Abstract
An attempt is made to discriminate between a ln2s and a ln s rise of πp and pp total cross sections. The crossing-even forward amplitudes A are parametrized in terms of an asymptotic form Aa above the momentum ka, which is taken in the FNAL energy range. The amplitude Aa is determined by means of a set of finite-energy sum rules, and its uncertainties are estimated in relation to experimental errors of the total cross-section data used in the sum rules. The criteria of the discrimination are: i) Te imaginary part of the ln2s term of Aa is definitely positive; ii) the predicted quantities, the total cross section above ka and the real part of A, are consistent with the experimental data; iii) when the determination of Aa is repeated with ka increased, the result becomes stable. The ln2s rise proves to be much more favorable than the ln s rise for both πp and pp processes.
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