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.

We present an analysis of the most precise set of Hadron-Electron Ring Accelerator (HERA) data within the color dipole formalism, by using an analytical gluon density, based on the double-logarithm approximation of the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equations in the asymptotic limit of the scaling variable, $\sigma =\log (1/x)\log (\log (Q^2/Q_0^2))\to \infty$. Fits to the data, including charm and bottom quarks, are performed and demonstrate the efficiency of the model in describing the reduced cross section, ${\sigma }_r$, in the wide range $Q^2:(1.5,500){\mathrm{GeV}}^2$ for two dipole models including parton saturation effects. We also give predictions to $F_2^{c\overline{c}}$, $F_2^{b\overline{b}}$ and $F_L$, all describing the data reasonably well in the range $Q^2:(2.5,120){\mathrm{GeV}}^2$. Total cross sections of exclusive photoproduction of $J/\psi$ and $\rho$ are also calculated and successfully compared to HERA data and recent measurements at LHCb.

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.

In this paper, we review and update the Amaral-Gay Ducati-Betemps-Soyez saturation model, by testing it against the recent H1-ZEUS combined data on deep inelastic scattering, including heavy quarks in the dipole amplitude. We obtain that this model, which is based on traveling wave solutions of the Balitsky-Kovchegov equation and built in the momentum space framework, yields very accurate descriptions of the reduced cross section, ${\sigma }_r(x,y,Q^2)$, as well as DIS structure functions such as $F_2(x,Q^2)$ and $F_L(x,Q^2)$, all measured at HERA. Additionally, it provides good descriptions of heavy quark structure functions, $F_2^{cc}$ and $F_2^{bb}$ at small-$x$ and $Q^2\lesssim 60{\mathrm{GeV}}^2$. We also use the improved model to make predictions for structure functions to be measured in the near future at LHeC.

Recent results for the total and inelastic hadronic cross sections from LHC experiments are compared with predictions from a single-channel eikonal minijet model driven by parton density functions and from an empirical model. The role of soft gluon resummation in the infrared region in taming the rise of minijets and their contribution to the increase of the total cross sections at high energies are discussed. Survival probabilities at the LHC, whose theoretical estimates range from circa 10% to a few per mille, are estimated in this model and compared with results from QCD-inspired models and from multichannel eikonal models. We revisit a previous calculation and examine the origin of these discrepancies.

In this work we consider the QCD parton saturation models to describe soft interactions at the high energy limit. The total and elastic cross sections, as well as the elastic slope parameter, are obtained for proton-proton and pion-proton collisions and compared to recent experimental results. The analyses are done within the color dipole formalism, taking into account saturation models which have been tested against deep inelastic scattering data. The main point is that the matching between soft and hard interaction occurs in the saturation region which can be described by high density QCD approaches. Discussion is performed on the main theoretical uncertainties associated with calculations.