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

Abstract

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 $(\Delta \Gamma /\Gamma {)}_{B_s}=(f_{B_s}/210MeV{)}^2[0.006B(m_b)+0.150B_S(m_b)-0.063]$ 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 $b\to u\bar{u}d$ decays, which measures $\sin 2\alpha$.

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