Spin dependence of meson thresholds in the diabatic dynamical diquark model

The diabatic dynamical diquark model is designed to unify diquark and molecular approaches for exotic hadrons by including the effects of dimeson thresholds on fundamental diquark-antidiquark states in order to form physical tetraquarks. We generalize this model by implementing the consequences of heavy-quark spin symmetry for each dimeson pair. We include the specific spin factors and mass differences associated with mesons related by this symmetry (such as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>D</a:mi> <a:mo>,</a:mo> <a:msup> <a:mi>D</a:mi> <a:mo>*</a:mo> </a:msup> </a:math> ), both features being necessary for the systematic incorporation of effects beyond the static, heavy-source limit inherent to the (adiabatic) Born-Oppenheimer treatment. We obtain explicit interaction potentials for all <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>J</c:mi> <c:mo>=</c:mo> <c:mn>0</c:mn> </c:math> , 1, 2 states, along the way deriving unusual variants of Fierz reordering identities, and discuss the application of the potentials to specific physical states such as <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>1</e:mn> </e:mrow> </e:msub> <e:mo stretchy="false">(</e:mo> <e:mn>3872</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:msub> <i:mi>T</i:mi> <i:mrow> <i:mi>c</i:mi> <i:mover accent="true"> <i:mi>c</i:mi> <i:mo stretchy="false">¯</i:mo> </i:mover> <i:mn>1</i:mn> </i:mrow> </i:msub> <i:mo stretchy="false">(</i:mo> <i:mn>3900</i:mn> <i:mo stretchy="false">)</i:mo> </i:math> .