Tcc in the diabatic diquark model: Effects of D*D isospin

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>T</a:mi><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow><a:mo>+</a:mo></a:msubsup></a:math> is an isoscalar 4-quark state with mass lying barely below the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>D</c:mi><c:mrow><c:mo>*</c:mo><c:mo>+</c:mo></c:mrow></c:msup><c:msup><c:mi>D</c:mi><c:mn>0</c:mn></c:msup></c:math> threshold, and several times further below the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>D</e:mi><e:mrow><e:mo>*</e:mo><e:mn>0</e:mn></e:mrow></e:msup><e:msup><e:mi>D</e:mi><e:mo>+</e:mo></e:msup></e:math> threshold. It allows both dimeson molecular and elementary diquark-antidiquark <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mo stretchy="false">(</g:mo><g:mi>c</g:mi><g:mi>c</g:mi><g:mo stretchy="false">)</g:mo><g:mo stretchy="false">(</g:mo><g:mover accent="true"><g:mi>u</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mover accent="true"><g:mi>d</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mo stretchy="false">)</g:mo></g:math> substructures. The diabatic generalization of the adiabatic approximation within the Born-Oppenheimer formalism rigorously incorporates the mixing of such elementary eigenstates with states corresponding to two-particle thresholds. We examine the separate influence of the two <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msup><q:mi>D</q:mi><q:mo>*</q:mo></q:msup><q:mi>D</q:mi></q:math> isospin channels and find that the influence of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>D</s:mi><s:mrow><s:mo>*</s:mo><s:mo>+</s:mo></s:mrow></s:msup><s:msup><s:mi>D</s:mi><s:mn>0</s:mn></s:msup></s:math> is larger than that of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msup><u:mi>D</u:mi><u:mrow><u:mo>*</u:mo><u:mn>0</u:mn></u:mrow></u:msup><u:msup><u:mi>D</u:mi><u:mo>+</u:mo></u:msup></u:math> but not overwhelmingly so, and that <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msubsup><w:mi>T</w:mi><w:mrow><w:mi>c</w:mi><w:mi>c</w:mi></w:mrow><w:mo>+</w:mo></w:msubsup></w:math> contains an <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>O</y:mi><y:mo stretchy="false">(</y:mo><y:mn>10</y:mn><y:mo>%</y:mo><y:mo stretchy="false">)</y:mo></y:math> <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mo stretchy="false">(</cb:mo><cb:mi>c</cb:mi><cb:mi>c</cb:mi><cb:mo stretchy="false">)</cb:mo><cb:mo stretchy="false">(</cb:mo><cb:mover accent="true"><cb:mi>u</cb:mi><cb:mo stretchy="false">¯</cb:mo></cb:mover><cb:mover accent="true"><cb:mi>d</cb:mi><cb:mo stretchy="false">¯</cb:mo></cb:mover><cb:mo stretchy="false">)</cb:mo></cb:math> component. We then explore the variation of these results if the isospin breaking between the dimeson thresholds is varied, and also the sensitivity of our results to variation of the mixing-potential parameters.