Systematic Study of Coupled-Channel Dynamics in Doubly Heavy Hadronic Molecules

Abstract

Heavy Quark Spin Symmetry (HQSS) is widely use to predict heavy molecules by extending the effective interactions fitted from low-lying states to heavier sectors. In this work, we systematically investigate the reliability of this approach for higher double heavy tetraquarks by comparing a single-channel effective interaction (Scheme I) with an explicit coupled-channel dynamics framework (Scheme II). The interactions are obtained within one-boson-exchange potential model and fixed by fitting the $T_{cc}^{+}$ lineshape. Utilizing the complex scaling method and $T$-matrix pole analysis, we extract the possible poles in the $S$-wave $D^{(\ast )}{D}^{(\ast )}$, ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ and $D^{(\ast )}{\bar{B}}^{(\ast )}$ systems with $J^P=1^{+}$. We find that both schemes provide consistent descriptions of the lowest-lying state. This confirms isoscalar-dominated $T_{cc}$ as a predominant $D{D}^{\ast }$ molecule (binding energy $\sim$ 381 keV), and predicts an isoscalar deeply bound $T_{bb}$ state ($40-60$ MeV) and an isovector $T_{bb}^{\prime }$ resonance in the bottom sector, together with a virtual $T_{bc}$ state. In contrast, significant differences emerge for higher-lying states. The inclusion of explicit coupled-channel dynamics modifies the effective interaction and reshapes the pole structure. The states predicted as bound or resonant in the single-channel framework can be shifted far from the physical region or disappear. These results indicate that while single-channel descriptions are adequate for near-threshold states, an explicit treatment of coupled-channel dynamics is required for reliable predictions of excited doubly heavy tetraquarks.

30 pages, 7 figures, and 8 tables