$π$-QCD; Proposal for Experiments at the GSI Pion Beam Facility
We propose to investigate the dynamics of hadronic matter in the strong QCD regime using the pion-beam facility at GSI in conjunction with HADES. This program will study hadron physics through elementary pion-nucleon interactions up to $\sqrt{s}\approx$2.35 GeV, bridging cold matter research with detailed analyses of exclusive reactions. Our goals include exploring baryon resonance formation and their electromagnetic structures. This will complement photo-production experiments (e.g., ELSA) and enhance our understanding of emissivity in dense, hot hadronic matter. Key topics include examining baryon couplings to mesons and virtual photons, analyzing hyperon weak decays in exclusive reactions, and using Partial Wave Analyses with differential cross sections and polarization observables to achieve unprecedented precision in baryon-meson coupling data ($ρ$N, $ω$N). Furthermore, e$^{+}$e$^{-}$ production measurements off 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 for the interpretation of results from the hot and dense environment created in $A+A$ collisions. This research also has broader implications. It will contribute to the modeling of neutrino-nucleus interactions, facilitate unprecedented investigations into hypernuclei formation, and enhance our understanding of strong interaction dynamics across different energy regimes.