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 $\ddot{I}„(\hat{I}{\text{c◯}}_{bb}^{-})\sim \ddot{I}„(\hat{I}{ž}_{bb}^{-})>\ddot{I}„(\hat{I}{ž}_{bb}^0)$. The $\hat{I}{ž}_{bb}^0$ baryon is shortest-lived owing to the $W$-exchange contribution, while $\hat{I}{ž}_{bb}^{-}$ and $\hat{I}{\text{c◯}}_{bb}^{-}$ have similar lifetimes as they both receive contributions from destructive Pauli interference. We find the lifetime ratio $\ddot{I}„(\hat{I}{ž}_{bb}^{-})/\ddot{I}„(\hat{I}{ž}_{bb}^0)=1.26$\,. The large $W$-exchange contribution to $\hat{I}{ž}_{bc}^0$ through the subprocess $cd\to us\to cd$ and the sizable destructive Pauli interference contribution to $\hat{I}{ž}_{bc}^{+}$ imply a substantial lifetime difference between $\hat{I}{ž}_{bc}^{+}$ and $\hat{I}{ž}_{bc}^0$. In the presence of subleading $1/m_c$ and $1/m_b$ corrections to the spectator effects, we find that $\ddot{I}„(\hat{I}{\text{c◯}}_{bc}^0)$ becomes longest-lived. This is because $\hat{I}{“}_{+}^{\mathrm{int}}$ and $\hat{I}{“}^{\mathrm{semi}}$ for $\hat{I}{\text{c◯}}_{bc}^0$ 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 $\hat{I}{“}_{\mathrm{int}+}^{cs}(\hat{I}{\text{c◯}}_{bc}^0)$, $\hat{I}{“}_{\mathrm{int}}^{\mathrm{SL},cs}(\hat{I}{\text{c◯}}_{bc}^0)$ be positive and $\hat{I}{“}_{\mathrm{int}-}^{cu}(\hat{I}{ž}_{bc}^{+})$ be negative, we conjecture that $1.68\times 10^{-13}s<\ddot{I}„(\hat{I}{\text{c◯}}_{bc}^0)<3.70\times 10^{-13}s$ , $4.09\times 10^{-13}s<\ddot{I}„(\hat{I}{ž}_{bc}^{+})<6.07\times 10^{-13}s$ and $0.93\times 10^{-13}s<\ddot{I}„(\hat{I}{ž}_{bc}^0)<1.18\times 10^{-13}s$. Hence, the lifetime hierarchy of ${\mathcal{B}}_{bc}$ baryons is expected to be the pattern $\ddot{I}„(\hat{I}{ž}_{bc}^{+})>\ddot{I}„(\hat{I}{\text{c◯}}_{bc}^0)>\ddot{I}„(\hat{I}{ž}_{bc}^0)$.

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