Electroexcitation of the Roper resonance for $1.7<Q^2<4.5{\mathrm{GeV}}^2$ in $\overrightarrow{e}p\to \mathit{en}{\pi }^{+}$

The helicity amplitudes of the electroexcitation of the Roper resonance are extracted for $1.7<Q^2<4.5{\mathrm{GeV}}^2$ from recent high precision JLab-CLAS cross section and longitudinally polarized beam asymmetry data for ${\pi }^{+}$ electroproduction on protons at $W=1.15-1.69$ GeV. The analysis is made using two approaches, dispersion relations and a unitary isobar model, which give consistent $Q^2$ behavior of the helicity amplitudes for the ${\gamma }^{*}p\to$N(1440)P${}_{11}$ transition. It is found that the transverse helicity amplitude $A_{1/2}$, which is large and negative at $Q^2=0$, becomes large and positive at $Q^2\simeq 2{\mathrm{GeV}}^2$, and then drops slowly with $Q^2$. The longitudinal helicity amplitude $S_{1/2}$, which was previously found from CLAS $\overrightarrow{e}p\to \mathit{ep}{\pi }^0,\mathit{en}{\pi }^{+}$ data to be large and positive at $Q^2=0.4,0.65{\mathrm{GeV}}^2$, drops with $Q^2$. Available model predictions for ${\gamma }^{*}p\to$N(1440)P${}_{11}$ allow us to conclude that these results provide strong evidence in favor of N(1440)P${}_{11}$ as a first radial excitation of the $3q$ ground state. The results of the present paper also confirm the conclusion of our previous analysis for $Q^2<1$ GeV${}^2$ that the presentation of N(1440)P${}_{11}$ as a q${}^3\mathrm{G}$ hybrid state is ruled out.

Figure 1

Our results for the Legendre moments of the $\overrightarrow{e}p\to \mathit{en}{\pi }^{+}$ structure functions in comparison with experimental data [11] for $Q^2=2.05$ GeV${}^2$. The solid (dashed) curves correspond to the results obtained using DR (UIM) approach. The dotted curves are obtained by switching off the N(1440)P${}_{11}$ resonance in the final DR results.

Figure 2

Helicity amplitudes for the ${\gamma }^{*}p\to$N(1440)P${}_{11}$ transition. The full circles are our results obtained from the analysis of ${\pi }^{+}$ electroproduction data [11]. The bands present the model uncertainties (I,II,III) added in quadrature; see text. The full boxes are the results obtained from CLAS data [13, 31, 34, 35, 36]; open boxes present the results of the combined analysis of CLAS single π and $2\pi$ electroproduction data [14]. The full triangle at $Q^2=0$ is the RPP estimate [17]. The thick curves correspond to the light-front relativistic quark models: dotted, dashed, dash-dotted, long-dashed, and solid curves are from Refs. [1, 37, 38, 39, 40], respectively. The thin solid curves are the predictions obtained for the Roper resonance treated as a quark core dressed by a meson cloud [7, 8]. The thin dashed curves are obtained assuming that N(1440)P${}_{11}$ is a $q^{3}G$ hybrid state [6].