$E2/M1$ Ratio for the $\gamma N\rightarrow \Delta$ Transition in the Chiral Quark Soliton Model

Abstract

We calculate the electric quadrupole to magnetic dipole transition ratio $E2/M1$ for the reaction $\gamma N \ra \Delta(1232)$ in the chiral quark soliton model. The calculated $E2/M1$ ratio is in a good agreement with the very new experimental data. We obtain non-zero negative value for the electric quadrupole $N-\Delta$ transition moment, which suggests an oblate deformed charge structure of the nucleon or/and the delta isobar. Other observables related to this quantity, namely the $N-\Delta$ mass splitting, the isovector charge radius, and isovector magnetic moment, are properly reproduced as well.