Next-to-Leading Order QCD Corrections to the Lifetime Difference of $B_s$ Mesons

Details Next-to-Leading Order QCD Corrections to the Lifetime Difference of $B_s$ Mesons Next-to-Leading Order QCD Corrections to the Lifetime Difference of $B_s$ Mesons

1998-08-22

arxiv.org/abs/hep-ph/9808385v2

Phys.Lett.B459:631-640,1999

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, LaTeX, 1 figure; minor modifications of the text, improved discussion of eq. (35), all results unchanged

Scientific paper

10.1016/S0370-2693(99)00684-X

We compute the QCD corrections to the decay rate difference in the $B_s-\bar B_s$ system, $\Delta\Gamma_{B_s}$, in the next-to-leading logarithmic approximation using the heavy quark expansion approach. Going beyond leading order in QCD is essential to obtain a proper matching of the Wilson coefficients to the matrix elements of local operators from lattice gauge theory. The lifetime difference is reduced considerably at next-to-leading order. We find $(\Delta\Gamma/\Gamma)_{B_s}=(f_{B_s}/210 MeV)^2 [0.006 B(m_b)+0.150 B_S(m_b)-0.063]$ in terms of the bag parameters $B, B_S$ in the NDR scheme. As a further application of our analysis we also derive the next-to-leading order result for the mixing-induced CP asymmetry in inclusive $b\to u\bar ud$ decays, which measures $\sin 2\alpha$.

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