Coupled-channel description of charmed heavy hadronic molecules within the meson-exchange model and its implication

Abstract

Motivated by the first observation of the double-charm tetraquark <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msubsup><a:mrow><a:mi>T</a:mi></a:mrow><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow><a:mrow><a:mo>+</a:mo></a:mrow></a:msubsup><a:mo stretchy="false">(</a:mo><a:mn>3875</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math> by the LHCb Collaboration, we investigate the nature of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mi>T</e:mi><e:mrow><e:mi>c</e:mi><e:mi>c</e:mi></e:mrow><e:mo>+</e:mo></e:msubsup></e:math> as an isoscalar <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>D</g:mi><g:msup><g:mi>D</g:mi><g:mo>*</g:mo></g:msup></g:math> hadronic molecule in a meson-exchange potential model incorporated by the coupled-channel effects and three-body unitarity. The <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:msup><i:mrow><i:mi>D</i:mi></i:mrow><i:mrow><i:mn>0</i:mn></i:mrow></i:msup><i:msup><i:mrow><i:mi>D</i:mi></i:mrow><i:mrow><i:mn>0</i:mn></i:mrow></i:msup><i:msup><i:mrow><i:mi>π</i:mi></i:mrow><i:mrow><i:mo>+</i:mo></i:mrow></i:msup></i:mrow></i:math> invariant mass spectrum can be well-described and the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:msubsup><k:mrow><k:mi>T</k:mi></k:mrow><k:mrow><k:mi>c</k:mi><k:mi>c</k:mi></k:mrow><k:mrow><k:mo>+</k:mo></k:mrow></k:msubsup></k:mrow></k:math> pole structure can be precisely extracted. Under the hypothesis that the interactions between the heavy flavor hadrons can be saturated by the light meson-exchange potentials, the near-threshold dynamics of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msubsup><m:mi>T</m:mi><m:mrow><m:mi>c</m:mi><m:mi>c</m:mi></m:mrow><m:mo>+</m:mo></m:msubsup></m:math> can shed light on the binding of its heavy-quark spin symmetry (HQSS) partner <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:msup><o:mrow><o:mi>D</o:mi></o:mrow><o:mrow><o:mo>*</o:mo></o:mrow></o:msup><o:msup><o:mrow><o:mi>D</o:mi></o:mrow><o:mrow><o:mo>*</o:mo></o:mrow></o:msup></o:mrow></o:math> (<q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>I</q:mi><q:mo>=</q:mo><q:mn>0</q:mn></q:math>) and on the nature of other heavy hadronic molecule candidates such as <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>X</s:mi><s:mo stretchy="false">(</s:mo><s:mn>3872</s:mn><s:mo stretchy="false">)</s:mo></s:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>Z</w:mi><w:mi>c</w:mi></w:msub><w:mo stretchy="false">(</w:mo><w:mn>3900</w:mn><w:mo stretchy="false">)</w:mo></w:math> in the charmed-anticharmed systems. The latter states can be related to <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msubsup><ab:mi>T</ab:mi><ab:mrow><ab:mi>c</ab:mi><ab:mi>c</ab:mi></ab:mrow><ab:mo>+</ab:mo></ab:msubsup></ab:math> in the meson-exchange potential model with limited assumptions based on the SU(3) flavor symmetry relations. The combined analysis, on the one hand, indicates the HQSS breaking effects among those HQSS partners, and on the other hand, highlights the role played by the short and long-distance dynamics for the near threshold <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msup><cb:mi>D</cb:mi><cb:mrow><cb:mo stretchy="false">(</cb:mo><cb:mo>*</cb:mo><cb:mo stretchy="false">)</cb:mo></cb:mrow></cb:msup><cb:msup><cb:mi>D</cb:mi><cb:mrow><cb:mo stretchy="false">(</cb:mo><cb:mo>*</cb:mo><cb:mo stretchy="false">)</cb:mo></cb:mrow></cb:msup></cb:math> and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mrow><ib:msup><ib:mrow><ib:mi>D</ib:mi></ib:mrow><ib:mrow><ib:mo stretchy="false">(</ib:mo><ib:mo>*</ib:mo><ib:mo stretchy="false">)</ib:mo></ib:mrow></ib:msup><ib:msup><ib:mrow><ib:mrow><ib:mover accent="true"><ib:mrow><ib:mi>D</ib:mi></ib:mrow><ib:mrow><ib:mo stretchy="false">¯</ib:mo></ib:mrow></ib:mover></ib:mrow></ib:mrow><ib:mrow><ib:mo stretchy="false">(</ib:mo><ib:mo>*</ib:mo><ib:mo stretchy="false">)</ib:mo></ib:mrow></ib:msup><ib:mo>+</ib:mo><ib:mi mathvariant="normal">c</ib:mi><ib:mo>.</ib:mo><ib:mi mathvariant="normal">c</ib:mi><ib:mo>.</ib:mo></ib:mrow></ib:math> systems. Published by the American Physical Society 2024

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