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Home > Physical Review D (APS) > Lifetimes of doubly heavy baryons <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub></mrow></math> and <math><msub><mi>B</mi><mrow><mi>b</mi><mi>c</mi></mrow></msub></math> |

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 $1.68\times {10}^{-13}s<\tau \left({\Omega}_{bc}^{0}\right)<3.70\times {10}^{-13}\text{}\text{}s$, $4.09\times {10}^{-13}s<\tau \left({\Xi}_{bc}^{+}\right)<6.07\times {10}^{-13}\text{}\text{}s$, and $0.93\times {10}^{-13}s<\tau \left({\Xi}_{bc}^{0}\right)<\phantom{\rule{0ex}{0ex}}1.18\times {10}^{-13}\text{}\text{}s$. 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)**
**Published by: **APS

**DOI: **10.1103/PhysRevD.99.073006

**License: **CC-BY-4.0