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 pp̄→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 p̄ 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 pp̄ 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 pp̄→χJ.