Pion-nucleus reference measurements with HADES for precision neutrino physics

Pion beams are important tools to study features of baryonic resonances and pion-nucleus dynamics. In 2014 the HADES collaboration has performed an experiment using the π- + C reaction at a momentum range of 0.61 - 0.8 GeV/c. This measurement provides a first insight on the π-nucleon dynamics in the energy range of the second resonance region (√s ∼ 1.5 GeV). At the momentum of 0.7 GeV/c measurements of protons and charged pions were provided in various inclusive and semi-inclusive exit channels (pπ±,pp,π+π-,pπ+π-,ppπ-...) and compared to predictions of the transport (SMASH,JAM2/RQMD.RMF, GIBUU) and the INCL++ cascade models. The results allow to test very selectively various reaction mechanisms like quasi-elastic, pion absorption or rescattering effects. This energy range is also in scope of interest of the next generation Long Base Line (LBL) neutrino experiments (Hyper-K, DUNE). To study such effects like CP violation or the neutrino mass hierarchy, the reduction of systematic errors, related to the modeling of the neutrino-nucleus interactions, used to reconstruct the neutrino energy, is the key issue. In this talk, I will try to explain how the input from hadron physics, specifically from HADES, can be apply in LBL neutrino experiments to extract precise oscillation parameters.