Implications from analyticity constraints used in a Landshoff-Donnachie fit

Landshoff and Donnachie[hep-ph/0509240, (2005)] parametrize the energy behavior of pp and p\bar p scattering cross sections with five parameters, using: \sigma^+=56.08 s^{-0.4525}+21.70s^{0.0808} for pp, \sigma^-=98.39 s^{-0.4525}+21.70s^{0.0808} for p\bar p. Using the 4 analyticity constraints of Block and Halzen[M. M. Block and F. Halzen, Phys. Rev. D {\bf 72}, 036006 (2005)], we simultaneously fit the Landshoff-Donnachie form to the same ``sieved'' set of pp and p\bar p cross section and \rho data that Block and Halzen used for a very good fit to a ln^2 s parametrization. We show that the satisfaction of the analyticity constraints will require complicated modifications of the Landshoff-Donnachie parametrization for lower energies, greatly altering its inherent appeal of simplicity and universality.