Protonium annihilation into two mesons

Abstract

The annihilation of a protonium atomic bound state into two mesons is analyzed in terms of threshold values of the helicity amplitudes for the annihilation process. One of the mesons is assumed to have spin 0 and the other either spin 0 or 1, all parity combinations being considered. Simple expressions for partial widths are derived and used, together with the total annihilation widths obtained from a parametrized potential to give branching ratios. We also derive expressions for the angular distribution of one meson with respect to the direction of the X-ray emitted in the transition which populated the level. The available experimental branching ratios are used to extract values for various helicity amplitudes. Where possible they are then compared to quark model predictions and to values obtained by extrapolation from higher energies. Reasonable agreement is found except for a quark model prediction for annihilation to π + π − from the 3P 0 level, which gives a much larger rate than the experimental value. This possibility of detailed comparison demonstrates the power of the analysis. Complete experiments are suggested for the determination of all necessary helicity amplitudes describing annihilation from a given atomic bound state.