We have performed numerical simulations of the single-polarized e+ e- --> vec p anti p process in kinematic conditions under discussion for a possible upgrade of the existing DAFNE facility. By fitting the cross section and spin asymmetry angular distributions with typical Born expressions, we can study the conditions for extracting information on moduli and phases of the proton electromagnetic form factors in the timelike region, which are poorly known and whose preliminary data show puzzling features. We have explored also non-Born contributions by introducing a further component in the angular fit, which is related to two-photon exchange diagrams. Using a dipole parametrization, we show that these corrections can be identified if larger than 5% of the Born contribution; we also explore the conditions for extracting information on the phase and, consequently, on the relative weight between their real and imaginary parts, which are presently unknown.
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