Determination of χc and χb polarizations from dilepton angular distributions in radiative decays

The angular distributions of the decay products in the successive decays χc(χb)→J/ψ(Υ)γ and J/ψ(Υ)→l+l- are calculated as a function of the angular momentum composition of the decaying χ meson and of the multipole structure of the photon radiation, using a formalism independent of production mechanisms and polarization frames. The polarizations of the χ states produced in high-energy collisions can be derived from the dilepton decay distributions of the daughter J/ψ or Υ 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 χc decay angular distributions are identified and clarified.