Study of doubly heavy baryon lifetimes

Abstract

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 $({\tau }_{{\Xi }_{cc}^{++}},{\tau }_{{\Xi }_{cc}^{+}},{\tau }_{{\Omega }_{cc}^{+}})=(2.67_{-0.94}^{+0.95},0.47_{-0.08}^{+0.09},1.79_{-0.62}^{+0.64})\times 10^{-13}\mathrm{s}$ and $({\tau }_{{\Xi }_{bb}^0},{\tau }_{{\Xi }_{bb}^{-}},{\tau }_{{\Omega }_{bb}^{-}})=(0.75_{-0.11}^{+0.13},0.92_{-0.15}^{+0.15},0.93_{-0.15}^{+0.15})\times 10^{-12}\mathrm{s}$. The lifetime hierarchy patterns are found to be $\tau ({\Xi }_{cc}^{++})>\tau ({\Omega }_{cc}^{+})>\tau ({\Xi }_{cc}^{+})$ 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 particular, for ${\Xi }_{cc}^{+}$ the dominant dimension-6 spectator effect, namely $W$-exchange, surpasses the nominally leading term. The same spectator operator is realized as destructive Pauli interference in $D^{+}$, owing to the $d$ versus $\bar{d}$ spectator. Although the ${\Xi }_{cc}^{+}$ case does not lead to the negative decay width encountered for $D^{+}$, the absolute value of $\tau ({\Xi }_{cc}^{+})$ should nevertheless be regarded as only indicative. 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.

Comments: 20 pages plus references, 3 figures; accepted for publication in JHEP