Electromagnetic logarithms in B¯→Xsℓ+ℓ−

The B¯→Xsℓ+ℓ− decay rate is known at the next-to-next-to-leading order in QCD. It is proportional to αem(μ)2αem(μ)2 and has a ±4%±4% scale uncertainty before including the O(αemln(MW2/mb2)) electromagnetic corrections. We evaluate these corrections and confirm the earlier findings of Bobeth et al. Furthermore, we complete the calculation of logarithmically enhanced electromagnetic effects by including also QED corrections to the matrix elements of four-fermion operators. Such corrections contain a collinear logarithm ln(mb2/mℓ2) that survives integration over the low dilepton invariant mass region 1GeV2