Four-quark Operators Relevant to B Meson Lifetimes from QCD Sum Rules

At the order of $1/m_b^3$, the B meson lifetimes are controlled by the hadronic matrix elements of some four-quark operators. The nonfactorizable magnitudes of these four-quark operator matrix elements are analyzed by QCD sum rules in the framework of heavy quark effective theory. The vacuum saturation for color-singlet four-quark operators is justified at hadronic scale, and the nonfactorizable effect is at a few percent level. However for color-octet four-quark operators, the vacuum saturation is violated sizably and the nonfactorizable effect cannot be neglected. The implication to the extraction of some of the parameters from B decays is discussed. The B meson lifetime ratio is predicted as $\tau(B^-)/\tau(B^0)=1.09\pm 0.02$. However, the experimental result of the lifetime ratio $\tau(\Lambda_b)/\tau(B^0)$ still cannot be explained.