A comparative study on some representative parametrizations for the total and elastic cross-sections as a function of energy is presented .
The dataset comprises pp and \bar { p } p scattering in the c.m energy interval 5 GeV - 8 TeV .
The parametrization for the total cross-section at low and intermediate energies follows the usual reggeonic structure ( non-degenerate trajectories ) .
For the leading high-energy pomeron contribution , we consider three distinct analytic parametrizations : either a power ( P ) law , or a log-squared ( L 2 ) law or a log-raised-to- \gamma ( L \gamma ) law , where the exponent \gamma is treated as a real free fit parameter .
The parametrizations are also extended to fit the elastic ( integrated ) cross-section data in the same energy interval .
Our main conclusions are the following : ( 1 ) the data reductions with the logarithmic laws show strong dependence on the unknown energy scale involved , which is treated here either as a free parameter or fixed at the energy threshold ; ( 2 ) the fit results with the P law , the L 2 law ( free scale ) and the L \gamma law ( fixed scale and exponent \gamma above 2 ) are all consistent within their uncertainties and with the experimental data up to 7 TeV , but they partially underestimate the high-precision TOTEM measurement at 8 TeV ; ( 3 ) once compared with these results , the L 2 law with fixed scale is less consistent with the data and , in the case of a free scale , this pomeron contribution decreases as the energy increases below the scale factor ( which lies above the energy cutoff ) ; ( 4 ) in all cases investigated , the predictions for the asymptotic ratio between the elastic and total cross-sections , within the uncertainties , do not exceed the value 0.430 ( therefore , below the black-disc limit ) and the results favor rational limits between 1/3 and 2/5 .
We are led to conclude that the rise of the hadronic cross-sections at the highest energies still constitutes an open problem , demanding further and detailed investigation .