  We discuss, in detail, the K* polarization states in the exclusive B meson
decay B0-> K*0(-> K-pi+)l^+l^- (l=e, \mu, \tau) in the low dilepton mass
region. We focus on the study of the angular distribution of this decay that
provides valuable information on the K* spin amplitudes A_perp, A_par, A0. This
can give us a handle on non-standard interactions that cannot be proved through
measurements of the branching ratio and lepton forward-backward asymmetry. We
explore the transverse asymmetries A_T^1(s), A_T^2(s), K* polarization
parameter \alpha_{K*}(s), the fraction of K* polarization F_L(s) and F_T(s) and
the corresponding integrated observables at NLL order, including factorizable
and non-factorizable corrections. We find, in particular, that the dependence
on hadronic uncertainties for the transverse asymmetries turns out to be very
small. This allow us to distinguish which observables are better suited to look
for physics beyond the SM. Finally, we study in a model independent way the
implications of New Physics for these observables.
