Analytic Amplitude Models for Forward Scattering

We report on fits of a large class of analytic amplitude models for forward scattering against the comprehensive data for all available reactions. To differentiate the goodness of the fits of many possible parametrizations to a large sample of data, we developed and used a set of quantitative indicators measuring statistical quality of the fits over and beyond the typical criterion of the $\Chi^2 /dof$. These indicators favor models with a universal $ log^2 s$ Pomeron term, which enables one to extend the fit down to $\sqrt s = 4$ GeV.