The importance of the measurement of ρ for the understanding of the high energy hadron-hadron scattering

It is shown both on general and phenomenological grounds, why the ρ-parameter (the ratio of the real over the imaginary part of the forward hadron amplitude) is the most suitable one for exploring Odderon effects in the present energy range. An almost model-independent analysis of the experimental data by taking into account the analytical constraints and the assumption of maximality is performed. Using the maximal Odderon approach as a guide, the following constrain at √s= 546 GeV is established: ρ(p-bar)p< or∼ 0.23. This bound leads to the conclusion that an experimental UA4/2 value centred around 0.20, say 0.20± 0.02, will constitute a strong and unambiguous signal of Odderon effects that will indicate that at high energy the σppT>σp-barpT relation exists. (R.P.) 14 refs., 3 figs