On the Role of the Subtraction Constant in Analytic Models for High Energy Forward Scattering

Analytic models for high energy forward scattering are characterized by the use of dispersion relations and parameterizations of the experimental data on total cross sections and the ρ parameter. In this communication we investigate the role played in the fit results by the subtraction constant, present in the dispersion relations. Making use of two analytic models with different asymptotic inputs and taking also into account the cosmic ray information on proton-proton cross sections at the highest energies, we show that the subtraction constant constrains the fits in both low and high energy regions.