On the basis of crossing symmetry a new set of exact relations involving theππ partial wave amplitudes have been derived, using Roskies’ amplitudes.

A model for high energy proton-proton system is developed which obeys several asymptotic bounds including Froissart bound. The amplitude taken has two parts, a Regge part and a pomeron part. The Regge part is described by the exchange degenerate pairw andP′. To calculate the pomeron part the Freund-Harari duality is invoked which states that the pomeron is dual to thes-channel background. Thes-channel background is estimated by parametrising the branch cuts inS through a conformal mapping method. Expressions for total cross-section, ratio of real-to-imaginary parts of forward amplitude and the slope parameter are presented. The corresponding quantities for$$p\tilde p$$ are also evaluated. Our analysis favours strong exchange degeneracy.

The high energy elastic scattering of pp,$$p\bar p$$, pπ⁺, pπ⁻, pk⁺ andpk⁻ processes is studied at forward directions. The expressions for total scattering cross-sections and the ratios of real-to-imaginary parts of the forward amplitude are derived inP+f model. For the Regge part of the scattering amplitude, the standard form is taken. For the pomeron part, the Harari-Freund conjecture is assumed. The background is assumed to get dominant contributions from the multiparticle exchanges in that channel. These contributions are obtained by parametrising the branch cuts by conformal mapping and polynomial expansion methods. The agreement with the experiment is good. The fits suggest strong exchange degeneracy forpp andkp which in turn is consistent with the Harari-Freund duality.