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

Abstract

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 $\Delta {\Gamma }_s$ 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 $\Delta {\Gamma }_s$.

22 pages, 2 figures

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