Predicting $B^{(\ast )}\bar{D}{}^{(\ast )}$ 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 $m_{\pi }\simeq 220$ 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 $B^{(\ast )}\bar{D}{}^{(\ast )}$ molecular states with quantum numbers $J^P=0^{+}$, $1^{+}$, and $2^{+}$. The predicted $J^P=0^{+}$ and $1^{+}$ $B\bar{D}$ and $B^{\ast }\bar{D}$ 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 $B^{\ast }\bar{D}{}^{\ast }$ and $B\bar{D}{}^{\ast }$ hadronic molecules, respectively. We also predict two previously unreported $B^{\ast }\bar{D}{}^{\ast }$ 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 $B^{(\ast )}\bar{D}{}^{(\ast )}$ systems.

arXiv comment24 pages, 3 figures