Can we use asymptotic analytic amplitude analyis in the energy region 5-1800 GeV?

We make an asymptotic analytic amplitude analysis of the t=0 parameters (σtot and ρ-values) for anti pp and pp collisions, in the energy region √s=5-1800 GeV. The parameters of all fits are essentially determined by the data at ISR energies and below. We find that, with or without a maximal odderon present: (1) The best fit with log2(s/s0) dependence, does not fit the higher-energy cross-section data; (2) a log(s/s0) dependence fits all the cross-section data well, but not the UA4ρ-value at 546 GeV. Our general conclusion is that such asymptotic fits do not lend support to either a log2s behavior for the total cross-section, or to the hypothesis of an asymptotically maximal odderon. We also emphasize that in all likelihood the energy region studied is simply too low to be in 'asymptopia'. (orig.)