  Recently the radiative B decay to the strange axial-vector mesons, B -->
K1(1270) gamma, has been observed with rather large branching ratio. This
process is particularly interesting as the subsequent K1 decay into its three
body final state allows us to determine the polarization of the photon, which
is mostly left- (right-)handed for Bbar (B) in the SM while various new physics
models predict additional right- (left-)handed components. A new method is
proposed to determine the polarization, exploiting the full Dalitz plot
distribution, which seems to reduce significantly the statistical errors. This
polarization measurement requires however a detailed knowledge of the K1--> K
pi pi strong interaction decays, namely, the various partial wave amplitudes
into the several possible quasi two-body channels, as well as their relative
phases. The pattern of partial waves is especially complex for the K1(1270). We
attempt to obtain the information through the combination of an experimental
input and a theoretical one, provided by the 3P0 quark-pair-creation model.
