Two-loop virtual corrections to B→ Xsℓ +ℓ − in the standard model

Abstract

We calculate O( α s ) two-loop virtual corrections to the differential decay width dΓ(B→X sℓ +ℓ −)/d s ̂ , where ŝ is the invariant mass squared of the lepton pair, normalized to m b 2. We also include those contributions from gluon bremsstrahlung which are needed to cancel infrared and collinear singularities present in the virtual corrections. Our calculation is restricted to the range 0.05⩽ s ̂ ⩽0.25 where the effects from resonances are small. The new contributions drastically reduce the renormalization scale dependence of existing results for dΓ(B→X sℓ +ℓ −)/d s ̂ . For the corresponding branching ratio (restricted to the above ŝ-range) the renormalization scale uncertainty gets reduced from ∼±13% to ∼±6.5%.