In a well-established many-body framework, successful in modeling a great variety of nuclear processes, we analyze the role of the spectral functions (SFs) accounting for the modifications of the dispersion relation of nucleons embedded in a nuclear medium. We concentrate in processes mostly governed by one-body mechanisms, and study possible approximations to evaluate the particle-hole propagator using SFs. We also investigate how to include together SFs and long-range RPA-correlation corrections in the evaluation of nuclear response functions, discussing the existing interplay between both type of nuclear effects. At low energy transfers (≤ 50 MeV), we compare our predictions for inclusive muon and radiative pion captures in nuclei, and charge-current (CC) neutrino-nucleus cross sections with experimental results. We also present an analysis of intermediate energy quasi-elastic neutrino scattering for various targets and both neutrino and antineutrino CC driven processes. In all cases, we pay special attention to estimate the uncertainties affecting the theoretical predictions. In particular, we show that errors on the σµ/σe ratio are much smaller than 5%, and also much smaller than the size of the SF+RPA nuclear corrections, which produce significant effects, not only in the individual cross sections, but also in their ratio for neutrino energies below 400 MeV. These latter nuclear corrections, beyond Pauli blocking, turn out to be thus essential to achieve a correct theoretical understanding of this ratio of cross sections of interest for appearance neutrino oscillation experiments. We also briefly compare our SF and RPA results to predictions obtained within other representative approaches.

The study of pion production in nuclei is important for signal and background determinations in current and future neutrino oscillation experiments. The first step, however, is to understand the pion production reactions at the free nucleon level. We present an exhaustive study of the chargedcurrent and neutral-current neutrino and antineutrino pion production off nucleons, paying special attention to the angular distributions of the outgoing pion. We show, using general arguments, that parity violation and time-reversal odd correlations in the weak differential cross sections are generated from the interference between different contributions to the hadronic current that are not relatively real. Next, we present a detailed comparison of three, state of the art, microscopic models for electroweak pion production off nucleons, and we also confront their predictions with polarized electron data, as a test of the vector content of these models. We also illustrate the importance of carrying out a comprehensive test at the level of outgoing pion angular distributions, going beyond comparisons done for partially integrated cross sections, where model differences cancel to a certain extent. Finally, we observe that all charged and neutral current distributions show sizable anisotropies, and identify channels for which parity-violating effects are clearly visible. Based on the above results, we conclude that the use of isotropic distributions for the pions in the center of mass of the final pion-nucleon system, as assumed by some of the Monte Carlo event generators, needs to be improved by incorporating the findings of microscopic calculations.

We present a study of the τ polarization in charged-current quasielastic (anti)neutrino-nucleus scattering. The spectral function formalism is used to compute the differential cross section and the polarization components for several kinematical setups, relevant for neutrino-oscillation experiments. The effects of the nuclear corrections in these observables are investigated by comparing the results obtained using two different realistic spectral functions, with those deduced from the relativistic global Fermi gas model, where only statistical correlations are accounted for. We show that the spectral functions, although they play an important role when predicting the differential cross sections, produce much less visible effects on the polarization components of the outgoing τ .PACS numbers: 13.15.+g,13.60.r arXiv:1906.05656v1 [nucl-th]