Structure of Forward pp and pp Elastic Amplitudes at Low Energies

Abstract

Exact analytical forms of solutions for Dispersion Relations for Amplitudes and Dispersion Relations for Slopes are applied in the analysis of pp and $\rm {p \bar p}$ scattering data in the forward range at energies below $\sqrt(s)\approx 30 \GeV$. As inputs for the energy dependence of the imaginary part, use is made of analytic form for the total cross sections and for parameters of the $t$ dependence of the imaginary parts, with exponential and linear factors. A structure for the $t$ dependence of the real amplitude is written, with slopes $B_R$ and a linear factor $ρ-μ_R t$ that allows compatibility of the data with the predictions from dispersion relations for the derivatives of the real amplitude at the origin. A very precise description is made of all $dσ/dt$ data, with regular energy dependence of all quantities. It is shown that a revision of previous calculations of total cross sections, slopes and $ρ$ parameters in the literatures is necessary, and stressed that only determinations based on $dσ/dt$ data covering sufficient $t$ range using appropriate forms of amplitudes can be considered as valid.