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 $\overline{\mathrm{MS}}$, kinetic, and, where applicable, ${\rm Y}$ 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 $\tau ({\Xi }_{bb}^0)<\tau ({\Xi }_{bb}^{-})\simeq \tau ({\Omega }_{bb}^{-})$, $\tau ({\Xi }_{cc}^{+})<\tau ({\Omega }_{cc}^{+})<\tau ({\Xi }_{cc}^{++})$, $\tau ({\Xi }_{bc}^0)\lesssim \tau ({\Omega }_{bc}^0)<\tau ({\Xi }_{bc}^{+})$ for $S_{bc}=0$, and $\tau ({\Xi }_{bc}^{\prime 0})<\tau ({\Omega }_{bc}^{\prime 0})<\tau ({\Xi }_{bc}^{\prime +})$ for $S_{bc}=1$. We also revisit the $B_c$ lifetime and discuss the impact of the newly included Darwin term.

53 pages, 4 figures