Theoretical Determination of the $\Delta N\gamma $ Electromagnetic Transition Amplitudes in the $\Delta (1232)$ Region

Abstract

We utilize non-perturbative and fully relativistic methods to calculate the\thinspace \thinspace $\Delta N\gamma $ electromagnetic transition amplitudes $G_{M}^{*}(q^{2})$ (related to the magnetic dipole moment $% M_{1^{+}}^{3/2}(q^{2})$), $G_{E}^{*}(q^{2})$ (related to the electric quadrupole moment $E_{1^{+}}^{3/2}(q^{2})$), the electromagnetic ratio $% R_{EM}(q^{2})\equiv -G_{E}^{*}(q^{2})/G_{M}^{*}(q^{2})=E_{1^{+}}^{3/2}(q^{2})/M_{1^{+}}^{3/2}(q^{2} ) $, and discuss their $q^{2}$ behavior in the $\Delta (1232)$ mass region. These are very important quantities which arise in all viable quark, QCD, or perturbative QCD models of pion electroproduction and photoproduction.