Analytic calculation of two-loop QCD corrections to b → sl+l- in the high q2 region

We present our results for the NNLL virtual corrections to the matrix elements of the operators O-1 and O-2 for the inclusive process b -> sl(+)l(-) in the kinematical region q(2) > 4m(c)(2), where q(2) is the invariant mass squared of the lepton-pair. This is the first analytic two-loop calculation of these matrix elements in the high q(2) region. We give the matrix elements as an expansion in m(c)/m(b) and keep the full analytic dependence on q(2). Making extensive use of differential equation techniques, we fully automatize the expanding of the Feynman integrals in mc/mb. In coincidence with an earlier work where the master integrals were obtained numerically [1], we find that in the high q(2) region the as corrections to the matrix elements < sl(+)l(-)vertical bar O-1,O-2 vertical bar b > calculated in the present paper lead to a decrease of the perturbative part of the q(2)-spectrum by 10% - 15% relative to the NNLL result in which these contributions are put to zero and reduce the renormalization scale uncertainty to similar to 2%.