Complete NNLO QCD analysis of B̄ → Xsℓ +ℓ and higher order electroweak effects

Journal article

We complete the next-to-next-to-leading order QCD calculation of the branching ratio for B̄ → Xsℓ+ℓ including recent results for the three-loop anomalous dimension matrix and two-loop matrix elements. These new contributions modify the branching ratio in the low-q2 region, BRℓℓ, by about +1% and -4%, respectively. We furthermore discuss the appropriate normalization of the electromagnetic coupling α and calculate the dominant higher order electroweak effects, showing that, due to accidental cancellations, they change BRℓℓ by only -1.5% if α(μ) is normalized at μ= O(mb), while they shift it by about -8.5% if one uses a high scale normalization μ = O(Mw). The position of the zero of the forward-backward asymmetry, q02, is changed by around +2%. After introducing a few additional improvements in order to reduce the theoretical error, we perform a comprehensive study of the uncertainty. We obtain BRℓℓ(1GeV2 ≤ q2 ≤ 6 GeV2) = (1.57 ± 0.16) × 10-6 and q 02 = (3.76 × 0.33) GeV2 and note that the part of the uncertainty due to the b-quark mass can be easily reduced. © SISSA/ISAS 2004.

Authors: Bobeth, C; Gambino, P; Gorbahn, M; Haisch, U

• Journal: Journal of High Energy Physics
• Volume: 8
• Issue: 4
• Pages: 1593-1618
• Publication date: 2004-04-01
• ISSN: 1029-8479
• Language: English
• Keywords: B-Physics; Rare Decays; NLO Computations; Standard Model