Journal Article

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

Gerlach, Marvin, Nierste, Ulrich, Shtabovenko, Vladyslav, Steinhauser, Matthias

2022

Overview

We complete the calculation of the element$$ {\\Gamma}_{12}^q $$Γ 12 q of the decay matrix in$$ {B}_q-{\\overline{B}}_q $$B q − 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$$ {\\alpha}_s^2 $$α 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$$ {\\Gamma}_{12}^s $$Γ 12 s is expressed in terms of the$$ \\overline{\\mathrm{MS}} $$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.