Calorimetric analysis for long-baseline neutrino experiments

In neutrino long-baseline experiments the energy of the incoming neutrino must be reconstructed from observations of the final state. We first discuss the problems that arise for energy conservation during the final-state interactions in a momentum-dependent potential. We then show, for the example of the Deep Underground Neutrino Experiment, that the presence of such a potential is necessarily connected with a large uncertainty in the reconstructed energy. This same uncertainty also affects the determination of energy- and four-momentum transfers in neutrino-nucleus reactions. We analyze the origins of these uncertainties using transport theory for the description of the evolution of the final state of the reaction. We show that the spectral functions of target nuclei play an essential role not only for the initial neutrino-nucleon interaction but also for the final state evolution.