Logarithmically enhanced corrections to the decay rate and forward-backward asymmetry in B¯→Xsℓ+ℓ−

We study logarithmically enhanced electromagnetic corrections to the decay rate in the high dilepton invariant mass region as well as corrections to the forward-backward asymmetry (FBA) of the inclusive rare decay B¯→Xsℓ+ℓ−. As expected, the relative effect of these corrections in the high dilepton mass region is around −8% for the muonic final state and therefore much larger than in the low dilepton mass region. We also present a complete phenomenological analysis, to improved NNLO accuracy, of the dilepton mass spectrum and the FBA integrated in the low dilepton mass region, including a new approach to the zero of the FBA. The latter represents one of the most precise predictions in flavour physics with a theoretical uncertainty of order 5%. We find (q02)μμ=(3.50±0.12) GeV2. For the high dilepton invariant mass region, we have B(B¯→Xsμμ)high=(2.40−0.62+0.69)×10−7. The dominant uncertainty is due to the 1/mb corrections and can be significantly reduced in the future. For the low dilepton invariant mass region, we confirm previous results up to small corrections.