Recent data from LHC13 by the TOTEM Collaboration indicate an unexpected decrease in the value of the $\rho$ parameter and a ${\sigma }_{\mathrm{tot}}$ value in agreement with the trend of previous measurements at 7 and 8 TeV. These data at 13 TeV are not simultaneously described by the predictions from Pomeron models selected by the COMPETE Collaboration but show agreement with the maximal Odderon dominance, as recently demonstrated by Martynov and Nicolescu. Here, we present a detailed analysis on the applicability of Pomeron dominance by means of a general class of forward scattering amplitude, consisting of even-under-crossing leading contributions associated with single, double, and triple poles in the complex angular momentum plane and subleading even and odd Regge contributions. The analytic connection between ${\sigma }_{\mathrm{tot}}$ and $\rho$ is obtained by means of singly subtracted dispersion relations, and we carry out fits to $pp$ and $\overline{p}p$ data in the interval 5 GeV–13 TeV. The data set comprises all the accelerator data below 7 TeV, and we consider two independent ensembles by adding either only the TOTEM data or the TOTEM and ATLAS data at the LHC energy region. In the data reductions to each ensemble, the uncertainty regions are evaluated with both one and two standard deviations ($\sim 68\%$ and $\sim 95\%\mathrm{CL}$, respectively). Besides the general analytic model, we investigate four particular cases of interest, three of them typical of outstanding models in the literature. We conclude that, within the experimental and theoretical uncertainties and both ensembles, the general model and three particular cases are not able to describe the ${\sigma }_{\mathrm{tot}}$ and $\rho$ data at 13 TeV simultaneously. However, if the discrepancies between the TOTEM and ATLAS data are not resolved, one Pomeron model, associated with double and triple poles and with only 7 free parameters, seems not to be excluded by the complete set of experimental information presently available.

We consider the effect of an energy-dependent dipole form factor in the high-energy behavior of the forward amplitude. The connection between the semihard parton-level dynamics and the hadron-hadron scattering is established by an eikonal QCD-based model. Our results for the proton-proton (pp) and antiproton-proton (̄pp) total cross sections, $\sigma^{pp,\bar{p}p}_{tot}(s)$, obtained using the CTEQ6L1 parton distribution function, are consistent with the recent data from the TOTEM experiment.

The LHC has released precise measurements of elastic proton-proton scattering that provide a unique constraint on the asymptotic behavior of the scattering amplitude at high energies. Recent reanalyses of part of these data indicate that the central values of some forward quantities would be different than initially observed. We introduce correlation information between the original and the reanalyzed data sets in a way suitable for a global fitting analysis of all data. The careful treatment of correlated errors leads to much less stringent limits on the $\rho$ uncertainty and sets up the stage for describing the forward data using a scattering amplitude dominated by only crossing-even terms. In the light of these correlated data, we determine the parameters of the soft Pomeron from the Regge theory. We use Born-level and eikonalized amplitudes. In the Born-level case, we estimate the contribution of the double Pomeron exchange, while in the latter case we investigate the role of the eikonalization in both the one- and two-channel models. The role of the proton-Pomeron vertex form and of the nearest $t$-channel singularity in the Pomeron trajectory receives particular attention. We discuss the implications of our results and present predictions for the total cross section and the $\rho$ parameter in proton-proton collisions at LHC and cosmic ray energies.

The role of low-xparton dynamics in dictating the high-energy behavior of forward scattering observables at LHC energies is investigated using a QCD-based model with even-under-crossing amplitude dominance at high-energies. We explore the effects of different sets of pre- and post-LHC fine-tuned parton distributions on the forward quantities $$\sigma _{tot}$$σtot and $$\rho $$ρ , fromppand $${\bar{p}}p$$p¯p scattering in the interval 10 GeV–13 TeV. We also investigate the role of the leading soft contribution, the low-energy cuttoff, and the energy dependence of the semihard form factor on these observables. We show that in all cases investigated the highly restrictive data on $$\rho $$ρ parameter at $$\sqrt{s}=13$$s=13 TeV indicate that a crossing-odd component may play a crucial role in forward elastic scattering at the highest energies, namely the Odderon contribution.

We perform the analysis of elastic scattering $pp$ and $\overline{p}p$ data at low momentum transfer $|t|<0.1{\mathrm{GeV}}^2$ within large collider energy interval $\sqrt{s}=50\mathrm{GeV}–13\mathrm{TeV}$ in order to evaluate quantitatively the possible Odderon contribution. We use the two-channel eikonal model, which naturally accounts for the screening of the Odderon amplitude by $C$-even (Pomeron) exchanges.