Nonspectator Effects and B Meson Lifetimes from a Field-theoretic Calculation

Abstract

The B meson lifetime ratios are calculated to the order of $1/m_b^3$ in the heavy quark expansion. The predictions of those ratios are dependent on four unknown hadronic parameters $B_1$, $B_2$, $ε_1$ and $ε_2$, where $B_1$ and $B_2$ parametrize the matrix elements of color singlet-singlet four-quark operators and $ε_1$ and $ε_2$ the matrix elements of color octet-octet operators. We derive the renormalization-group improved QCD sum rules for these parameters within the framework of heavy quark effective theory. The results are $B_1(m_b)=0.96\pm 0.04$, $B_2(m_b)=0.95\pm 0.02$, $ε_1(m_b)=-0.14\pm 0.01$, and $ε_2(m_b)=-0.08\pm 0.01$ to zeroth order in $1/m_b$. The resultant $B$ meson lifetime ratios are $τ(B^-)/τ(B_d)=1.11\pm 0.02$ and $τ(B_s)/τ(B_d)\approx 1$ in SU(3) symmetry limit.