Diffractive excitation in $pp$ and $pA$ collisions at high energies

In this paper we consider the Good - Walker approach for the diffractive excitation and updated the Miettinen -- Pumplin (MP) model for $pp/\bar{p}p$ 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.