Quark model approach to the $\eta$ meson electroproduction on the proton

A recently developed quark model approach to pseudoscalar meson photoproduction is extended to electroproduction process for the $\eta$ meson in the kinematics of momentum transfer $Q^2 \leq$ 4 (GeV/c)$^2$ and total center of mass energy $W \leq$ 1.6 GeV. Existing data are well reproduced and the roles of the $S_{11}(1535)$ and $D_{13}(1520)$ resonances are closely investigated. In the study of the longitudinal excitation of the $S_{11}(1535)$ resonance, a reliable constraint on the $S_{11}(1535)$ properties is obtained by cleanly removing the electromagnetic transition from the $\gamma_{(v)} p \to S_{11}(1535) \to \eta p$ amplitude. Thus, the fitted quantities can be determined with an uncertainty of about 15%. This could be the first direct constraint on the $S_{11}(1535)$ properties in theory.