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A novel mechanism of H0 and strangelet production in hadronic interactions within the Gribov-Regge approach is presented. In contrast to traditional distillation approaches, here the production of multiple (strange) quark bags does not require large baryon densities or a QGP. The production cross section increases with center of mass energy. Rapidity and transverse momentum distributions of the H 0 are predicted for pp collisions at E_lab = 160 AGeV (SPS) and \sqrt s = 200 AGeV (RHIC). The predicted total H 0 multiplicities are of order of the Omega-baryon yield and can be accessed by the NA49 and the STAR experiments.

We discuss in some detail the physics content of the new model, QGSJET-III-01, focusing on major problems related to the treatment of semihard processes in the very high energy limit. A special attention has been payed to the main improvement, compared to the QGSJET-II model, which is related to a phenomenological treatment of leading power corrections corresponding to final parton rescattering off soft gluons. In particular, this allowed us to use a twice smaller separation scale between the soft and hard parton physics, compared to the previous model version, QGSJET-II-04. Preliminary results obtained with the new model are also presented.

I review the state-of-the-art concerning the treatment of high energy cosmic ray interactions in the atmosphere, discussing in some detail the underlying physical concepts and the possibilities to constrain the latter by current and future measurements at the Large Hadron Collider. The relation of basic characteristics of hadronic interactions tothe properties of nuclear-electromagnetic cascades induced by primary cosmic rays in the atmosphere is addressed.

We apply the phenomenological Reggeon field theory framework to investigate rapidity gap survival (RGS) probability for diffractive dijet production in proton–proton collisions. In particular, we study in some detail rapidity gap suppression due to elastic rescatterings of intermediate partons in the underlying parton cascades, described by enhanced (Pomeron–Pomeron interaction) diagrams. We demonstrate that such contributions play a subdominant role, compared to the usual, so-called “eikonal”, rapidity gap suppression due to elastic rescatterings of constituent partons of the colliding protons. On the other hand, the overall RGS factor proves to be sensitive to color fluctuations in the proton. Hence, experimental data on diffractive dijet production can be used to constrain the respective model approaches.

The KASCADE-Grande experiment has significantly contributed to the current knowledge about the energy spectrum and composition of cosmic rays for energies between the knee and the ankle. Meanwhile, post-LHC versions of the hadronic interaction models are available and used to interpret the entire data set of KASCADE-Grande. In addition, a new, combined analysis of both arrays, KASCADE and Grande, was developed significantly increasing the accuracy of the shower observables. First results of the new analysis with the entire data set of the KASCADE-Grande experiment will be the focus of this contribution.

The differences between contemporary Monte Carlo generators of high energy hadronic interactions are discussed and their impact on the interpretation of experimental data on ultra-high energy cosmic rays (UHECRs) is studied. Key directions for further model improvements are outlined. The prospect for a coherent interpretation of the data in terms of the UHECR composition is investigated.

Predictions of popular cosmic ray interaction models for some basic characteristics of cosmic ray-induced extensive air showers are analyzed in view of experimental data on proton-proton collisions, obtained at the Large Hadron Collider. The differences between the results are traced down to different approaches for the treatment of hadronic interactions, implemented in those models. Potential measurements by LHC and cosmic ray experiments, which could be able to discriminate between the alternative approaches, are proposed.

Steep rise of parton densities in the limit of small parton momentum fraction x poses a challenge for describing the observed energy-dependence of the total and inelastic proton-proton cross sections σtot/inelpp : considering a realistic parton spatial distribution, one obtains a too-strong increase of σtot/inelpp in the limit of very high energies. We discuss various mechanisms which allow one to tame such a rise, paying special attention to the role of parton-parton correlations. In addition, we investigate a potential impact on model predictions for σtotpp, related to dynamical higher twist corrections to parton-production process.