# Lifetimes of doubly heavy baryons ${B}_{bb}$ and ${B}_{bc}$

Cheng, Hai-Yang (Institute of Physics, Academia Sinica, Taipei, Taiwan 115, Republic of China) ; Xu, Fanrong (Department of Physics, Jinan University, Guangzhou 510632, People’s Republic of China)

16 April 2019

Abstract: Lifetimes of the doubly heavy baryons ${B}_{bb}$ and ${B}_{bc}$ 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 $\tau \left({\Omega }_{bb}^{-}\right)\sim \tau \left({\Xi }_{bb}^{-}\right)>\tau \left({\Xi }_{bb}^{0}\right)$. 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 $\tau \left({\Xi }_{bb}^{-}\right)/\tau \left({\Xi }_{bb}^{0}\right)=1.26$. 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 $\tau \left({\Omega }_{bc}^{0}\right)$ 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 ${\Gamma }_{\mathrm{int}+}^{cs}\left({\Omega }_{bc}^{0}\right)$, ${\Gamma }_{\mathrm{int}}^{\mathrm{SL},cs}\left({\Omega }_{bc}^{0}\right)$ be positive and ${\Gamma }_{\mathrm{int}-}^{cu}\left({\Xi }_{bc}^{+}\right)$ be negative, we conjecture that $1.68×{10}^{-13}s<\tau \left({\Omega }_{bc}^{0}\right)<3.70×{10}^{-13}\text{}\text{}s$, $4.09×{10}^{-13}s<\tau \left({\Xi }_{bc}^{+}\right)<6.07×{10}^{-13}\text{}\text{}s$, and $0.93×{10}^{-13}s<\tau \left({\Xi }_{bc}^{0}\right)<\phantom{\rule{0ex}{0ex}}1.18×{10}^{-13}\text{}\text{}s$. Hence, the lifetime hierarchy of ${B}_{bc}$ baryons is expected to be $\tau \left({\Xi }_{bc}^{+}\right)>\tau \left({\Omega }_{bc}^{0}\right)>\tau \left({\Xi }_{bc}^{0}\right)$.

Published in: Physical Review D 99 (2019)