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

Abstract

A bstract We complete the calculation of 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:mi>B</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mo>−</mml:mo> <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 , 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 $$ {\alpha}_s^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> , 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 $$ {\Gamma}_{12}^s $$ <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>s</mml:mi> </mml:msubsup> </mml:math> is expressed in terms of the $$ \overline{\mathrm{MS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> b-quark mass, while we find ∆Γ s /∆ M s = (4 . 70 ± 0 . 96) · 10 −3 instead for the use of the pole mass.

Topics & Concepts