Bochum 2009 – wissenschaftliches Programm
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HK: Fachverband Hadronen und Kerne
HK 42: Few-body physics
HK 42.1: Gruppenbericht
Dienstag, 17. März 2009, 16:30–17:00, H-ZO 100
Current conservation and analytic determination of the magnetic moment of the Delta-resonances. — Amand Faessler1 and •Alexander Machavariani2 — 1Institute für Theoretische Physik der Univesität Tübingen, Tübingen D-72076, Germany — 2High Energy Physics Institute of Tbilisi State University, University str. 9, Tbilisi 380086, Georgia
The pion-nucleon bremsstrahlung π+N=⇒γ′+π′+N′ is studied within a new form of the Ward-Takahashi identities for the on shell amplitudes. Based on this current conservation it is shown, that the double Δ exchange diagram with the Δ−γ′ Δ′ vertex cancel exactly against the appropriate longitudinal part of the external particle radiation diagrams. Consequently, a model independent relation between the magnetic dipole moments of the Δ resonances and the full magnetic moment of the proton µp and neutron µn is obtained. In particular, µΔ+= MΔ/mp µp, µΔo= MΔ/mo µn and µΔ++=3/2µΔ+, µΔ−=3/2µΔo. This result is generalized within the field theoretical formulation with the quark degrees of freedom, where pions and nucleons are treated as the bound systems of quarks. It is shown that relations generated by current conservation for the on shell π N bremsstrahlung amplitude with composite nucleons and pions have the same form as in the usual quantum field theory without quark degrees of freedom. Consequently, the model independent relations for the magnetic dipole moments of the Δ resonances remain be the same in the quantum field theory with the quark degrees of freedom.