The width difference in $$ B-\overline{B} $$ beyond mixing at order αs and

A bstract We complete the calculation of element $$ {\Gamma}_{12}^q Γ 12 q decay matrix in {B}_q-{\overline{B}}_q B − ¯ mixing, q = d , s to order α leading power Heavy Quark Expansion. To this end we compute one- and two-loop contributions involving two four-quark penguin operators. Furthermore, present QCD corrections a chromomagnetic operator either current-current or operator. Such are {\alpha}_s^2 α s 2 i.e. next-to-next-to-leading-order. also one-loop results operators which formally next-to-next-to-leading next-to-next-to-next-to-leading-order, respectively. With our new obtain Standard-Model prediction ∆Γ /∆ M (5 . 20 ± 0 69) · 10 − 3 if {\Gamma}_{12}^s is expressed terms \overline{\mathrm{MS}} MS b-quark mass, while find (4 70 96) −3 instead for use pole mass.