New Predictions for the Lifetimes of Doubly Heavy Baryons and the $B_c$ Meson

Abstract

We present updated predictions for the lifetimes of all weakly decaying doubly heavy baryons, including $bb$, $cc$, and $bc$ baryons, as well as for the $B_c$ meson. The analysis includes NNLO corrections to the leading dimension-three contribution, NLO corrections to the chromomagnetic term, and the complete set of currently known NLO corrections to the dimension-six heavy-light quark spectator contributions, including penguin terms. We also compare the results in the $\overline{\rm MS}$, kinetic, and, where applicable, $\Upsilon$ mass schemes. For the $bc$ baryons, we present predictions for both possible ground-state diquark-spin assignments, $S_{bc}=0$ and $S_{bc}=1$. In the kinetic scheme we obtain the lifetime hierarchies $\tau(\Xi^0_{bb})<\tau(\Xi^-_{bb})\simeq\tau(\Omega^-_{bb})$, $\tau(\Xi^+_{cc})<\tau(\Omega^+_{cc})<\tau(\Xi^{++}_{cc})$, $\tau(\Xi^0_{bc})\lesssim\tau(\Omega^0_{bc})<\tau(\Xi^+_{bc})$ for $S_{bc}=0$, and $\tau(\Xi^{\prime\, 0}_{bc})<\tau(\Omega^{\prime\, 0}_{bc})<\tau(\Xi^{\prime\, +}_{bc})$ for $S_{bc}=1$. We also revisit the $B_c$ lifetime and discuss the impact of the newly included Darwin term.