Spectator effects and quark-hadron duality in inclusive beauty decays

The two important issues concerning the theory of inclusive decays are studied: (1) evaluation of expectation values of four-quark operators in order to systematically include the spectator effects and (2) estimation of duality breaking corrections in heavy quark expansion. Our study leads to the theoretical prediction of the ratio of lifetimes of $\Lambda_b$ and $B$ close to the experimental one and the duality breaking corrections of about 10% of the leading decay rate.