">(</od:mo><od:mo>*</od:mo><od:mo stretchy="false">)</od:mo></od:mrow></od:msup></od:math> molecular candidates, we utilize the constituent quark model to analyze their M1 radiative decay behaviors and magnetic moments based on the obtained mass spectra and spatial wave functions, which can offer significant information to determine their spin-parity quantum numbers and configurations in the forthcoming experiments. We suggest that our experimental colleagues search for the predicted <vd:math xmlns:vd="http://www.w3.org/1998/Math/MathML" display="inline"><vd:msubsup><vd:mi mathvariant="normal">Ξ</vd:mi><vd:mi>c</vd:mi><vd:mrow><vd:mo stretchy="false">(</vd:mo><vd:mo>′</vd:mo><vd:mo>,</vd:mo><vd:mo>*</vd:mo><vd:mo stretchy="false">)</vd:mo></vd:mrow></vd:msubsup><vd:msup><vd:mi>D</vd:mi><vd:mrow><vd:mo stretchy="false">(</vd:mo><vd:mo>*</vd:mo><vd:mo stretchy="false">)</vd:mo></vd:mrow></vd:msup></vd:math> molecular states. Published by the American Physical Society 2024

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