Predicting $B^{(*)}\bar D{}^{(*)}$ states from a reanalysis of lattice QCD data

Abstract

We reanalyze the lattice QCD data for the isoscalar $\bar b\bar c ud$ systems with $J^P=0^+$ and $1^+$ at $m_π\simeq 220$ MeV, incorporating both short- and long-range interactions constrained by heavy-quark spin and chiral symmetries. Using the interaction fitted to the lattice results, we predict a spectrum of isoscalar $B^{(*)}\bar D{}^{(*)}$ molecular states with quantum numbers $J^P=0^+$, $1^+$, and $2^+$. The predicted $J^P=0^+$ and $1^+$ $B\bar D$ and $B^*\bar D$ bound states are consistent with the lattice results. Furthermore, the two resonances reported by the lattice collaboration in the $J^P=0^+$ and $1^+$ $\bar b\bar c ud$ channels can be naturally interpreted as $B^*\bar D{}^*$ and $B\bar D{}^*$ hadronic molecules, respectively. We also predict two previously unreported $B^*\bar D{}^*$ states with $J^P=1^+$ and $2^+$: a bound state and a shallow state whose pole may correspond to either a virtual state or a bound state, respectively. Our results provide a unified interpretation of the lattice spectrum and highlight the interplay between short- and long-range interactions in the dynamics of the $B^{(*)}\bar D{}^{(*)}$ systems.