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Measurements of $ep \to e^\prime π^+n$ at W = 1.6 - 2.0 GeV and extraction of nucleon resonance electrocouplings at CLAS

Differential cross sections of the exclusive process $e p \to e^\prime π^+ n$ were measured with good precision in the range of the photon virtuality $Q^2 = 1.8 - 4.5$ GeV$^2$, and the invariant mass range of the $π^+ n$ final state W = 1.6 - 2.0 GeV using the CEBAF Large Acceptance Spectrometer. Data were collected with nearly complete coverage in the azimuthal and polar angles of the $nπ^+$ center-of-mass system. More than 37,000 cross section points were measured. The contributions of the isospin $I = {1\over 2}$ resonances $N(1675){5\over 2}^-$, $N(1680){5\over 2}^+$ and $N(1710){1\over 2}^+$ were extracted at different values of $Q^2$ using a single-channel, energy-dependent resonance amplitude analysis. Two different approaches, the unitary isobar model and the fixed-$t$ dispersion relations, were employed in the analysis. We observe significant strength of the $N(1675){5\over 2}^-$ in the $A_{1/2}$ amplitude, which is in strong disagreement with quark models that predict both transverse amplitudes to be strongly suppressed. For the $N(1680){5\over 2}^+$ we observe a slow changeover from the dominance of the $A_{3/2}$ amplitude at the real photon point ($Q^2=0$) to a $Q^2$ where $A_{1/2}$ begins to dominate. The scalar amplitude $S_{1/2}$ drops rapidly with $Q^2$ consistent with quark model prediction. For the $N(1710){1\over 2}^+$ resonance our analysis shows significant strength for the $A_{1/2}$ amplitude at $Q^2 < 2.5$ GeV$^2$.