The width difference in B − B ¯ $$ B-\overline{B} $$ beyond mixing at order α s and

Abstract

Abstract We complete the calculation of the element Γ 12 q $$ {\Gamma}_{12}^q $$ of the decay matrix in B q − B ¯ q $$ {B}_q-{\overline{B}}_q $$ mixing, q = d, s, to order α s in the leading power of the Heavy Quark Expansion. To this end we compute one- and two-loop contributions involving two four-quark penguin operators. Furthermore, we present two-loop QCD corrections involving a chromomagnetic operator and either a current-current or four-quark penguin operator. Such contributions are of order α s 2 $$ {\alpha}_s^2 $$ , i.e. next-to-next-to-leading-order. We also present one-loop and two-loop results involving two chromomagnetic operators which are formally of next-to-next-to-leading and next-to-next-to-next-to-leading-order, respectively. With our new corrections we obtain the Standard-Model prediction ∆Γ s /∆M s = (5.20 ± 0.69) · 10 −3 if Γ 12 s $$ {\Gamma}_{12}^s $$ is expressed in terms of the MS ¯ $$ \overline{\mathrm{MS}} $$ b-quark mass, while we find ∆Γ s /∆M s = (4.70 ± 0.96) · 10−3 instead for the use of the pole mass.

Keywords

• Bottom Quarks
• CP Violation
• Higher-Order Perturbative Calculations