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 $B_1$, $B_2$, ${\epsilon }_1$ and ${\epsilon }_2$, where $B_1$ and $B_2$ parametrize the matrix elements of color singlet-singlet four-quark operators and ${\epsilon }_1$ and ${\epsilon }_2$ 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 $B_1(m_b)=0.96\pm 0.04$, $B_2(m_b)=0.95\pm 0.02$, ${\epsilon }_1(m_b)=-0.14\pm 0.01$, and ${\epsilon }_2(m_b)=-0.08\pm 0.01$ 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.

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

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• Flavor changing neutral current processes in $B$ and $K$ decays in the supergravity model
• Explicit Quark-hadron Duality in Heavy-light Meson Weak Decays in the 't Hooft Model
• Four-quark Operators Relevant to B Meson Lifetimes from QCD Sum Rules
• Cancellation of $1/m_Q$ Corrections to the Inclusive Decay Width of a Heavy Quark

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