Two-loop QCD penguin contribution to the width difference in Bs ? $$ {\overline{B}}_s $$ mixing

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