Four-quark operators relevant toBmeson 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 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 $B$ 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 $\ensuremath{\tau}{(B}^{\ensuremath{-}})/\ensuremath{\tau}{(B}^{0})=1.09\ifmmode\pm\else\textpm\fi{}0.02$. However, the experimental result of the lifetime ratio $\ensuremath{\tau}({\ensuremath{\Lambda}}_{b})/\ensuremath{\tau}{(B}^{0})$ still cannot be explained.