Models for total, elastic and diffractive cross sections

The LHC has brought much new information on total, elastic and diffractive cross sections, which is not always in agreement with extrapolations from lower energies. The default framework in the Pythia event generator is one case in point. In this article we study and implement two recent models, as more realistic alternatives. Both describe total and elastic cross sections, whereas one also includes single diffraction. Noting some issues at high energies, a variant of the latter is proposed, and extended also to double and central diffraction. Further, the experimental definition of diffraction is based on the presence of rapidity gaps, which however also could be caused by colour reconnection in nondiffractive events, a phenomenon that is studied in the context of a specific model. Throughout comparisons with LHC and other data are presented.