Sensitivity studies of the decay $B^0_d \to K^*{0}(K^{+}pi^{-})\mu^{+}mu^{-}$ at LHCb

The rare decay B^0_d to K^*0 mu^+mu^-, with K^*0 -> K^+pi^-, is expected to be very sensitive to deviations from Standard Model. We present here a preliminary evaluation of the LHCb sensitivity to this decay. For the distributions in terms of the squared dimuon mass s we use a toy Monte Carlo to access this information. We conclude that, for an integrated luminosity of 2 fb^-1(nominal one year of data taking), LHCb will be able to measure the decay branching ratio up to a precision of 1.7-2.5% and the CP asymmetry on the branching ratios up to 0.017-0.025. For the squared dimuon mass s distribution LHCb will attain a precision in the range of 6%(high s) to 14%(low s). The uncertainty on the forward-backward asymmetry for the B^0 (or anti-B^0) decays varies from 0.09(high s) to 0.26(low s). The zero of this asymmetry will be measured with a precision of +-1.4 GeV^2. With 10 fb^-1 the corresponding results for the squared dimuon mass distribution and forward-backward asymmetry are 2.5% to 6.5% and 0.04 to 0.10. In this case the zero of the asymmetry would be determined with a precision of +-0.7 GeV^2. If we combine B^0 and anti-B^0 decays, which relies on the assumption that CP is conserved, we obtain for the uncertainties on the forward-backward asymmetry 0.06 to 0.16(2 fb^-1) and 0.03 to 0.08(10 fb^-1), while the zero of the asymmetry would be measured with a precision of +-1.2 GeV^2(2 fb^-1) and +-0.5 GeV^2(10 fb^-1). These numbers are for intervals of 1 GeV^2. Better precisions are obtained when we integrate on larger regions of the squared dimuon mass. We conclude that LHCb will discriminate among different models just after the first year of data taking, attaining a better precision as we accumulate more data.