A Comparative Study of the Decays $B\to (K,K^{\ast }){\ell }^{+}{\ell }^{-}$ in Standard Model and Supersymmetric Theories

Abstract

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 $B\to (K,K^{\ast }){\ell }^{+}{\ell }^{-}$ (${\ell }^{\pm }=e^{\pm },{\mu }^{\pm },{\tau }^{\pm }$) 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 $\mathcal{B}(B\to K^{\ast }{\mu }^{+}{\mu }^{-})$ provide interesting bounds on the coefficients of the underlying effective theory. We argue that the FB-asymmetry in $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ 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.

Comments: 36 pages, 12 figures (require epsfig.sty), 8 Tables, LaTeX2e; subsection 6.4 corrected, minor changes in numerical results, Figures 3 and 9 to 12 modified; submitted to Physical Review D