Beauty hadron lifetime ratios and the problem of $\tau(\Lambda_b)$

We describe a theoretical approach to compute inclusive widths of heavy hadrons, based on a systematic expansion in the inverse powers of the heavy quark mass. The method reproduces quite well the experimental ratios of $B$ mesons lifetimes. As for $\tau(\Lambda_b)/\tau(B_d)$, we present a QCD sum rule calculation of the $O(m_b^{-3})$ contribution to $\tau(\Lambda_b)$; we conclude that such correction is not responsible of the small experimental value of $\tau(\Lambda_b)/\tau(B_d)$.