Width Difference in the B-B[over ¯] System at Next-to-Next-to-Leading Order of QCD

We extend the theoretical prediction for the width difference ΔΓ_{q} in the mixing of neutral B mesons in the Standard Model to next-to-next-to-leading order in α_{s}. To this aim, we calculate three-loop diagrams with two |ΔB|=1 current-current operators analytically. In the matching between |ΔB|=1 and |ΔB|=2 effective theories, we regularize the infrared divergences dimensionally and take into account all relevant evanescent operators. Further elements of the calculation are the two-loop renormalization matrix Z_{ij} for the |ΔB|=2 operators and the O(α_{s}^{2}) corrections to the finite renormalization that ensures the 1/m_{b} suppression of the operator R_{0} at two-loop order. Our theoretical prediction reads ΔΓ_{s}/ΔM_{s}=(4.33±0.93)×10^{-3} if expressed in terms of the bottom mass in the MS[over ¯] scheme and ΔΓ_{s}/ΔM_{s}=(4.20±0.95)×10^{-3} for the use of the potential-subtracted mass. While the controversy on |V_{cb}| affects both ΔΓ_{s} and ΔM_{s}, the ratio ΔΓ_{s}/ΔM_{s} is not affected by the uncertainty in |V_{cb}|.