A note on spectator effects and quark-hadron duality in inclusive beauty decays

In this paper, we evaluate the expectation values of four-quark operators for the inclusive beauty decays from the differences in the inclusive total decay rates, assuming that the heavy quark expansion converges at O(1/m3). The obtained expectation values yields the ratio τ(Λb)/τ(B) close to the experimental one. We further point out that the quark-hadron duality violation would be rather small allowing predictions of inclusive quantities.