Electroproduction of $p{\pi }^{+}{\pi }^{-}$ off protons at $0.2<Q^2<0.6$ ${\mathrm{GeV}}^2$ and $1.3<W<1.57$ GeV with the CLAS detector

This paper reports on the most comprehensive data set obtained on differential and fully integrated cross sections for the process $ep\to e^{\text{'}}p{\pi }^{+}{\pi }^{-}$. The data were collected with the CLAS detector at Jefferson Laboratory. Measurements were carried out in the as yet unexplored kinematic region of photon virtuality $0.2<Q^2<0.6$ ${\mathrm{GeV}}^2$ and invariant mass of the final hadron system $W$ from 1.3 to 1.57 GeV. For the first time, nine independent one-fold differential cross sections were determined in each bin of $W$ and $Q^2$ covered by the measurements. A phenomenological analysis of the data allowed us to establish the most significant mechanisms contributing to the reaction. The nonresonant mechanisms account for a major part of cross sections. However, we find sensitivity to $s$-channel excitations of low-mass nucleon resonances, especially to the $N(1440)P_{11}$ and $N(1520)D_{13}$ states in kinematic dependencies of the one-fold differential cross sections.

Figure 1

Cross-sectional views of the CLAS detector. The left panel shows a cut along the beamline and through the midplane of two opposite sectors. The right panel shows a cut perpendicular to the beamline and through the nominal target center. Descriptions of the detector elements are given in the text of Sec. 3a.

Figure 2

Distribution of photoelectrons in the Cherenkov counter for $0.3<Q^2<0.4\hspace{0.5em}{\mathrm{GeV}}^2$ in two $W$ bins centered at the values shown in each plot. The curves represent a Poisson fit.

Figure 3

Distributions for the energies deposited in the outer part ($E_{\mathrm{out}}$) vs the energies deposited in the inner part ($E_{\mathrm{in}}$) of the EC normalized to the momenta of the outgoing particles ($P_{e^{\text{'}}}$). The distribution for the accumulated triggers is shown in the top plot, while the distribution for the events selected, applying the photoelectron cut, is shown in the bottom plot.

Figure 4

$\beta$ vs momentum for positively charged hadrons; solid curves show the cuts used to identify pions and protons; dashed curves show the explicit $\beta$ vs $p$ relationships, using the pion and proton mass, respectively. The events near $\beta =1$ and $p=0.1$ GeV are positrons, e.g., from ${\pi }^0$ Dalitz decay. The data were collected in a single scintillator bar.

Figure 5

Distribution of squared missing mass $M^2(e^{\text{'}}p{\pi }^{+}X)$ (${\mathrm{GeV}}^2$). The arrows show the exclusivity cut.

Figure 6

$Q^2$ (${\mathrm{GeV}}^2$) vs $W$ (GeV) distribution for the selected $2\pi$ events. The grid shows the binning used for the evaluation of the cross section. Only cells inside the allowed phase space were used for that purpose.

Figure 7

Kinematic variables for the $ep\to e^{\text{'}}{p}^{\text{'}}{\pi }^{+}{\pi }^{-}$ reaction (choice 2 in Sec. 5a). The left plot shows the ${\pi }^{-}$ spherical angles ${\theta }_{{\pi }^{-}}$ and ${\phi }_{{\pi }^{-}}$, while the right plot shows the angle ${\alpha }_{({\pi }^{-}p)({\pi }^{+}{p}^{\text{'}})}$ of the plane defined by the momenta of the final $p\hspace{0.5em}{\pi }^{+}$ pair with respect to the plane comprised by the momenta of the initial proton $p$ and ${\pi }^{-}$.

Figure 8

Comparison of fully integrated charged double pion cross sections, obtained with (squares) and without (open circles) accounting for contributions from the CLAS areas of zero acceptance, as described in Sec. 5c.

Figure 9

Mass distributions of $p{\pi }^{+}$ (top left) and ${\pi }^{+}{\pi }^{-}$ (top right), and ${\pi }^{-}$ angular (bottom) distributions, obtained from different ways of interpolating the five-fold differential cross sections into the CLAS areas of zero acceptance. Open squares correspond to one-fold differential cross sections estimated without the contributions from the CLAS areas of zero acceptance. One-fold differential cross sections, obtained with the $R_j$ coefficients in Eq. (10) calculated within the framework of the JM03 and JM05 models, are shown by triangles and stars, respectively. One-fold differential cross sections, estimated by excluding contributions from ϕ-dependent parts in Eq. (9) are shown by full circles. Note that points are spread out for clarity.

Figure 10

$W$ and $Q^2$ distributions for measured and accepted MC events ($N_f$), normalized to unity. The black lines represents data; the gray (red) lines, simulation.

Figure 11

Comparison between measured (solid lines) and simulated (dashed lines) event distributions normalized to unity ($N_f$) for various final state variables. ($W=1.4125$ GeV, $Q^2=0.525$ ${\mathrm{GeV}}^2$).

Figure 12

Corrections for mass distribution in the cross sections near threshold. The filled circles represent the preliminary cross sections obtained with the nominal bin size. The lowest mass bin of nominal size is shown by the solid vertical lines. Preliminary cross sections obtained using a bin size reduced by a factor of 4 are shown by the open squares. The mass bins of reduced size are shown by the vertical dashed lines. The bin of lowest invariant masses $\Delta M$, where corrected cross sections were evaluated, covers the interval from the dashed to the solid lines connected by the double-sided arrow. Corrected cross sections are given by the integrals from interpolating curves inside the $\Delta M$ bin over the bin width.

Figure 13

Comparison of mass distribution cross sections before (filled circles) and after (open squares) improvements, described in Secs. 5d and 5e.

Figure 14

Comparison between ${\pi }^{+}p$ and ${\pi }^{-}{\pi }^{+}$ mass distribution cross sections, obtained by integration of the five-fold differential cross sections for various choices of the final state kinematic variables (choices from 1 to 3 are shown by full circles, open squares, and triangles, respectively), defined in the Sec. 5a.

Figure 15

Comparison between fully integrated charged double pion cross sections, obtained in the integration of the five-fold differential cross sections over three various choices of the final state variables, described in the Sec. 5a. Choices 1–3 for kinematic variables are shown by triangles and the open and full squares, respectively.

Figure 16

Fully integrated $2\pi$ cross section at various $Q^2$. Crossed areas represent systematic uncertainties. Full calculations within the framework of the JM06 model [33] are shown by solid curves. The contributions from $s$-channel resonances and from nonresonant mechanisms are shown by the dot-dashed and dashed curves, respectively.

Figure 17

The mechanisms of JM05 model [32, 52] contributing to $2\text{−}\pi$ electroproduction at low $W$ and $Q^2$.

Figure 18

CLAS $p{\pi }^{+}{\pi }^{-}$ data compared with JM05 calculations (solid lines). The contributions from direct $2\pi$ production, resulting in discrepancies in the description of ${\pi }^{+}$ and $p$ angular distributions, are shown as dashed lines.

Figure 19

Direct charged double pion production mechanisms in JM06 model.

Figure 20

CLAS charged double pion differential cross sections at $W=1.51$ GeV and $Q^2=0.425\hspace{0.5em}{\mathrm{GeV}}^2$ within the framework of the JM06 model. The full calculations are shown by the solid lines. The contributions from ${\pi }^{-}{\Delta }^{++}$ and ${\pi }^{+}{\Delta }^0$ isobar channels are shown by the dashed and dotted lines, respectively. The contributions from direct charged double pion production processes are shown by the dot-dashed lines. ${\alpha }_i$ angular distributions were calculated with the JM06 parameters fit to the other six differential cross sections.

Figure 21

Resonant (dot-dashed lines) and nonresonant (dashed lines) contributions to the charged double pion differential cross sections at $W=1.51$ GeV and $Q^2=0.425\hspace{0.5em}{\mathrm{GeV}}^2$. The full JM06 calculations are shown by solid lines.