π+π+pResonance—A Static-Model Calculation

The ${\pi }^{+}{\pi }^{+}p$ scattering amplitude in the $J=\frac{5}{2}$ (even-parity) state is calculated, in the static-nucleon approximation. The isobar model is not used, and the symmetry required by Bose statistics is maintained throughout. As a consequence, although the static model radically simplifies the three-body problem, the solution displays some interesting three-body features. A discussion of the physical interpretation of the solution is presented, especially with regard to the definition of a three-particle resonance. Such a resonance is found; rough values for the position and half-width are 1550 and 125 MeV, respectively. No arbitrary parameters are used in obtaining these numbers, which agree rather well with recently reported experimental values of a ${\pi }^{+}{\pi }^{+}p$ enhancement in the final state of ${\pi }^{+}+p\to {\pi }^{-}+{\pi }^{+}+{\pi }^{+}+p$.