$T_{bc\bar s}$ states in the process $\Upsilon \to D^{-} \bar B^{0} D_s^{+}$

We perform a theoretical study of the decay process $\Upsilon \to D^{-} \bar{B}^{0} D_s^{+}$ in search of the doubly heavy tetraquark states $T_{bc\bar{s}}$ with quark content $bc\bar{s}\bar{d}$. These $T_{bc\bar{s}}$ states are assumed to be dynamically generated molecular states from the S-wave interactions between $\bar{B}_s^{(*)0} D^{(*)+}$ and $\bar{B}^{(*)0} D_s^{(*)+}$ meson pairs. Based on the total angular momentum and the type of the constituent mesons (pseudoscalars $P$ or vectors $V$), they are labeled as $T_{bc\bar{s}}^{0, PP}$, $T_{bc\bar{s}}^{0, VV}$, and $T_{bc\bar{s}}^{2, VV}$, respectively. The $\bar{B}^{0} D_s^{+}$ invariant mass distribution for this decay is calculated using current algebra, incorporating contributions from $T_{bc\bar{s}}$ states arising from final-state interactions. Our results reveal a clear peak structure in the $7415 - 7425$ MeV region, which is attributed to the $T_{bc\bar{s}}^{2, VV}$ state. Additionally, a distinct dip structure appears near the $\bar{B}^{*0} D_s^{*+}$ threshold, characteristic of the $T_{bc\bar{s}}^{2, VV}$ as a hadronic molecular state. A near-threshold enhancement associated with the $T_{bc\bar{s}}^{0, PP}$ state and a dip arising from the $T_{bc\bar{s}}^{0,\,VV}$ state are also identified, though the manifestation of these features depends sensitively on model parameter fine-tuning. Therefore, with increased experimental statistics, the decay channel $\Upsilon \to D^{-} \bar{B}^{0} D_s^{+}$ offers a promising avenue for discovering and characterizing the $T_{bc\bar{s}}$ states.