Angular distribution of photons in the parity-changing one-photon radiative decays of quarkonia

We derive a general expression, correct to order v2c2 and valid in any potential model, for the angular distribution of photons in the parity-changing one-photon radiative decays of quarkonia, in terms of its different multipole contributions E1, M2, and E3. The expression is given in terms of Clebsch-Gordan coefficients and six reduced matrix elements. We make detailed numerical calculations for the radiative decays of charmonium using Buchm̈ller-Tye and Gupta-Radford-Repko potential models and find that there is not much difference in the angular distributions between the two models. It is interesting to note that the E3 contributions to the decays 2+ and 2+ are nonvanishing only and have admixtures of D states in them.