$T_{cc}$ in the Diabatic Diquark Model: Effects of $D^*D$ Isospin

TL;DR

This paper investigates the structure of the $T_{cc}^+$ tetraquark using a diabatic diquark model, analyzing the effects of $D^*D$ isospin channels and mixing, revealing a mixed molecular and diquark component.

Contribution

It introduces a diabatic generalization of the Born-Oppenheimer approximation to study $T_{cc}^+$, accounting for mixing of molecular and diquark states with threshold effects.

Findings

$T_{cc}^+$ contains about 10% diquark-antidiquark component.

The $D^{*+} D^0$ channel has a larger influence than $D^{*0} D^+$.

Results are sensitive to isospin breaking and mixing potential parameters.

Abstract

$T_{cc}^+$ is an isoscalar 4-quark state with mass lying barely below the $D^{*+} D^0$ threshold, and several times further below the $D^{*0} D^+$ threshold. It allows both di-meson molecular and elementary diquark-antidiquark $(cc)(\bar u \bar d)$ 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 $D^* \! D$ isospin channels and find that the influence of $D^{*+} D^0$ is larger than that of $D^{*0} D^+$ but not overwhelmingly so, and that $T_{cc}^+$ contains an $O(10\%)$ $(cc)(\bar u \bar d)$ component. We then explore the variation of these results if the isospin breaking between the di-meson thresholds is varied, and also the sensitivity of our results to variation of the mixing-potential parameters.