The rare decay B --> X_s l^+ l^- to NNLL precision for arbitrary dilepton invariant mass

Abstract

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 $M_{{\ell }^{+}{\ell }^{-}}^2$ region, and to provide an independent check of previously published results in the low $M_{{\ell }^{+}{\ell }^{-}}^2$ region. The numerical impact of these NNLL corrections in the high-mass region ($M_{{\ell }^{+}{\ell }^{-}}^2>14.4Ge{V}^2$) 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.

Comments: 40 pages, 12 figures. v2: extended phenomenological discussion; results unchanged; published version