Complete NNLO QCD Analysis of B̄ → X s l + l − and Higher Order Electroweak Effects

We complete the next-to-next-to-leading-order QCD calculation of the branching ratio for B̄ → Xsll 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-q region, BRll, by about +2% and −2%, respectively. We furthermore discuss the appropriate normalization of the electromagnetic coupling α, and calculate the dominant higher order electroweak effects, showing that they affect BRll by around −5% to +3%, depending on the normalization scale adopted for α(μem), and also the zero of the forwardbackward asymmetry, q 0 , which is changed by −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(1GeV 2 ≤ q ≤ 6GeV) = (1.702± 0.160)× 10 and q 0 = (3.23± 0.12)GeV.