Spectator Effects in Inclusive Decays of Beauty Hadrons

Abstract

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 much larger than those of the factorizable ones, limiting considerably the usefulness of the vacuum insertion approximation. Non-factorizable contributions to the lifetime ratio $τ(B^-)/τ(B_d)$ could naturally be of order 10--20%, and not even the sign of these contributions can be predicted at present. In the case of the $Λ_b$ 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 $τ(Λ_b)/τ(B_d)$, it is necessary that these baryon matrix elements be much larger than those estimated in quark models. We have also reexamined the theoretical predictions for the semileptonic branching ratio of $B$ mesons and charm counting, finding that, given the present theoretical and experimental uncertainties, there is no significant discrepancy with experiment.