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We complete the next-to-next-to-leading order QCD calculation of thebranching ratio for B -> X_s l^+ l^- including recent results for thethree-loop anomalous dimension matrix and two-loop matrix elements. These newcontributions modify the branching ratio in the low-q^2 region, BR_ll, by about+1% and -4%, respectively. We furthermore discuss the appropriate normalizationof the electromagnetic coupling alpha and calculate the dominant higher orderelectroweak effects, showing that, due to accidental cancellations, they changeBR_ll by only -1.5% if alpha(mu) is normalized at mu = O(m_b), while they shiftit by about -8.5% if one uses a high scale normalization mu = O(M_W). Theposition of the zero of the forward-backward asymmetry, q_0^2, is changed byaround +2%. After introducing a few additional improvements in order to reducethe theoretical error, we perform a comprehensive study of the uncertainty. Weobtain BR_ll(1 GeV^2 <= q^2 <= 6 GeV^2) = (1.57 +- 0.16) x 10^-6 and q_0^2 =(3.76 +- 0.33) GeV^2 and note that the part of the uncertainty due to theb-quark mass can be easily reduced.Comment: 26 pages, 7 figures; v5: corrected normalisation in Eq. (5),  numerical results unchange

Complete NNLO QCD Analysis ofB Xsl l and Higher Order Electroweak Effects

Complete NNLO QCD Analysis ofB X_slland Higher Order Electroweak Effects