Bound on Inelastic Total Cross-Sections

We prove that the total inelastic cross-section is bounded by inelastic < 4m2 (ln s)2 , i.e. a bound 4 times smaller than the bound obtained by L. Lukaszuk and the author on the total cross-section in 1967. With some extra assumptions, which look reasonable to most people, we show that the bound on the total cross-section itself is divided by 2. For details see [1, 2].