Electromagnetic interaction of baryon resonances from - 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 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 • Neutral vector mesons have the same quantum numbers as --> 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 – , 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 ) - 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 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