A study of the $P_{11}(1440)$ and $D_{13}(1520)$ resonances from CLAS data on $ep \rightarrow e'\pi^{+} \pi^{-} p'$

The transition helicity amplitudes from the proton ground state to the $P_{11}(1440)$ and $D_{13}(1520)$ excited states ($\gamma_{v}pN^*$ 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 0.25\enskip {\rm GeV$^{2}$} $<$ $Q^{2}$ $<$ 0.60 \enskip {\rm GeV$^{2}$}. The phenomenological reaction model was employed for separation of the resonant and non-resonant contributions to the final state. The $P_{11}(1440)$ and $D_{13}(1520)$ electrocouplings were obtained from the resonant amplitudes parametrized within the framework of a unitarized Breit-Wigner ansatz. They are consistent with results obtained in the previous CLAS analyses of the $\pi^+n$ and $\pi^0p$ channels. The successful description of a large body of data in dominant meson-electroproduction channels off protons with the same $\gamma_{v}pN^*$ electrocouplings offers clear evidence for the reliable extraction of these fundamental quantities from meson-electroproduction data. This analysis also led to the determination of the long-awaited hadronic branching ratios for the $D_{13}(1520)$ decay into $\Delta\pi$ (24%-32%) and $N\rho$ (8%-17%).