New Results from the Studies of the $N(1440)1/2^+$, $N(1520)3/2^-$, and $\Delta(1620)1/2^-$ Resonances in Exclusive $ep \to e'p' \pi^+ \pi^-$ Electroproduction with the CLAS Detector

The transition helicity amplitudes from the proton ground state to the $N(1440)1/2^+$, $N(1520)3/2^-$, and $\Delta(1620)1/2^-$ resonances ($\gamma_vpN^*$ electrocouplings) were determined from the analysis of nine independent one-fold differential $\pi^+ \pi^- p$ electroproduction cross sections off a proton target, taken with CLAS at photon virtualities 0.5 GeV$^2$ $< Q^2 <$ 1.5 GeV$^2$. The phenomenological reaction model employed for separation of the resonant and non-resonant contributions to this exclusive channel was further developed. The $N(1440)1/2^+$, $N(1520)3/2^-$, and $\Delta(1620)1/2^-$ electrocouplings were obtained from the resonant amplitudes of charged double-pion electroproduction off the proton in the aforementioned area of photon virtualities for the first time. Consistent results on $\gamma_vpN^*$ electrocouplings available from independent analyses of several $W$-intervals with different non-resonant contributions offer clear evidence for the reliable extraction of these fundamental quantities. These studies also improved the knowledge on hadronic branching ratios for the $N(1440)1/2^+$, $N(1520)3/2^-$, and $\Delta(1620)1/2^-$ decays to the $\pi \Delta$ and $\rho N$ final states. These new results provide a substantial impact on the QCD-based approaches that describe the $N^*$ structure and demonstrate the capability to explore fundamental ingredients of the non-perturbative strong interaction that are behind the excited nucleon state formation.