Meson-meson molecular binding potentials in the diabatic dynamical diquark model

Using the diabatic formalism, a rigorous generalization of the Born-Oppenheimer approximation, we study the effects of introducing simple meson-meson molecular potentials to an established diquark model for tetraquark states, and calculate mixed bound states composed of both diquark-antidiquark and meson-meson molecular components. We examine the behavior of properties of the states as one varies the parameters of the dimeson potential, and find that significant regions of parameter space occur in which one may produce mass eigenstates exactly matching the specific examples of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>χ</a:mi><a:mrow><a:mi>c</a:mi><a:mn>1</a:mn></a:mrow></a:msub><a:mo stretchy="false">(</a:mo><a:mn>3872</a:mn><a:mo stretchy="false">)</a:mo></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>χ</e:mi><e:mrow><e:mi>c</e:mi><e:mn>0</e:mn></e:mrow></e:msub><e:mo stretchy="false">(</e:mo><e:mn>3915</e:mn><e:mo stretchy="false">)</e:mo></e:math>. We also find regions in which a pure dimeson molecular state emerges, and study the same state properties in such cases.