Study of doubly heavy baryon lifetimes

We study the lifetimes and inclusive semileptonic decay widths of doubly heavy baryons within the framework of heavy quark expansion. Our analysis includes next-to-leading-order corrections to the dimension-3, -5, and -6 operators, together with the leading dimension-7 contributions, while the nonperturbative matrix elements are evaluated in a bag model with translationally improved baryon wave functions. We obtain $( \tau_{\Xi_{cc}^{++}} , \tau_{\Xi_{cc}^{+}} , \tau_{\Omega_{cc}^{+}} ) = ( 2.67 \pm 0.94,\, 0.47 \pm 0.08,\, 1.79 \pm 0.62 ) \times 10^{-13}\,{\rm s}$ and $( \tau_{\Xi_{bb}^{0}} , \tau_{\Xi_{bb}^{-}} , \tau_{\Omega_{bb}^{-}} ) = ( 0.75 \pm 0.11,\, 0.92 \pm 0.15,\, 0.93 \pm 0.15 ) \times 10^{-12}\,{\rm s}$, where the uncertainties here arise from the heavy quark pole masses and the hadronic scale adopted in the quark model. Hence, the lifetime hierarchy patterns are $\tau(\Xi_{cc}^{++})>\tau(\Omega_{cc}^+)>\tau(\Xi_{cc}^+)$ and $\tau(\Omega_{bb}^{-})\sim\tau(\Xi_{bb}^-)>\tau(\Xi_{bb}^0)$ for doubly charmed and bottom baryons, respectively. The $W$-exchange contribution plays a crucial role in generating the large lifetime splitting in the doubly charmed sector and remains phenomenologically important for doubly bottom baryons. In addition to the total lifetimes, we calculate the separate nonleptonic and semileptonic contributions, which allow us to trace the pattern of spectator effects in each baryon channel. We also evaluate the inclusive semileptonic decay widths and the decay width asymmetries, which provide complementary probes of the underlying decay mechanisms.