Rise of proton proton total cross section and inclusive spectra

The origin of the rise of p-p total cross section (σ_t(pp)) is investigated by making use of the inclusive sum rule. The contribution to the rise of σ_t(pp) from the development of sharp peak near the kinematical boundary in the process p+p→p+ “anything” is almost completely canceled out by the decrease of the cross section in other x-region between s=45 (GeV/c)² and s=2820 (GeV/c)². Then the net contribution to the rise of σ_t(pp) from the process p+p→p+ “anything” is very likely to be zero. The true origin of the rise of σ_t(pp) is found to be the increase of inclusive cross sections at x ? 0 between PS and ISR energies. The contribution from the process p+p→π+ “anything” at x ? 0 to the rise of σ_t(pp) is estimated to be 3.2 mb, that from the process p+p→K + “anything”, 0.71 mb and that from the process p+p→$\text{p}$ “anything”, 0.62 mb. According to our conclusion we expect that all total cross sections will rise with energy at high energy.