We develop a model for the weak pion production off the nucleon, which besides the Delta pole mechanism (weak excitation of the ∆(1232) resonance and its subsequent decay into N π), includes also some background terms required by chiral symmetry. We re-fit the C A 5 (q 2 ) form factor to the flux averaged νµp → µ − pπ + ANL q 2 −differential cross section data, finding a substantially smaller contribution of the Delta pole mechanism than traditionally assumed in the literature. Within this scheme, we calculate several differential and integrated cross sections, including pion angular distributions, induced by neutrinos and antineutrinos and driven both by charged and neutral currents. In all cases we find that the background terms produce quite significant effects and that they lead to an overall improved description of the data, as compared to the case where only the Delta pole mechanism is considered. We also show that the interference between the Delta pole and the background terms produces parity-violating contributions to the pion angular differential cross section, which are intimately linked to T −odd correlations in the contraction between the leptonic and hadronic tensors. However, these latter correlations do not imply a genuine violation of time reversal invariance because of the existence of strong final state interaction effects.

The Quasi-Elastic (QE) contribution of the nuclear inclusive electron scattering model developed in Ref.[1] is extended to the study of electroweak Charged Current (CC) induced nuclear reactions, at intermediate energies of interest for future neutrino oscillation experiments. The model accounts for, among other nuclear effects, long range nuclear (RPA) correlations, Final State Interaction (FSI) and Coulomb corrections. Predictions for the inclusive muon capture in 12 C and the reaction 12 C (νµ, µ − )X near threshold are also given. RPA correlations are shown to play a crucial role and their inclusion leads to one of the best existing simultaneous description of both processes, with accuracies of the order of 10-15% per cent for the muon capture rate and even better for the LSND measurement.

We have developed a model for neutrino-induced coherent pion production off nuclei in the energy regime of interest for present and forthcoming neutrino oscillation experiments. It is based on a microscopic model for pion production off the nucleon that, besides the dominant ∆ pole contribution, takes into account the effect of background terms required by chiral symmetry. Moreover, the model uses a reduced nucleon-to-∆ resonance axial coupling, which leads to coherent pion production cross sections around a factor two smaller than most of the previous theoretical estimates. In the coherent production, the main nuclear effects, namely medium corrections on the ∆ propagator and the final pion distortion, are included. We have improved on previous similar models by taking into account the nucleon motion and employing a more sophisticated optical potential. As found in previous calculations the modification of the ∆ self-energy inside the nuclear medium strongly reduces the cross section, while the final pion distortion mainly shifts the peak position to lower pion energies. The angular distribution profiles are not much affected by nuclear effects. Nucleon motion increases the cross section by ∼ 15% at neutrino energies of 650 MeV, while Coulomb effects on charged pions are estimated to be small. Finally, we discuss at length the deficiencies of the Rein-Sehgal pion coherent production model for neutrino energies below 2 GeV, and in particular for the MiniBooNE and T2K experiments. We also predict flux averaged cross sections for these two latter experiments and K2K.

The N ∆ axial form factors are determined from neutrino induced pion production ANL & BNL data by using a state of the art theoretical model, which accounts both for background mechanisms and deuteron effects. We find violations of the off diagonal Goldberger-Treiman relation at the level of 2σ which might have an impact in background calculations for T2K and MiniBooNE low energy neutrino oscillation precision experiments.PACS numbers: 25.30. Pt,13.15.+g The ∆(1232) resonance is the lightest baryonic excitation of the nucleon. In addition, it couples very strongly to the lightest meson, the pion, and to the photon. As a consequence, the ∆(1232) is of the utmost importance in the description of a wide range of hadronic and nuclear phenomenology going from low and intermediate energy processes [1, 2] to the GZK cut-off of the cosmic ray flux [3,4]. On the other hand, despite its large width, it is well separated from other resonances what facilitates its experimental investigation. In particular, the electromagnetic nucleon to ∆(1232) excitation processes, induced by electrons and photons, have been extensively studied at many experimental facilities like LEGS, BATES, ELSA, MAMI, and J-LAB. For a recent review see Ref. [5], where also many of the recent theoretical advances in the understanding of the resonance have been addressed.There has also been a great theoretical interest in the axial nucleon ∆ transition form factors. Recently, they have been studied using quark models [6], Light Cone QCD Sum Rules [7], Lattice QCD [8] and Chiral Perturbation Theory (χPT) [9,10]. These form factors are of topical importance in the background analysis of some of the neutrino oscillation experiments (e.g. [11]). However, their experimental knowledge is less than satisfactory. Although the feasibility of their extraction in parityviolating electron scattering has been considered [12], the best available information comes from old bubble chamber neutrino scattering experiments at ANL [13,14] and BNL [15,16]. These experiments measured pion production in deuterium at relatively low energies where the dominant contribution is given by the ∆ pole (∆P ) mechanism: weak excitation of the ∆(1232) resonance and its subsequent decay into N π. Only very recently, π 0 production cross sections have been measured at low neutrino energies and with good statistics [17]. However, the target was mineral oil what implies large and difficult to disentangle nuclear effects. Thus, these data are less well suited for the extraction of the N ∆ axial form factors.Besides the original experimental publications, there are many studies of the ANL and/or the BNL data in the literature [18][19][20][21][22][23] with different advantages and shortcomings. Some of those studies are discussed below. In this letter, we analyze the ANL and BNL data incorporating the deuteron effects, with a proper consideration of statistical and systematical uncertainties and taking advantage of several recent developments: improved vector form factors and a new model fo...