Four-quark operators relevant to [Formula presented] meson lifetimes from QCD sum rules

At the order of (Formula presented), the (Formula presented) 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 the 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 so that the nonfactorizable effect cannot be neglected for the (Formula presented) meson lifetimes. The implication to the extraction of some of the parameters from (Formula presented) decays is discussed. The (Formula presented) meson lifetime ratio is predicted as (Formula presented). However, the experimental result of the lifetime ratio (Formula presented) still cannot be explained.