Unitary states for three pions

Recent angular momentum analyses of the three-pion system produced in the reaction π^-p→π^-π⁺π^-p have been criticized because the three-pion states used in the analysis do not satisfy unitarity. In order to answer this criticism we develop a set of unitarity equations which can be solved to yield a set of three-pion states which explicitly satisfy both three-particle unitarity and two-particle unitarity (Watson's theorem). A numerical method for solving the equations is given. When the unitary states are used to reanalyze the data for the reaction π^-p→π^-π⁺π^-p we find some changes in the detailed numerical fits but no change in the general conclusions. In particular, the phase of the amplitude for the A₁ state varies only slightly in the A₁ mass region, in contrast with the behavior expected for a resonant state.