Possibility of a locally, strongly increasing total cross section and related large real amplitude for anti p(p)-p scattering up to 1000 TeV

Using a new form for the diffractive amplitude, we show the possibility of a local increase above asymptotic behavior in the anti p(p)-p total cross section well up in the TeV range with values of about 180 mb reached at 100 TeV and 316 mb at 1000 TeV. Use of this locally, relatively strongly rising cross section in the dispersion relation leads to evaluation of the real to imaginary part ratio ρ, for the forward scattering amplitude up into the TeV range. This quantity increases; we obtain ρ=18% at 40 TeV. On the basis of a physical picture involving the growth of average multiplicities, it appears possible that asymptotic, bounded growth for the cross section may be reached only at collision energies in the vicinity of 1000 TeV. In this domain, certain global measures of partonic behavior come close to the behavior of the produced physical hadrons. (orig.)