Electromagnetic interaction of baryon resonances from pion- nucleon collisions Miklós Zétényi Wigner RCP Zimányi School 2020 Dileptons in Heavy-ion collisions • Electromagnetic probes (후, e+e-): penetrate out from the dense phase • BUT: they are created in all stages of the reaction in many different processes • even for ultrarelativistic HIC, a hadron gas phase is always there • need for Hadronic Transport models • hadron reactions in vacuum should be known • In the hadron gas phase many nucleons are excited to baryon resonance states Vector Meson Dominance • Electromagnetic interaction of hadrons • Neutral vector mesons have the same quantum numbers as photons --> they can mediate E.M. interaction • Example: cross section of (including mixing) Vector Meson Dominance Vector Meson Dominance Vector Meson Dominance Sakurai: Theory of Strong Interactions • gauge theory a'la Yang & Mills – isospin, hypercharge, baryon number • mediated by vector mesons • covariant derivative: • Higgs phenomenon unknown at that time - massive vector mesons? Vector Meson Dominance • Electromagnetic interaction (e.g. of pions) - two versions: pion current: rho field-strength tensor: Vector Meson Dominance • Electromagnetic interaction (e.g. of pions) - two versions: hadron-rho interaction pion current: rho field-strength tensor: Vector Meson Dominance rho-omega transition • Electromagnetic interaction (e.g. of pions) - two versions: hadron-rho interaction pion current: rho field-strength tensor: Vector Meson Dominance rho-omega transition • Electromagnetic interaction (e.g. of pions) - two versions: hadron-rho interaction pion current: rho field-strength tensor: Vector Meson Dominance rho-omega transition • Electromagnetic interaction (e.g. of pions) direct- two photon versions:-pion coupling hadron-rho interaction pion current: rho field-strength tensor: Vector Meson Dominance rho-omega transition • Electromagnetic interaction (e.g. of pions) direct- two photon versions:-pion coupling hadron-rho interaction pion current: rho field-strength tensor: Vector Meson Dominance rho-omega transition • Electromagnetic interaction (e.g. of pions) direct- two photon versions:-pion coupling hadron-rho interaction pion current: photon mass term !!! rho field-strength tensor: Vector Meson Dominance Non-zero photon mass? - Summation of self-energy diagrams:rho-omega transition • Electromagnetic interaction (e.g. of pions) direct- two photon versions:-pion coupling hadron-rho interaction pion current: massless propagator photon mass term !!! rho field-strength tensor: Vector Meson Dominance • Electromagnetic interaction (e.g. of pions) - two versions: The two models are equivalent pion current: rho field-strength tensor: Dileptons in Heavy-ion collisions • Electromagnetic probes (후, e+e-): penetrate out from the dense phase • BUT: they are created in all stages of the reaction in many different processes • even for ultrarelativistic HIC, a hadron gas phase is always there • need for Hadronic Transport models • hadron reactions in vacuum should be known • In the hadron gas phase many nucleons are excited to baryon resonance states EM transition form factors of baryon resonances Domains of : e+e- annihilation : N* Dalitz-decay : photoproduction : electroproduction HADES @GSI: pion-induced reactions @ = 1.49 GeV (future: 1.7 GeV) N* and Delta resonances Interaction with vector mesons is poorly known N* and Delta resonances Disentangle overlapping resonances: study angular distributions (e.g. Partial Wave Analysis, PWA) Interaction with vector mesons is poorly known Density matrix • Representation of a general QM state including mixed states • unpolarized beam/target: mixed state (incoherent mixture of different polarizations) • The system is in state with probability : • Expectation value of operator 푂: • two-step process: • probability of in final state: production and decay density matrices: Density matrix polarization of baryon resonance = pol. of incoming nucleon -> we can start the calculation with the baryon resonance, if we are only interested in angular distribution (and not the magnitude of the cross section) creation of virtual photon ( R→Nγ* ) decay of virtual photon hadronic process ( γ*→e+e- ) leptonic process Spin density matrix of a decay process A particle of spin-J decays into two particles with spins s1 and s2: Final state in terms of eigenstates of total angular momentum: Wigner matrix helicity amplitude Decay density matrix: Spin density matrix of the decay process The spin density matrix (i.e. the polarization state) of the virtual photon can be reconstructed from the angular distribution of dileptons -> we can learn about the process it was created in. Spin density matrix of the production process spin-3/2 resonance: normalization: spin - 3/2- resonance: e.g. spin - 5/2+ resonance: spin - 7/2- resonance: Thank You! Co-workers, Acknowledgements Baiyang Zhang, Deniz Nitt, Enrico Speranza Michael Buballa, Bengt Friman Members of HADES: Tetyana Galatyuk, Piotr Salabura, Beatrice Ramstein, Joachim Stroth Federico Scozzi, Amel Belounnas.