$B \to K^* \ell^+ \ell^-\big (\rho \ell \nu_{\ell}\big)$ helicity analysis in the LEET

Abstract

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 single (and total) 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. 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.