Three-Pion Decays of Unstable Particles

Abstract

The properties of particles of arbitrary spin and parity that decay into three pseudoscalar mesons are surveyed, with primary attention to $3\pi$ decays, in order to find efficient means of detecting such particles. Among the topics considered are the general forms of amplitudes subject to invariance and symmetry requirements, the regions of vanishing density in the Dalitz plot, branching ratios, angular correlations among vectors normal to and lying in the production and decay planes, and special decay modes through two-particle resonances. The angular correlations are discussed in detail for processes independent of the intrinsic spin of the production particles, as is appropriate in coherent nuclear processes, and a framework of analysis is provided for more complex problems. A complete characterization of $K\to 3\pi$ decays is given in terms of $\Delta I$ rules and final-state isospin. The suggestion is made that a second pion, with the same quantum numbers as the ordinary pion, should be found at an energy less than 2 BeV. This prediction is based on the possibility that the pion is primarily a nucleon-antinucleon bound $S$ state and that the force of binding is therefore so strong that it should produce more than one bound $S$ state.