Neutrino event generators: foundation, status and future

Neutrino event generators are an essential tool needed for the extraction of neutrino mixing parameters, the mass hierarchy and a CP violating phase from long-baseline experiments. In this article I first describe the theoretical basis and the approximations needed to get to present-days generators. I also discuss the strengths and limitations of theoretical models used to describe semi-inclusive neutrino-nucleus reactions. I then confront present day's generators with this theoretical basis by detailed discussions of the various reaction processes. Finally, as examples I then show for various experiments results of the generator GiBUU for lepton semi-inclusive cross sections as well as particle spectra. I also discuss features of these cross sections in terms of the various reaction components, with predictions for DUNE. Finally, I argue for the need for a new neutrino generator that respects our present-day knowledge of both nuclear theory and nuclear reactions and is as much state-of-the-art as the experimental equipment. I outline some necessary requirements for such a new generator.