Dynamical study of D*DK and D*DD¯</mml:…

Inspired by the recent report from the LHCb Collaboration on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>T</a:mi><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow></a:msub></a:math>, which can be interpreted as a molecular <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>D</c:mi><c:msup><c:mi>D</c:mi><c:mo>*</c:mo></c:msup></c:math>, we investigated two trimeson systems of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>T</e:mi><e:mrow><e:mi>c</e:mi><e:mi>c</e:mi></e:mrow></e:msub></e:math> partner with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>I</g:mi><g:msup><g:mi>J</g:mi><g:mi>P</g:mi></g:msup><g:mo>=</g:mo><g:mn>0</g:mn><g:msup><g:mn>1</g:mn><g:mo>−</g:mo></g:msup></g:math> in the framework of a chiral quark model. In the first case, because of the attraction between <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>D</i:mi><i:mo>*</i:mo></i:msup></i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mover accent="true"><k:mi>D</k:mi><k:mo stretchy="false">¯</k:mo></k:mover></k:math>, we explored the existence of bound states in the system <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>D</o:mi><o:mo>*</o:mo></o:msup><o:mi>D</o:mi><o:mover accent="true"><o:mi>D</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math>, which is obtained by adding <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mover accent="true"><s:mi>D</s:mi><s:mo stretchy="false">¯</s:mo></s:mover></s:math> into the molecular bound state <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>T</w:mi><w:mrow><w:mi>c</w:mi><w:mi>c</w:mi></w:mrow></w:msub></w:math> (<y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>D</y:mi><y:msup><y:mi>D</y:mi><y:mo>*</y:mo></y:msup></y:math>). Similarly, in the second case, we explored whether there is a bound state in the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msup><ab:mi>D</ab:mi><ab:mo>*</ab:mo></ab:msup><ab:mi>D</ab:mi><ab:mi>K</ab:mi></ab:math> system, which is obtained by adding <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>K</cb:mi></cb:math> into the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>T</eb:mi><eb:mrow><eb:mi>c</eb:mi><eb:mi>c</eb:mi></eb:mrow></eb:msub></eb:math>, given the attraction between <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>D</gb:mi></gb:math> and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>K</ib:mi></ib:math>. The results show that both of them are bound states, in which the binding energy of the molecular state <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>D</kb:mi><kb:msup><kb:mi>D</kb:mi><kb:mo>*</kb:mo></kb:msup><kb:mi>K</kb:mi></kb:math> is relatively small, only <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mn>0.4</mb:mn><mb:mo>±</mb:mo><mb:mn>0.4</mb:mn><mb:mtext> </mb:mtext><mb:mtext> </mb:mtext><mb:mi>MeV</mb:mi></mb:math>, while the binding energy of <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>D</ob:mi><ob:msup><ob:mi>D</ob:mi><ob:mo>*</ob:mo></ob:msup><ob:mover accent="true"><ob:mi>D</ob:mi><ob:mo stretchy="false">¯</ob:mo></ob:mover></ob:math> is up to <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mn>1.6</sb:mn><sb:mo>±</sb:mo><sb:mn>0.3</sb:mn><sb:mtext> </sb:mtext><sb:mtext> </sb:mtext><sb:mi>MeV</sb:mi></sb:math>. According to the calculation results of the root-square-mean distances, the spatial structure of the two systems shows the obvious <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mrow><ub:mo stretchy="false">(</ub:mo><ub:mi>D</ub:mi><ub:msup><ub:mrow><ub:mi>D</ub:mi></ub:mrow><ub:mrow><ub:mo>*</ub:mo></ub:mrow></ub:msup><ub:mo stretchy="false">)</ub:mo><ub:mtext>−</ub:mtext><ub:mo stretchy="false">(</ub:mo><ub:mover accent="true"><ub:mrow><ub:mi>D</ub:mi></ub:mrow><ub:mrow><ub:mo stretchy="false">¯</ub:mo></ub:mrow></ub:mover><ub:mo>/</ub:mo><ub:mi>K</ub:mi><ub:mo stretchy="false">)</ub:mo></ub:mrow></ub:math> structure, in which <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:mi>D</cc:mi></cc:math> is close to <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:msup><ec:mi>D</ec:mi><ec:mo>*</ec:mo></ec:msup></ec:math> while <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:mi>D</gc:mi><gc:msup><gc:mi>D</gc:mi><gc:mo>*</gc:mo></gc:msup></gc:math> as a whole is relatively distant from the third hadron (<ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:mover accent="true"><ic:mi>D</ic:mi><ic:mo stretchy="false">¯</ic:mo></ic:mover><ic:mo>/</ic:mo><ic:mi>K</ic:mi></ic:math>), which are similar to the nucleon-electron structure. As a result, we strongly recommend that these bound states <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"><mc:mi>D</mc:mi><mc:msup><mc:mi>D</mc:mi><mc:mo>*</mc:mo></mc:msup><mc:mover accent="true"><mc:mi>D</mc:mi><mc:mo stretchy="false">¯</mc:mo></mc:mover></mc:math> and <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:mi>D</qc:mi><qc:msup><qc:mi>D</qc:mi><qc:mo>*</qc:mo></qc:msup><qc:mi>K</qc:mi></qc:math> are searched for experimentally.