  The angular distributions of the decay products in the successive decays
chi_c (chi_b) to J/psi (Upsilon) gamma and J/psi (Upsilon) to l+l- are
calculated as a function of the angular momentum composition of the decaying
chi meson and of the multipole structure of the photon radiation, using a
formalism independent of production mechanisms and polarization frames. The
polarizations of the chi states produced in high energy collisions can be
derived from the dilepton decay distributions of the daughter J/psi or Upsilon
mesons, with a reduced dependence on the details of the photon reconstruction
or simulation. Moreover, this method eliminates the dependence of the
polarization measurement on the actual details of the multipole structure of
the radiative transition. Problematic points in previous calculations of the
chi_c decay angular distributions are identified and clarified.
