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

Abstract

$T_{cc}^{+}$ is an isoscalar 4-quark state with mass lying barely below the $D^{\ast +}{D}^0$ threshold, and several times further below the $D^{\ast 0}{D}^{+}$ 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 $D^{\ast }D$ isospin channels and find that the influence of $D^{\ast +}{D}^0$ is larger than that of $D^{\ast 0}{D}^{+}$ 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.

Comments: 12 pages, 4 figures