Lifetimes of the doubly heavy baryons ${ \cal B}_{ bb}$ and ${ \cal B}_{ bc}$ 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 $\Gamma^{ \rm int}_+$ and $\Gamma^{ \rm semi}$ 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 $\Gamma^{ cs}_{ { \rm int+}}(\Omega_{ bc}^0)$, $\Gamma^{ { \rm SL},cs}_{ \rm int}(\Omega_{ bc}^0)$ be positive and $\Gamma^{ cu}_{ { \rm int-}}(\Xi^+_{ bc})$ 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 ${ \cal B}_{ bc}$ baryons is expected to be the pattern $\tau(\Xi_{ bc}^{ +})>\tau(\Omega_{ bc}^0)>\tau(\Xi_{ bc}^0)$.
Categories: hep-ph hep-ex