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, in particular pp and pˉp
scattering. Starting with integral relations with one subtraction and
considering parametrizations for the total cross sections belonging to the
class of entire functions in the logarithm of the energy, 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 previous approximation and the subtraction constant
affect the fit results at both low and high energies and therefore, the
subtraction constant can not be disregarded; (4) from a practical point of
view, for single-pole Pomeron and secondary reggeons parametrizations and
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. A detailed review on the
conditions of validity and assumptions related with the replacement of integral
by derivative relations is also presented and discussed.Comment: Revised version, 30 pages, 16 eps-figures, elsart.cls (included), to
appear in Nucl Phys.
