Angular distribution functions for the decay of charmonium states directly produced by polarized proton-antiproton collisions

We calculate the combined angular distribution functions in the cascade process p bar p→χJ→ψγ→(e+e-)γ (J=0,1,2) in terms of the complex angular momentum helicity amplitudes or equivalently in terms of the multipole transition amplitudes in χJ→ψγ, when the proton (p) and the antiproton (bar p) are both arbitrarily polarized. The results are expressed as a sum over products of linearly independent spherical harmonics. We discuss the results for the special cases when neither particle is polarized, a single particle is polarized, and both particles are polarized. In general, by measuring the angular distributions in polarized p bar p collisions we are not only able to get the magnitudes, but also the relative phases of the decay amplitudes in the process χJ→ψγ and of the production amplitudes in p bar p→χJ