Exploring bottom-charmed molecular tetraquarks with the complex scaling method

In this work, we adopt the one-boson exchange model to analyze the $D^{(*)}_{(s)}B^{(*)}_{(s)}$ interactions from a coupled-channel perspective. For the $I(J^{P})=1(1^{+})$ $DB^{*}/D^*B/D^*B^{*}$ system, employing the complex scaling method, we obtain a loosely bound state and two resonant states located below the $DB^{*}$, $D^*B$, and $D^*B^{*}$ thresholds, respectively. Assuming that the charmonium-like states $T_{c\bar{c}1}(3900)$ and $T_{c\bar{c}1}(4020)$, as well as the bottomonium-like states $T_{b\bar{b}1}(10610)$ and $T_{b\bar{b}1}(10650)$, are molecular states near their respective thresholds, we suggest that the predicted states in the $I(J^P)=1(1^+)$ $D^{(*)}_{(s)}B^{(*)}_{(s)}$ system could be their bottom-charmed analogues. In addition, we extend our analysis to other $D^{(*)}_{(s)}B^{(*)}_{(s)}$ combinations with various quantum numbers. Our results suggest that some exotic structures may exist in the bottom-charmed sector. Finally, we collect the possible decay channels for future experimental observations. The $B_c/B_c^*$ plus a light meson are the ideal final state to search for the bound states, while the $D_{(s)}^{(*)}B_{(s)}^{(*)}$ channels are suitable for the resonances. We highly recommend that the future experiments hunt for these bottom-charmed exotic particles.