Two-loop QCD penguin contribution to the width difference in Bs − $$ {\overline{B}}_s $$ mixing
Marvin Gerlach, Ulrich Nierste, Vladyslav Shtabovenko, Matthias Steinhauser
Abstract
A bstract We consider two-loop QCD corrections to the element $$ {\Gamma}_{12}^q $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Γ</mml:mi> <mml:mn>12</mml:mn> <mml:mi>q</mml:mi> </mml:msubsup> </mml:math> of the decay matrix in B q − $$ {\overline{B}}_q $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>q</mml:mi> </mml:msub> </mml:math> 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 ∆Γ 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 ∆Γ s .