Neutrino generators: Foundation, Status and Future.

Neutrino generators are an essential tool needed for the extraction of neutrino mixing parameters, the mass hierarchy and a possibly CP violating phase from long-baseline experiments. In this article I first describe in quite general terms the theoretical basis and the approximations needed to get to present-days generators. I then confront present day's generators with this theoretical basis by detailed discussions of the various reaction processes. I also discuss the strengths and limitations of theoretical models used to describe semi-inclusive neutrino-nucleus reactions. As examples I then show results of the generator GiBUU for lepton semi-inclusive cross sections as well as particle spectra and discuss some features of these cross sections in terms of the various reaction components. 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 I outline some necessary requirements for such a generator.