Lifetimes of doubly heavy baryons Bbb and Bbc

Lifetimes of the doubly heavy baryons Bbb and Bbc 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 τ(Ωbb−)∼τ(Ξbb−)>τ(Ξbb0). The Ξbb0 baryon is shortest-lived owing to the W-exchange contribution, while Ξbb− and Ωbb− have similar lifetimes as they both receive contributions from destructive Pauli interference. We find the lifetime ratio τ(Ξbb−)/τ(Ξbb0)=1.26. The large W-exchange contribution to Ξbc0 through the subprocess cd→us→cd and the sizable destructive Pauli interference contribution to Ξbc+ imply a substantial lifetime difference between Ξbc+ and Ξbc0. In the presence of subleading 1/mc and 1/mb corrections to the spectator effects, we find that τ(Ωbc0) becomes longest-lived. This is because Γ+int and Γsemi for Ωbc0 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 Γint+cs(Ωbc0), ΓintSL,cs(Ωbc0) be positive and Γint−cu(Ξbc+) be negative, we conjecture that 1.68×10−13s