Theoretical studies of exclusive rare B decays in the Standard Model and Supersymmetric theories

We calculate the independent helicity amplitudes in the decays $B \to K^* \ell^+ \ell^-$ and $B \to \rho \ell \nu_\ell$ in the so-called Large-Energy-Effective-Theory (LEET). Taking into account the dominant $O(\alpha_s)$ and SU(3) symmetry-breaking effects, we calculate various Dalitz distributions in these decays making use of the presently available data and decay form factors calculated in the QCD sum rule approach. Differential decay rates in the dilepton invariant mass and the Forward-Backward asymmetry in $B \to K^* \ell^+ \ell^-$ are worked out. We also present the decay amplitudes in the transversity basis which has been used in the analysis of data on the resonant decay $B \to K^* J/\psi (\to \ell^+ \ell^-)$. Measurements of the ratios $R_i(s) \equiv d \Gamma_{H_i}(s)(B \to K^* \ell^+ \ell^-)/ d \Gamma_{H_i}(s)(B \to \rho \ell \nu_\ell)$, involving the helicity amplitudes $H_i(s)$, $i=0,+1, -1$, as precision tests of the standard model in semileptonic rare B-decays are emphasized. We argue that $R_0(s)$ and $R_{-}(s)$ can be used to determine the CKM ratio $| V_{ub}|/| V_{ts} |$ and search for new physics, where the later is illustrated by supersymmetry.