NNLL QCD Corrections to the Decay $B\to X_s{\ell }^{+}{\ell }^{-}$

Abstract

We briefly discuss the status of the NNLL QCD calculations in the inclusive rare B decay $B\to X_s{\ell }^{+}{\ell }^{-}$. Two important ingredients, the two-loop matrix elements of the four quark operator ${\mathcal{O}}_2$ and the bremsstrahlung contributions, were quite recently finalised. The new contributions significantly improve the sensitivity of the inclusive decay $B\to X_s{l}^{+}{l}^{-}$ decay in testing extensions of the standard model in the sector of flavour dynamics; for instance the two-loop calculation cuts the low- scale uncertainty in half and the bremsstrahlung calculation leads to a 10% shift of the position of the zero of the forward- backward asymmetry.

Comments: 7 pages, latex, 5 figures, references added