Critical analysis of derivative dispersion relations at high energies

We discuss some formal and fundamental aspects related with the replacement of integral dispersion relations by derivative forms, and their practical uses in high energy elastic hadron scattering. Starting with integral relations with one subtraction and after using, as a framework, the Donnachie-Landshoff parametrization for the total cross sections on pp and p(bar)p scattering, a series of results is deduced and our main conclusions are the following: (1) except for the subtraction constant, the derivative forms do not depend on any additional free parameter; (2) the only approximation in going from integral to derivative relations (at high energies) concerns to assume as zero the lower limit in the integral form; (3) the subtraction constant affects the fit results at both low and high energies and therefore can not be disregarded; (4) from a practical point of view, for center-of-mass energies above 5 GeV, the derivative relations with the subtraction constant as a free fit parameter are completely equivalent to the integral forms with finite (non-zero) lower limit