In this paper we prove a new optimal bound on the logarithmic slope of the elastic slope b when: σ_(el) and dσ/dΩ(1) and dσ/dΩ(-1), are known from experimental data. The results on the experimental tests of this new optimal bound are presented in Sect. 3 for the principal meson-nucleon elastic scatterings: (π ± P → π ± P and K± P→K ± P) at all available energies. Then we show that the saturation of this optimal bound is observed with high accuracy practically at all available energies in meson-nucleon scattering.
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