Recent data from LHC13 by the TOTEM Collaboration on $sigma_{tot}$ and $rho$ have indicated disagreement with all the Pomeron model predictions by the COMPETE Collaboration (2002). On the other hand, as recently demonstrated by Martynov and Nicolescu (MN), the new $sigma_{tot}$ datum and the unexpected decrease in the $rho$ value are well described by the maximal Odderon dominance at the highest energies. Here, we discuss the applicability of Pomeron dominance through fits to the textit{most complete set} of forward data from $pp$ and $bar{p}p$ scattering. We consider an analytic parametrization for $sigma_{tot}(s)$ consisting of non-degenerated Regge trajectories for even and odd amplitudes (as in the MN analysis) and two Pomeron components associated with double and triple poles in the complex angular momentum plane. The $rho$ parameter is analytically determined by means of dispersion relations. We carry out fits to $pp$ and $bar{p}p$ data on $sigma_{tot}$ and $rho$ in the interval 5 GeV - 13 TeV (as in the MN analysis). Two novel aspects of our analysis are: (1) the dataset comprises all the accelerator data below 7 TeV and we consider textit{three independent ensembles} by adding: either only the TOTEM data (as in the MN analysis), or only the ATLAS data, or both sets; (2) in the data reductions to each ensemble, uncertainty regions are evaluated through error propagation from the fit parameters, with 90 % CL. We argument that, within the uncertainties, this analytic model corresponding to soft Pomeron dominance, does not seem to be excluded by the textit{complete} set of experimental data presently available.
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