A Comparative study of the decays $B \to$ ($K$, $K^{*)} \ell^+ \ell^-$ in standard model and supersymmetric theories

Using improved theoretical calculations of the decay form factors in the Light Cone-QCD sum rule approach, we investigate the decay rates, dilepton invariant mass spectra and the forward-backward (FB) asymmetry in the decays $B \to (K,K^*) \ell^+ \ell^-$ ($\ell^\pm =e^\pm,\mu^\pm,\tau^\pm$) in the standard model (SM) and a number of popular variants of the supersymmetric (SUSY) models. Theoretical precision on the differential decay rates and FB-asymmetry is estimated in these theories taking into account various parametric uncertainties. We show that existing data on $B \to X_s \gamma$ and the experimental upper limit on the branching ratio ${\cal B}(B \to K^* \mu^+ \mu^-)$ provide interesting bounds on the coefficients of the underlying effective theory. We argue that the FB-asymmetry in $B \to K^* \ell^+ \ell^-$ constitutes a precision test of the SM and its measurement in forthcoming experiments may reveal new physics. In particular, the presently allowed large-$\tan \beta$ solutions in SUGRA models, as well as more general flavor-violating SUSY models, yield FB-asymmetries which are characteristically different from the corresponding ones in the SM