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 $\tau (B^{-})/\tau (B_d)=1.11\pm 0.02$ and $\tau (B_s)/\tau (B_d)\approx 1$ in SU(3) symmetry limit.

Comments: 22 pages, 2 figures. (i) Sec.II is shortened, (ii) numerical results for epslion_i are revised, and (iii) Fig.2 is revised