The rare decay $B \to X_{s}l^{+}l^{-}$ to NNLL precision for arbitrary dilepton invariant mass

We present a new phenomenological analysis of the inclusive rare decay $B \to X_s \ell^+\ell^-$. In particular, we present the first calculation of the NNLL contributions due to the leading two-loop matrix elements, evaluated for arbitrary dilepton invariant mass. This allows to obtain the first NNLL estimates of the dilepton mass spectrum and the lepton forward-backward asymmetry in the high $ M^2_{\ell^+ \ell^-}$ region, and to provide an independent check of previously published results in the low $ M^2_{\ell^+ \ell^-}$ region. The numerical impact of these NNLL corrections in the high-mass region ($ M^2_{\ell^+ \ell^-} > 14.4 GeV^2$) amounts to -13% in the integrated rate, and leads to a reduction of the scale uncertainty to $\pm 3%$. The impact of non-perturbative contributions in this region is also discussed in detail.