Comparative study of the decays<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mo>)</mml:mo><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi>−</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>in the 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 $\stackrel{\ensuremath{\rightarrow}}{B}{(K,K}^{*}{)l}^{+}{l}^{\ensuremath{-}}$ ${(l}^{\ifmmode\pm\else\textpm\fi{}}{=e}^{\ifmmode\pm\else\textpm\fi{}},{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}},{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}})$ 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 $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}\ensuremath{\gamma}$ and the experimental upper limit on the branching ratio $\mathcal{B}(\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})$ provide interesting bounds on the coefficients of the underlying effective theory. We argue that the FB asymmetry in $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{*}{l}^{+}{l}^{\ensuremath{-}}$ constitutes a precision test of the SM and its measurement in forthcoming experiments may reveal new physics. In particular, the presently allowed large-$\mathrm{tan}\ensuremath{\beta}$ 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.