Effects of the scalar FCNC in $b\rightarrow sl^ + l^-$ transitions and supersymmetry

Abstract

We investigate the potential effects of the scalar flavour changing neutral currents that are generated e.g. in supersymmetry with $\tan\beta\gg1$ in the $b\to sl^+l^-$ transitions. Using the experimental upper limit on $BR(B^0_s\to\mu^+\mu^-)$ we place stringent model independent constraints on the impact these currents may have on the rates $BR(B\to X_s\mu^+\mu^-)$ and $BR(B\to K\mu^+\mu^-)$. We find that in the first case, contrary to the claim made recently in the literature, the maximal potential effects are always smaller than the uncertainty of the Standard Model NNLO prediction, that is of order 5-15%. In the second case, the effects can be large but the experimental errors combined with the unsettled problems associated with the relevant formfactors do not allow for any firm conclusion about the detectability of a new physics signal in this process. In supersymmetry the effects of the scalar flavour changing neutral currents are further constrained by the experimental lower limit on the $B^0_s$-$\bar B^0_s$ mass difference, so that most likely no detectable signal of the supersymmetry generated scalar flavour changing neutral currents in processes $B\to X_s\mu^+\mu^-$ and $B\to K\mu^+\mu^-$ is possible.