Measurements of $e p \to e' \pi^+ \pi^- p'$ Cross Sections with CLAS at $1.40 < W < 2.0$ GeV and $2.0 < Q^2 < 5.0$ GeV$^2$

This paper reports new exclusive cross sections for $e p \to e' \pi^+ \pi^- p'$ using the CLAS detector at Jefferson Laboratory. These results are presented for the first time at photon virtualities 2.0 GeV^2 < Q^2 < 5.0 GeV^2 in the center-of-mass energy range 1.4 GeV < W < 2.0 GeV, which covers a large part of the nucleon resonance region. Using a model developed for the phenomenological analysis of electroproduction data, we see strong indications that the relative contributions from the resonant cross sections at W < 1.74 GeV increase with $Q^2$. These data considerably extend the kinematic reach of previous measurements. Exclusive $e p \to e' \pi^+ \pi^- p'$ cross section measurements are of particular importance for the extraction of resonance electrocouplings in the mass range above 1.6 GeV.