Supersymmetric effects on Forward Backward asymmetries of $B\to K{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$

Leptonic and semi-leptonic rare decays of B-mesons are very clean (both theoretically and experimentally) signatures of any new physics beyond the Standard Model (SM). More specifically the decay \btokll has been theoretically observed to be very sensitive to new physics as the Forward Backward (FB) asymmetry in this decay mode vanishes in the SM. Supersymmetry, however, predicts a non-vanishing value of this asymmetry. In this work we will study the polarized lepton pair FB asymmetry, i.e. the FB asymmetry of the lepton when one (or both) final state lepton(s) are polarized. We will study these asymmetries both within the SM and for Supersymmetric corrections to the SM.