  We study the Standard Model and the new physics predictions for the
lepton-flavour-universality violating (LFUV) ratios in various $b\to s
\ell^+\ell^-$ channels with scalar, pseudoscalar, vector, axial-vector, and
$\Lambda$ baryon final states, considering both unpolarized and polarized final
state hadrons. In order to formulate physical observables, we use the model
independent effective Hamiltonian approach and employ the helicity formalism.
We provide the explicit expressions of the helicity amplitudes in terms of the
Wilson coefficients and the hadronic form factors by using the same kinematical
configuration and polarization conventions for all the decay channels.We
perform the numerical analysis with new physics scenarios selected from the
recent global fits to $b\to s\ell^+\ell^-$ data, having specific new physics
model interpretations. We find that some of the LFUV ratios for these
complementary channels in different kinematical regions have high sensitivity
to new physics and the future measurements of them in Belle II and LHCb
experiments, along with testing new physics/LFUV, can help to distinguish among
some of the different new physics possibilities.
