In this paper we consider the Good -Walker approach for the diffractive excitation and updated the Miettinen -Pumplin (MP) model for pp/pp collisions considering the recent LHC data for the total and elastic pp cross sections. The behavior of the total, elastic and diffractive cross sections is analyzed and predictions for the energies of Run 3 of the LHC and those of the Cosmic Rays experiments are derived. Our results demonstrate that the MP model is able to describe the current data and that it implies that the cross section for the diffraction excitation in pp collisions is almost constant in the energy range probed by the LHC and slowly decreases at higher energies. Our results indicate that the Pumplin bound is not reached at the LHC and Cosmic Ray energies. Moreover, the implications of the diffractive excitation in pA collisions is discussed. In particular, the MP model, constrained by the pp data, is used to derive the main quantities present in the treatment of the diffractive excitation in pA collisions. Predictions for the total, elastic and diffractive pA cross sections are presented considering different nuclei. We demonstrate that the effect of fluctuations decreases at larger energies and heavier nuclei. The energy dependence of the diffractive excitation cross section in pA collisions is estimated for different nuclei and compared with the predictions for the proton dissociation induced by photon interactions.

The production of a quarkonium -pair in exclusive and diffractive processes in pp collisions at the LHC and FCC energies is investigated. We consider the J/ΨJ/Ψ and ΥΥ production in these processes and present predictions for the transverse momentum and rapidity distributions considering the kinematical ranges expected to be covered by central and forward detectors. Results for the cross sections are also presented. Our results indicate that the double J/Ψ production is dominated by the exclusive process, while the double Υ production receive a large contribution of the diffractive process. The impact of the modelling of the gap survival factor on our predictions is discussed.

The double quarkonium production in single and double diffractive processes is investigated considering pp collisions at the Run 2 LHC energy. Using the nonrelativistic QCD factorization formalism for the quarkonium production and the resolved Pomeron model to describe the diffractive processes, we estimate the rapidity and transverse momentum dependencies of the cross sections for the J=ΨJ=Ψ and ϒϒ production. The contributions of the color-singlet and color-octet channels are estimated, and predictions for the total cross sections in the kinematical regions of the LHC experiments are also presented. Our results demonstrate that the double quarkonium production in diffractive processes is not negligible and that its study can be useful to test the underlying assumptions present in the description of the single and double diffractive processes.