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

Abstract

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 that the nonfactorizable effect cannot be neglected for the B meson lifetimes. 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.