Lifetimes of Doubly Heavy Baryons ${\mathcal{B}}_{bb}$ and ${\mathcal{B}}_{bc}$

Abstract

Lifetimes of the doubly heavy baryons ${\mathcal{B}}_{bb}$ and ${\mathcal{B}}_{bc}$ are analyzed within the framework of the heavy quark expansion (HQE). Lifetime differences arise from the spectator effects such as $W$-exchange and Pauli interference. For doubly bottom baryons, the lifetime pattern is $\tau ({\Omega }_{bb}^{-})\sim \tau ({\Xi }_{bb}^{-})>\tau ({\Xi }_{bb}^0)$. The ${\Xi }_{bb}^0$ baryon is shortest-lived owing to the $W$-exchange contribution, while ${\Xi }_{bb}^{-}$ and ${\Omega }_{bb}^{-}$ have similar lifetimes as they both receive contributions from destructive Pauli interference. We find the lifetime ratio $\tau ({\Xi }_{bb}^{-})/\tau ({\Xi }_{bb}^0)=1.26$\,. The large $W$-exchange contribution to ${\Xi }_{bc}^0$ through the subprocess $cd\to us\to cd$ and the sizable destructive Pauli interference contribution to ${\Xi }_{bc}^{+}$ imply a substantial lifetime difference between ${\Xi }_{bc}^{+}$ and ${\Xi }_{bc}^0$. In the presence of subleading $1/m_c$ and $1/m_b$ corrections to the spectator effects, we find that $\tau ({\Omega }_{bc}^0)$ becomes longest-lived. This is because ${\Gamma }_{+}^{\mathrm{int}}$ and ${\Gamma }^{\mathrm{semi}}$ for ${\Omega }_{bc}^0$ are subject to large cancellation between dimension-6 and -7 operators. This implies that the subleading corrections are too large to justify the validity of the HQE. Demanding that ${\Gamma }_{\mathrm{int}+}^{cs}({\Omega }_{bc}^0)$, ${\Gamma }_{\mathrm{int}}^{\mathrm{SL},cs}({\Omega }_{bc}^0)$ be positive and ${\Gamma }_{\mathrm{int}-}^{cu}({\Xi }_{bc}^{+})$ be negative, we conjecture that $1.68\times 10^{-13}s<\tau ({\Omega }_{bc}^0)<3.70\times 10^{-13}s$ , $4.09\times 10^{-13}s<\tau ({\Xi }_{bc}^{+})<6.07\times 10^{-13}s$ and $0.93\times 10^{-13}s<\tau ({\Xi }_{bc}^0)<1.18\times 10^{-13}s$. Hence, the lifetime hierarchy of ${\mathcal{B}}_{bc}$ baryons is expected to be the pattern $\tau ({\Xi }_{bc}^{+})>\tau ({\Omega }_{bc}^0)>\tau ({\Xi }_{bc}^0)$.

arXiv comment22 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1809.08102

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