Next-to-next-to leading logarithmic corrections to the angular distribution and to the forward-backward asymmetries in b → Xsl+l- -: art. no. 094013

We present next-to-next-to leading logarithmic (NNLL) results for the double differential decay width dGamma(b-->X(s)l(+)l)/[d (s) over cap d cos(theta)], where (s) over cap =sm(b)(2) is the invariant mass squared of the lepton pair and theta is the angle between the momentum 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, as these quantities are known to be very sensitive to new physics. While the principal steps in the calculation of the double differential decay width are the same as for dGamma(b-->X(s)l(+)l(-))/d (s) over cap, which is already known to NNLL precision, genuinely new calculations for the combined virtual and gluon bremsstrahlung corrections associated with the operators O-7, O-9, and O-10 are necessary. In this paper, we neglected certain other bremsstrahlung contributions, which are known to have only a small impact on dGamma(b-->X(s)l(+)l(-))/d (s) over cap. We find that the NNLL corrections drastically reduce the renormalization scale (mu) dependence of the forward-backward asymmetries. In particular, (s) over cap (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 (s) over cap (NNLL)(0)=0.162+/-0.005, where the error is dominated by the uncertainty in m(c)/m(b). This is to be compared with (s) over cap (NLL)(0)=0.144+/-0.020, where the error is dominated by uncertainties due to the choice of mu.