Calculations of two-loop virtual corrections to b→sl+l- in the standard model -: art. no. 074004

We present in detail the calculation of the virtual O(alpha(s)) corrections to the inclusive semileptonic rare decay b-->sl(+)l(-). We also include those O(alpha(s)) bremsstrahlung contributions which cancel the infrared and mass singularities showing up in the virtual corrections. In order to avoid large resonant contributions, we restrict the invariant mass squared s of the lepton pair to the range 0.05less than or equal tos/m(b)(2)less than or equal to0.25. The analytic results are represented as expansions in the small parameters (s) over cap =s/m(b)(2), z=m(c)(2)/m(b)(2) and s/(4m(c)(2)). The new contributions drastically reduce the renormalization scale dependence of the decay spectrum. For the corresponding branching ratio (restricted to the above s range) the renormalization scale uncertainty gets reduced from similar to+/-13% to similar to+/-6.5%.