Spectator Effects in Inclusive Decays of Beauty Hadrons

We present a model-independent study of spectator effects, which are responsible for the lifetime differences between beauty hadrons. These effects can be parametrized in terms of hadronic matrix elements of four four-quark operators. For $B$ mesons, the coefficients of the non-factorizable operators turn out to be a factor 10--100 larger than those of the factorizable ones, and so the vacuum insertion approximation cannot be trusted. Theoretically, the deviation of $\tau(B^-)/\tau(B_d)$ from unity could be as large as 20\%, and even the sign of this deviation cannot be predicted at present. In the case of the $\Lambda_b$ baryon, heavy-quark symmetry is used to reduce the number of independent matrix elements from four to two. In order to explain the large deviation from unity in the experimental result for $\tau(\Lambda_b)/\tau(B_d)$, it is necessary that these baryon matrix elements be much larger than those estimated in quark models. We also study spectator effects in the semi-leptonic branching ratio of $B$ mesons and find that they could conceivably lower $B_{\rm SL}$ by up to 1\%.