Off-Mass-Shell $π$N Scattering and $pp \to pp π^0$

We adapt the off-shell $π$N amplitude of the Tucson-Melbourne three-body force to the half-off-shell amplitude of the pion rescattering contribution to $pp \to pp π^0$ near threshold. This {\em pion} rescattering contribution, together with the impulse term, provides a good description of the data when the half-off-shell amplitude is linked to the phenomenological invariant amplitudes obtained from meson factory $π$N scattering data.

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