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Telescope Array (TA) has completed analysis of nearly nine years of data measuring the atmospheric depth of air shower maximum ($X_{\textrm{max}}$) utilizing the TA surface detector array and the Black Rock Mesa and Long Ridge fluorescence…
Great advances have been made in the study of ultra-high energy cosmic rays (UHECR) in the past two decades. These include the discovery of the spectral cut-off near 5 x 10^19 eV and complex structure at lower energies, as well as…
We discuss that hadron-induced atmospheric air showers from ultra-high energy cosmic rays are sensitive to QCD interactions at very small momentum fractions x where nonlinear effects should become important. The leading partons from the…
The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description…
The predictions of hadronic interaction models for cosmic-ray induced air showers contain inherent uncertainties due to limitations of available accelerator data. This leads to differences in shower simulations using each of those models.…
We extend a quantum kinetic approach to the description of hadronic showers in space, time and momentum space to deep-inelastic $ep$ collisions, with particular reference to experiments at HERA. We follow the history of hard scattering…
Very high energy cosmic rays are typically studied by measuring extensive air showers formed by secondary particles produced in collisions with air nuclei. The indirect character of the measurement makes the physics interpretation of cosmic…
The analytical representation of the longitudinal hadronic shower development from the face of a calorimeter is presented and compared with experimental data. The suggested formula is particularly useful at designing, testing and…
In the past decade the observation of cross section modification for leading hadrons, heavy flavor and two particle correlations in heavy ion collisions has provided important insights into the dynamics of parton propagation in dense…
The present status of high energy cosmic ray interaction models is discussed, concentrating on recent model updates inspired by the data from Run 1 of the LHC. A special attention is devoted to the remaining differences in the model…
In these lectures, we present and discuss the most recent results on inclusive diffraction from the HERA and Tevatron colliders and give the prospects for the future at the LHC. Of special interest is the exclusive production of Higgs boson…
The detection of extensive air showers (EAS) induced by cosmic rays via radio signals has undergone significant advancements in the last two decades. Numerous ultra-high energy cosmic ray experiments routinely capture radio pulses in the…
We evaluate the consistency of hadronic interaction models in the CORSIKA simulation package with publicly available fluorescence telescope data from the Pierre Auger Observatory. By comparing the first few central moments of the extended…
We discuss HERA data on the high energy behavior of the total gamma*p cross section and on diffraction in deep inelastic scattering. We outline their novelty in comparison with diffraction in high energy hadron hadron scattering. As a…
Proton-proton collisions at the LHC can be classified as elastic, non-diffractive, and diffractive. In this paper we discuss various measurements of these above processes at various LHC experiments. We report about the total proton-proton…
Hadronic cross sections at ultra-high energy have a significant impact on the development of extensive air shower cascades. Therefore the interpretation of air shower data depends critically on hadronic interaction models that extrapolate…
Mass composition is important for understanding the origin of ultra-high-energy cosmic rays. However, interpretation of mass composition from air shower experiments is challenging, owing to significant uncertainty in hadronic interaction…
We study basic characteristics of distributions of the depths of shower maximum in air showers caused by cosmic rays with the highest energies. The consistency between their average values and widths, and their energy dependences are…
The properties of cosmic rays with energies above 10**6 GeV have to be deduced from the spacetime structure and particle content of the air showers which they initiate. In this review we summarize the phenomenology of these giant air…
In this article, I will review how observations performed with extensive air showers are being used to probe hadronic interactions at high energy. I will briefly overview the new studies exploring the connection between the dynamics of air…