Calculation of two loop virtual corrections to $b \to  s l^+ l^-$ in the standard model

We present in detail the calculation of the virtual O(alpha_s) corrections to the inclusive semi-leptonic rare decay b --> s l+ 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 0.05 < s/mb^2 < 0.25. The analytic results are represented as expansions in the small parameters s/mb^2, z = mc^2/mb^2 and s/(4 mc^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 +/-13% to +/-6.5%.

Note:

41 pages including 9 postscript figures; in version 2 some typos and inconsistent notation corrected

13.20.He
11.10.Ef
12.39.Hg
bottom
quark: semileptonic decay
quark: rare decay
quark: branching ratio
quark: width
correction: higher-order
bremsstrahlung

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