Two-loop QCD penguin contribution to the width difference in $B_s-\bar{B}_s$ mixing

TL;DR

This paper calculates two-loop QCD corrections involving penguin operators to the decay matrix element in B_s meson mixing, refining theoretical predictions for the width difference to match experimental precision.

Contribution

It provides the first complete analytic calculation of two-loop QCD corrections involving penguin operators to $ ext{Γ}_{12}^q$ in B_q mixing, improving the theoretical accuracy.

Findings

Corrections are comparable to current experimental errors.

Corrections slightly increase the predicted width difference $ ext{ΔΓ}_s$.

Analytic results are expanded in $m_c/m_b$ up to second order.

Abstract

We consider two-loop QCD corrections to the element $\Gamma_{12}^q$ of the decay matrix in $B_q-\bar{B}_q$ 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 $\Delta\Gamma_s$ 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 $\Delta\Gamma_s$.