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We present our results for the NNLL virtual corrections to the matrixelements of the operators O_1 and O_2 for the inclusive process b\tos\ell^+\ell^- in the kinematical region q^2>4m_c^2, where q^2 is the invariantmass squared of the lepton-pair. This is the first analytic two-loopcalculation of these matrix elements in the high q^2 region. We give the matrixelements as an expansion in m_c/m_b and keep the full analytic dependence onq^2. Making extensive use of differential equation techniques, we fullyautomatize the expanding of the Feynman integrals in m_c/m_b. In coincidencewith an earlier work where the master integrals where calculated numerically(Ghinculov et al.) we find that in the high q^2 region the \alpha_s correctionsto the matrix elements <s \ell^+ \ell^-|O_{1,2}|b> calculated in the presentpaper lead to a decrease of the q^2-spectrum by 10%-15% relative to the NNLLresult in which these contributions are put to zero and reduce therenormalization scale uncertainty to ~2%.

Analytic calculation of two-loop QCD corrections to b\to s\ell^+\ell^- in the high q^2 region