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

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