Two-loop QCD penguin contribution to the width difference in $B_s-bar{B}_s$ mixing

We consider two-loop QCD corrections to the element $Gamma_{12}^q$ of the decay matrix in $B_q-bar{B}_q$ mixing, $q=d,s$, in the leading power of the Heavy Quark Expansion. The calculated contributions involve one current-current and one penguin operator and constitute the next step towards a theory prediction for the width difference $DeltaGamma_s$ matching the precise experimental data. We present compact analytic results for all matching coefficients in an expansion in $m_c/m_b$ up to second order. Our new corrections are comparable in size to the current experimental error and slightly increase $DeltaGamma_s$.