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White paper summarizing ideas for experiments with pion beam in the years 2026-2030.

The present proposal explores the dynamics of hadronic matter in the strong regime of Quantum Chromodynamics (QCD) through the use of the pion-beam facility at GSI in conjunction with HADES. The aim is to study hadron physics through elementary pion-nucleon interactions up to √s ≈2.35 GeV, thereby bridging research into cold matter with detailed analyses of exclusive reactions. The objectives of this programme are threefold: firstly, to explore the formation of baryon resonances and their electromagnetic structures up to the third resonance region; secondly, to complement photo-production experiments (e.g. ELSA); and thirdly, to enhance understanding of emissivity in dense, hot hadronic matter. Key topics include the study of baryon couplings to mesons and virtual photons, the analysis of hyperon weak decays in exclusive reactions, and the use of Partial Wave Analyses with differential cross sections and polarization observables to achieve unprecedented precision in baryon-meson coupling data (ρN, ωN).
Furthermore, e+e- production measurements of nucleons will provide insight into the electromagnetic transition form factors of baryons in the time-like region, revealing the role of vector mesons (ρ, ω). Reactions on nuclear targets allow for detailed studies of hadron properties, including vector-meson line shapes and strengths in cold nuclear matter. These measurements provide a critical reference between elementary π-nucleon interactions and the complex hot and dense environment in A + A collisions. The research also has broader implications, including contributions to the modelling of neutrino-nucleus interactions, facilitating unprecedented investigations into hypernuclei formation, and enhancing our understanding of strong interaction dynamics across different energy regimes.