Probing exotic JPC resonances from deeply bound charmoniumlike molecules: Insights for identifying exotic hadrons

We investigate the resonance phenomenon in deeply bound charmoniumlike states. By interpreting the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Y</a:mi><a:mo stretchy="false">(</a:mo><a:mn>4220</a:mn><a:mo stretchy="false">)</a:mo></a:math>, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>Y</e:mi><e:mo stretchy="false">(</e:mo><e:mn>4360</e:mn><e:mo stretchy="false">)</e:mo></e:math>, and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>ψ</i:mi><i:mo stretchy="false">(</i:mo><i:mn>4415</i:mn><i:mo stretchy="false">)</i:mo></i:math> states as deeply <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>S</m:mi></m:math>-wave bound <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>D</o:mi><o:msub><o:mover accent="true"><o:mi>D</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mn>1</o:mn></o:msub></o:math>, <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>D</s:mi><s:mo>*</s:mo></s:msup><s:msub><s:mover accent="true"><s:mi>D</s:mi><s:mo stretchy="false">¯</s:mo></s:mover><s:mn>1</s:mn></s:msub></s:math>, and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msup><w:mi>D</w:mi><w:mo>*</w:mo></w:msup><w:msubsup><w:mover accent="true"><w:mi>D</w:mi><w:mo stretchy="false">¯</w:mo></w:mover><w:mn>2</w:mn><w:mo>*</w:mo></w:msubsup></w:math> molecules, respectively, we robustly predict the existence of 4 <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mrow><ab:mi>S</ab:mi></ab:mrow></ab:math>-wave deeply bound <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>C</cb:mi></cb:math>-parity partner states and 13 <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mrow><eb:mi>P</eb:mi></eb:mrow></eb:math>-wave charmoniumlike molecular resonances. These states, formed by exchanging the light mesons and pinpointed through the complex scaling method, include 3 <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mrow><gb:mi>S</gb:mi></gb:mrow></gb:math>-wave bound states with exotic quantum numbers <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>I</ib:mi><ib:mo stretchy="false">(</ib:mo><ib:msup><ib:mi>J</ib:mi><ib:mrow><ib:mi>P</ib:mi><ib:mi>C</ib:mi></ib:mrow></ib:msup><ib:mo stretchy="false">)</ib:mo><ib:mo>=</ib:mo><ib:mn>0</ib:mn><ib:mo stretchy="false">(</ib:mo><ib:msup><ib:mn>1</ib:mn><ib:mrow><ib:mo>−</ib:mo><ib:mo>+</ib:mo></ib:mrow></ib:msup><ib:mo stretchy="false">)</ib:mo></ib:math> and 5 <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mrow><ob:mi>P</ob:mi></ob:mrow></ob:math>-wave resonances with exotic <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>0</qb:mn><qb:mrow><qb:mo>−</qb:mo><qb:mo>+</qb:mo></qb:mrow></qb:msup><qb:mo stretchy="false">)</qb:mo></qb:math> and <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:mrow><ub:mo>+</ub:mo><ub:mo>−</ub:mo></ub:mrow></ub:msup><ub:mo stretchy="false">)</ub:mo></ub:math>. We expect future experiments to search for such exotic molecular resonances, which will not only enrich the ongoing construction of “Particle Zoo 2.0” but also help to scrutinize the hadronic molecular assignments of the <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mi>Y</yb:mi></yb:math>- family particles including the <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mi>Y</ac:mi><ac:mo stretchy="false">(</ac:mo><ac:mn>4220</ac:mn><ac:mo stretchy="false">)</ac:mo></ac:math>, <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:mi>Y</ec:mi><ec:mo stretchy="false">(</ec:mo><ec:mn>4360</ec:mn><ec:mo stretchy="false">)</ec:mo></ec:math>, and <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:mi>ψ</ic:mi><ic:mo stretchy="false">(</ic:mo><ic:mn>4415</ic:mn><ic:mo stretchy="false">)</ic:mo></ic:math> states. Published by the American Physical Society 2024