NNLL corrections to the angular distribution and to the forward-backward asymmetries in b -> X_s l+ l-

We present NNLL results for the double differential decay width dGamma(b -> X_s l+ l-)/(dsh dcos(theta)), where theta is the angle between the momenta of the b-quark and the l+, measured in the rest-frame of the lepton pair. From these results we also derive NNLL results for the lepton forward-backward asymmetries. Genuinely new calculations for the combined virtual- and gluon bremsstrahlung corrections associated with the operators O_7, O_9 and O_10 are necessary. We find that the NNLL corrections drastically reduce the renormalization scale dependence of the forward-backward asymmetries. In particular, sh_0, the position at which the forward-backward asymmetries vanish, is essentially free of uncertainties due to the renormalization scale at NNLL precision. We find sh_0(NNLL)=0.162 +/- 0.005, where the error is dominated by the uncertainty in (m_c/m_b). This is to be compared with sh_0(NLL)=0.144 +/- 0.020, where the error is dominated by uncertainties due to the choice of mu.