Finite-Energy Sum Rules and Evidence for Rapid Rise of πp and pp Total Gross Sections

概要

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An attempt is made to discriminate between a ln^2 s 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 A^a above the momentum k_a, which is taken in the FNAL energy range. The amplitude A^a 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) The imaginary part of the ln^2 s term of A^a is definitely positive ; ii) the predicted quantities, the total cross section above k_a and the real part of A, are consistent with the experimental data ; iii) when the determination of A^a is repeated with k_a increased, the result becomes stable. The ln^2 s proves to be much more favorable than the ln s rise for both πp and pp processes.
理論物理学刊行会の論文
1976-05-25