- th / 0 30 71 14 v 1 3 0 Ju l 2 00 3 1 Pion re - scattering in π 0 production near threshold

Due to isospin suppression of the otherwise dominant low-energy isovector WeinbergTomosawa πN term in the re-scattering diagram, and the negative interference between the remaining impulse and isoscalar pion re-scattering terms[1], the empirical data for pp → ppπ near threshold is only explained by phenomenological non-pionic, short-range, twobody mechanisms[2], or alternatively by an off-shell extrapolation of the πN amplitude[3]. The high quality data for pp → ppπ becomes therefore specially interesting by allowing to establish the importance of the short-range mechanisms, which are difficult to constrain: they are subsumed in the low energy constants appearing also in the twoand threenucleon potentials, but so far these constants have not yet been precisely determined[4]. Nevertheless, any conclusion to be read off from the π production data is only meaningful and quantitative provided that the calculation of the re-scattering diagram[5] is under absolute control. This is not the case in calculations performed till now, where approximations at the level of the energy integration of the corresponding Feynman diagram were considered. Namely, non-relativistic reductions of the Feynman π-exchange diagram were done, through choices for the energy of the exchanged pion, both for its propagator and for the πN − πN amplitude at the re-scattering vertex. This work investigates the validity of the mostly used approximations. It generalizes the work of Refs.[5] which considers a toy model for scalar particles and interactions. Our calculation employs a physical model for nucleons and pions, with a pseudo-vector coupling for the πNN vertex; the χPt πN −πN re-scattering amplitude[1] and the Bonn B potential for the nucleon-nucleon interaction in the final state.