Integral and derivative dispersion relations, analysis of the forward scattering data

Abstract

Integral and derivative dispersion relations (DR) are considered for the forward scattering $pp$ and $\bar{p}p$ amplitudes. A new representation for the derivative DR, valid not only at high energy, is obtained. The data on the total cross sections for $pp(\bar{p}p)$ interaction as well as the data on the parameter $\rho$ are analyzed within the various forms of the DR and high-energy Regge models. It is shown that three models for the Pomeron, Simple pole Pomeron, Tripole Pomeron and Dipole Pomeron (the both with the intercept equal unit) lead to practically equivalent description of the data at $\sqrt{s}>$5 GeV. It is also shown that the correctly calculated low-energy part of the dispersion integral (from the two-proton threshold up to $\sqrt{s}=$5 GeV) allows to reproduce well the $\rho$ data at low energies without additional free parameters.

Comments: LaTeX, 3 pages, 2 eps figures, talk presented by E. Martynov at the International Europhysics Conference on High Energy Physics (HEP 2003), 17-23 July 2003, Aachen, Germany