We present a theory of neutrino interactions with nuclei aimed at the description of the partial cross sections, namely quasielastic and multinucleon emission, coherent and incoherent single-pion production. For this purpose, we use the theory of nuclear responses treated in the random-phase approximation, which allows a unified description of these channels. It is particularly suited for the coherent pion production where collective effects are important, whereas they are moderate in the other channels. We also study the evolution of the neutrino cross sections with the mass number from carbon to calcium. We compare our approach to the available neutrino experimental data on carbon. We put a particular emphasis on the multinucleon channel, which at present is not easily distinguishable from the quasielastic events. This component turns out to be quite relevant for the interpretation of experiments (K2K, MiniBooNE, SciBooNE). It can account in particular for the unexpected behavior of the quasielastic cross section.

We investigate the interaction of neutrinos and antineutrinos with nuclei. We explore, in particular, the role played by multinucleon excitations, which can contaminate the quasielastic cross section. For neutrinos the multinucleon term produces a sizable increase in the quasielastic cross section. Part of the effect arises from tensor correlations. For antineutrinos this influence is smaller, owing to the axial-vector interference, which increases the relative importance of the terms that are not affected by these multinucleon excitations.

Neutrino oscillations physics is entering an era of high precision. In this context, accelerator-based neutrino experiments need a reduction in systematic errors to the level of a few percent. Today, one of the most important sources of systematic errors are neutrino–nucleus cross sections which, in the energy region of hundreds of MeV to a few GeV, are known to a precision not exceeding 20%. In this article we review the present experimental and theoretical knowledge of neutrino–nucleus interaction physics. After introducing neutrino-oscillation physics and accelerator-based neutrino experiments, we give an overview of general aspects of neutrino–nucleus cross sections, from both the theoretical and experimental point of view. Then, we focus on these cross sections in different reaction channels. We start with the quasi-elastic and quasi-elastic-like cross section, placing a special emphasis on the multinucleon emission channel, which has attracted a lot of attention in the last few years. We review the main aspects of the different microscopic models for this channel by discussing analogies and the differences among them. The discussion is always driven by a comparison with the experimental data. We then consider the one-pion production channel where agreement between data and theory remains highly unsatisfactory. We describe how to interpret pion data, and then analyze, in particular, the puzzle related to the difficulty of theoretical models and Monte Carlo to simultaneously describe MiniBooNE and MINERvA experimental results. Inclusive cross sections are also discussed, as well as the comparison between the ν μ and ν e cross sections, relevant for the charge-conjugation-parity violation experiments. The impact of nuclear effects on the reconstruction of neutrino energy and on the determination of the neutrino-oscillation parameters is also reviewed. Finally, we look to the future by discussing projects and efforts in relation to future detectors, beams, and analysis.

We investigate the double differential neutrino-carbon quasielastic cross sections as measured by the MiniBooNE experiment. Our present treatment incorporates relativistic corrections in the nuclear response functions and includes the multinucleon component. We confirm our previous conclusion that it is possible to account for all the data without any modification of the axial mass. We also introduce the $Q^2$ distribution for charged and neutral current. The data point at a sizable multinucleon component beside the genuine quasielastic peak. They are also indicative of the collective character of the nuclear response, of interest for hadronic physics.

We discuss the accuracy of the usual procedure for neutrino energy reconstruction which is based on the quasielastic kinematics. Our results are described in terms of a probability distribution for a real neutrino energy value. Several factors are responsible for the deviations from the reconstructed value. The main one is the multinucleon component of the neutrino interaction which in the case of Cherenkov detectors enters as a quasielastic cross section, increasing the mean neutrino energy which can differ appreciably from the reconstructed value. As an application we derive, for excess electron events attributed to the conversion of muon neutrinos, the true neutrino energy distribution based on the experimental one which is given in terms of the reconstructed value. The result is a reshaping effect. For MiniBooNE the low energy peak is suppressed and shifted at higher energies, which may influence the interpretation in terms of oscillation. For T2K at the Super Kamiokande far detector the reshaping translates into a narrowing of the energy distribution.