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An analysis of p-air cross section data from Extensive Air Shower (EAS) measurements is presented, based on an analytical representation of the pp scattering amplitudes that describes with high precision all available accelerator data at ISR, SPS and LHC energies. The theoretical basis of the representation, together with the very smooth energy dependence of parameters controlled by unitarity and dispersion relations, permits reliable extrapolation to high energy cosmic ray and asymptotic energy ranges. Calculations of the p-air production cross section based on Glauber formalism are made using the input values of the pp forward scattering parameters at high energies, with attention given to the independence of the real and imaginary slope parameters. The influence of contributions of diffractive intermediate states, according to Good-Walker formalism, is examined. The comparison with cosmic ray data is very satisfactory in the whole pp energy interval from 1 to 100 TeV. High energy asymptotic behavior of p-air cross sections is investigated in view of the geometric scaling property of the pp amplitudes. The observed energy dependence of the ratio between p-air and pp cross sections in the data is shown to be related to the nature of the pp cross section at high energies, that does not agree with the black disk image.
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We make some educated guesses for the extrapolations of typical soft-inclusive (minimum-bias, pileup, underlying-event) observables to proton-proton collisions at center-of-mass energies in the range 13 - 100 TeV. The numbers should be interpreted with (at least) a 10% uncertainty.
The hadron inclusive spectra in pp collisions at high energies are analyzed within a soft QCD model, namely the quark-gluon string model. In addition to the sea quark distribution in the incoming proton we consider also the unintegrated gluon distribution that has an increasing behaviour when the gluon transverse momentum grows. It leads to an increase of the inclusive spectra of hadrons and their multiplicity in the central rapidity region of pp collision at LHC energies.
We argue that the increase of the ratio baryon/meson due to the presence of strong colour fields and percolation in ultra-high energy hadronic collisions, helps to explain some of the global features of ultra-high energy cosmic ray cascades at E>10^18 eV and, in particular the observed excess in the number of muons with respect to current models of hadronic interactions. A reasonable agreement with the small value and slope of the average depth of shower maximum Xmax vs shower energy -- as seen in data collected at the Pierre Auger Observatory -- can be obtained with a fast increase of the p-Air production cross-section compatible with the Froissart bound.
We compute the leading-order evolution of parton distribution functions for all the Standard Model fermions and bosons up to energy scales far above the electroweak scale, where electroweak symmetry is restored. Our results include the 52 PDFs of the unpolarized proton, evolving according to the SU(3), SU(2), U(1), mixed SU(2) x U(1) and Yukawa interactions. We illustrate the numerical effects on parton distributions at large energies, and show that this can lead to important corrections to parton luminosities at a future 100 TeV collider.
A phenomenological model for the description of the single and double diffractive excitation in $pp$ collisions at high energies is presented. Considering the Good -- Walker approach, we propose a model for the eigenstates of the scattering operator and for the treatment of the interaction between them, with the high energy behavior of the cross section driven by perturbative QCD. The behavior of the total, elastic, single and double diffractive cross sections are analyzed and predictions for the energies of Run 3 of the LHC and those of the Cosmic Rays experiments are derived. We demonstrate that the model describes the current data for the energy dependence of the cross sections. A comparison with the recent data for the $rho$ parameter and the differential elastic cross section are also presented and shortcomings of the current model are discussed.
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