The Bloch-Nordsieck model for the parton distribution of hadrons in impact parameter space, constructed using soft gluon summation, is investigated in detail. Its dependence upon the infrared structure of the strong coupling constant and proton-antiproton cross-sections, where screening, due to soft gluon emission from the initial valence quarks, becomes evident

Very precise data on elastic proton-proton scattering at $\sqrt{s}=7$, 8 and 13 TeV have been obtained by the TOTEM group at LHC in the near-forward region (momentum transfers down to $|t|=6\times {10}^{-4}{\mathrm{GeV}}^2$ at $\sqrt{s}=8$ and 13 TeV). The Coulomb-nuclear interference has been measured with sufficient accuracy for TOTEM to establish the falloff of the $\rho$ parameter with increasing energy. The predictions from a previously studied model are shown to be in good agreement with the data and thus allow us to draw rather firm conclusions about the structure of the near-forward nuclear amplitude. We point out that due to a zero in the real part of the nuclear amplitude occurring at a very small momentum transfer—that can migrate into the Coulomb-nuclear interference (CNI) region at higher energies—much care is needed in extracting the numerical value of $\rho$ for such energies. Thus, the true value of $\rho$ would be higher than the TOTEM value for $\rho$ found under the hypothesis that the real part of the elastic nuclear amplitude is devoid of such a zero in the CNI region.

We show that the onset and rise of QCD minijets provide the dynamical mechanism behind the appearance of a soft edge in $pp$ collisions around CERN intersecting storage rings (ISR) energies, and thus such a soft edge is built in our minijet model with soft gluon resummation. Here the model is optimized for the LHC at $\sqrt{s}=7$, 8 TeV and predictions made for higher LHC and cosmic ray energies. Further, we provide a phenomenological picture to discuss the breakup of the total cross section into its elastic, uncorrelated, and correlated inelastic pieces in the framework of a one-channel eikonal function.

The dynamic Casimir effect, which concerns two photon radiation processes due to time dependent frequency modulations, is computed in the one photon loop approximation. An instability is signaled by the production of an unphysically large number of photons. We show how it is tamed and a saturation in the number of photons reached through higher order processes. Explicit results are obtained for a recently proposed experiment.