Experimental study of the $P_{11}\left(1440\right)$ and $D_{13}\left(1520\right)$ resonances from the CLAS data on $ep\to e^{\prime }{\pi }^{+}{\pi }^{-}{p}^{\prime }$

The transition helicity amplitudes from the proton ground state to the $P_{11}\left(1440\right)$ and $D_{13}\left(1520\right)$ excited states (${\gamma }_{v}p{N}^{*}$ 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 of $0.25<Q^2<0.60$ GeV${}^2$. The phenomenological reaction model was employed for separation of the resonant and nonresonant contributions to the final state. The $P_{11}\left(1440\right)$ and $D_{13}\left(1520\right)$ 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 ${\pi }^{0}p$ channels. The successful description of a large body of data in dominant meson-electroproduction channels off protons with the same ${\gamma }_{v}p{N}^{*}$ 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 $D_{13}\left(1520\right)$ decay into $\Delta \pi$ (24$\%$–32$\%$) and $N\rho$ (8$\%$–17$\%$).

Figure 1

Kinematic variables for the description of $ep\to e^{\prime }{p}^{\prime }{\pi }^{+}{\pi }^{-}$ in the CM frame of the final-state hadrons corresponding to the first assignment presented in Sec. 2a. (a) The ${\pi }^{-}$ spherical angles ${\theta }_{{\pi }^{-}}$ and ${\varphi }_{{\pi }^{-}}$. (b) The angle ${\alpha }_{\left[p{\pi }^{-}\right]\left[p^{\prime }{\pi }^{+}\right]}$ between the two planes: one of them (plane A) is defined by the three-momenta of the initial proton and the final ${\pi }^{-}$; the other (plane B) is defined by the three-momenta of the two other final hadrons, ${\pi }^{+}$ and the proton. The unit vectors $\overline{\gamma }$ and $\overline{\beta }$ are normal to the ${\pi }^{-}$ three-momentum in the planes A and B, respectively.

Figure 2

Reaction mechanisms of the JM model [43] that contribute to ${\pi }^{+}{\pi }^{-}p$ electroproduction in the kinematic region covered by recent CLAS measurements [41] with $W<1.6$ GeV and $0.25<Q^2<0.6$ GeV${}^2$: (a) three-body mechanisms, (b) $\pi \Delta$ isobar channels, and [(c) and (d)] direct two-pion production mechanisms that correspond to different assignments for the final state hadrons. The $t_i$ ($i=1,...,3)$ stand for the squared transferred momenta in the exchange processes by unspecified particle(s), as described in [43] and shown by blobs in panels (c) and (d).

Figure 3

Diagrams showing the unitarized BW ansatz of the JM model, which incorporates transitions via the dressed resonance propagator between states listed in Table 1 for the same $N_{\alpha }=N_{\beta }$ (top) and different $N_{\alpha }\ne N_{\beta }$ resonances as allowed by the conservation laws of the strong interaction (bottom).

Figure 4

Resonant (blue triangles) and nonresonant (green open circles) contributions to the differential cross sections (red lines) obtained from the CLAS data [41], fit within the framework of the JM model at $W=1.51$ GeV, $Q^2=0.38$ GeV${}^2$. The solid blue and dotted-dashed green lines stand for the resonant and nonresonant contributions, respectively, which were computed for minimal ${\chi }^2/\mathrm{dp}$ achieved in the data fit. The points for resonant and nonresonant contributions are shifted on each panel for $a$better visibility. Dashed lines show selected fits.

Figure 5

The same as in Fig. 4 at $W=1.51$ GeV, $Q^2=0.43$ GeV${}^2$.

Figure 6

Electrocouplings and full error bars of the $P_{11}\left(1440\right)$ state. The results from the analysis of the CLAS ${\pi }^{+}{\pi }^{-}p$ electroproduction data [41] are shown by triangles. Electrocouplings from the analysis of the $N\pi$ electroproduction data [13] are shown by circles.

Figure 7

Electrocouplings and full error bars of the $D_{13}\left(1520\right)$ state. The analysis of the CLAS ${\pi }^{+}{\pi }^{-}p$ electroproduction data [41] is shown by triangles. Electrocouplings from the analysis of the $N\pi$ electroproduction data [13] are shown by circles.

Figure 8

Comparison between the final results on $S_{1/2}$ electrocouplings for the $P_{11}\left(1440\right)$ from this analysis of CLAS ${\pi }^{+}{\pi }^{-}p$ electroproduction data [41] (triangles) with the values obtained by employing a regular BW ansatz for the resonant amplitudes and with the contributions from the $S_{11}\left(1535\right)$ state turned off (squares).

Figure 9

Photo- and electrocouplings of the $P_{11}\left(1440\right)$ resonance in comparison with predictions of quark models. The photocouplings are taken from RPP [53] (open square) and the CLAS data analysis [60] (open triangle). Other data points are the same as in Fig. 6. The results of relativistic light-front quark models [8, 11] are shown by solid and dashed lines, respectively. Results of the covariant valence quark spectator diquark model [68] are shown by the dashed dotted line.

Figure 10

Processes that contribute to meson-baryon dressing in the $N^{*}$ photo- and electroexcitations within the EBAC-DCC approach.

Figure 11

Description of the CLAS data on $D_{13}\left(1520\right)$ electrocouplings within the hQCM (solid lines) [77]. The symbols associated with the experimental data are the same as in Fig. 9.

Figure 12

Helicity asymmetry $A_{hel}$ of Eq. (16) for the transverse electrocouplings of the $D_{13}\left(1520\right)$ from this analysis of ${\pi }^{+}{\pi }^{-}p$ (filled triangles) and $N\pi$ (open circles) exclusive electroproduction channels measured with CLAS. The curve represents the nonrelativistic quark model calculations [79].