First measurement of target and double spin asymmetries for $\overrightarrow{e}\overrightarrow{p}\to \mathit{ep}{\pi }^0$ in the nucleon resonance region above the $\Delta (1232)$

The exclusive channel $\overrightarrow{p}(\overrightarrow{e},e^{\text{'}}p){\pi }^0$ was studied in the first and second nucleon resonance regions in the $Q^2$ range from $0.187$ to $0.770\hspace{0.5em}{\mathrm{GeV}}^2$ at Jefferson Lab using the CEBAF Large Acceptance Spectrometer. Longitudinal target and beam-target asymmetries were extracted over a large range of center-of-mass angles of the ${\pi }^0$ and compared to the unitary isobar model MAID, the dynamic model by Sato and Lee, and the dynamic model DMT. A strong sensitivity to individual models was observed, in particular for the target asymmetry and in the higher invariant mass region. This data set, once included in the global fits of the above models, is expected to place strong constraints on the electrocoupling amplitudes $A_{1/2}$ and $S_{1/2}$ for the Roper resonance $N(1400)P_{11}$ and the $N(1535)S_{11}$ and $N(1520)D_{13}$ states.

Figure 1

Schematic diagram of ${\pi }^0$-nucleon electroproduction. $\overrightarrow{e}$ represents the incident polarized electron, $e^{\text{'}}$ is the outgoing electron, ${\gamma }^{*}$ is the virtual photon, and $p$ and $p^{\text{'}}$ are the nucleon in the initial and final states, respectively.

Figure 2

Tree-level diagrams of single $p{\pi }^0$ electroproduction for (a) $s$-channel resonance production, (b) $s$-channel nucleon exchange, and (c) $t$-channel ω meson exchange.

Figure 3

Number of electron events as a function of the vertex $z$ position. The dashed and the solid lines represent the distribution before and after the raster correction, respectively. The vertical lines indicate the cut applied to the data to remove the peaks coming from the scattering off the exit windows of the target.

Figure 4

$\beta$ vs. $p$ for positively charged particles. The lines show how protons are selected in the analysis.

Figure 5

$M_x^2$ spectra of ${}^{15}{\mathrm{NH}}_3$, normalized ${}^{12}\mathrm{C}$, and their subtraction for $0<\cos \theta <0.2$ and invariant masses of $1.15\hspace{0.5em}\mathrm{GeV}<W<1.2\hspace{0.5em}\mathrm{GeV}$ (a) and $1.4\hspace{0.5em}\mathrm{GeV}<W<1.5\hspace{0.5em}\mathrm{GeV}$ (b). The lines show the $2\sigma$ cut applied to select ${\pi }^0$ events.

Figure 6

The product $\left|P_e{P}_t\right|$ as a function of $Q^2$ for positive (filled circles) and negative (open triangles) target polarization runs. The six values for each polarization were fitted with a constant to obtain the average values $P_e{P}_t^a=0.517\pm 0.002$ and $P_e{P}_t^b=-0.483\pm 0.003$.

Figure 7

Kinematic coverage in $Q^2$ and $W$. The dashed lines indicate how the data were subdivided.

Figure 8

The target asymmetries $A_t$ for $Q^2=0.385$ ${\mathrm{GeV}}^2,{\varphi }^{*}={120}^{°}$, and invariant masses $W=1.225\hspace{0.5em}\mathrm{GeV}$ (a) and $W=1.35$ ${\mathrm{GeV}}^2$ (b). Systematic uncertainties are shown as shaded bars. The curves correspond to the MAID07 (solid), DMT (dotted), Sato and Lee (dashed), and MAID03 (dashed dotted) calculations.

Figure 9

The target asymmetries $A_{\mathrm{et}}$ for $Q^2=0.252$ ${\mathrm{GeV}}^2,{\varphi }^{*}={120}^{°}$, and invariant masses $W=1.225\hspace{0.5em}\mathrm{GeV}$ (a) and $W=1.65\hspace{0.5em}\mathrm{GeV}$ (b). Systematic uncertainties are shown as shaded bars. The curves correspond to the MAID07 (solid), DMT (dotted), Sato and Lee (dashed), and MAID03 (dashed dotted) calculations.

Figure 10

$A_{\mathrm{et}}$ as a function of the invariant mass $W$, integrated over the whole range in $\cos {\theta }^{*},Q^2$, and $60{}^{\circ }<{\varphi }^{*}<156{}^{\circ }$. The curves correspond to the MAID07 (solid), DMT (dotted), Sato and Lee (dashed), MAID03 (dashed dotted), MAID00 (long-dashed-dotted) calculations. The long-dashed curve is the MAID00 calculation without the $D_{13}(1520)$ contribution.

Figure 11

$A_t$ as a function of the invariant mass $W$, integrated over the whole range in $\cos {\theta }^{*},Q^2$, and $60{}^{\circ }<{\varphi }^{*}<156{}^{\circ }$. The curves correspond to the MAID07 (solid), DMT (dotted), Sato and Lee (dashed), MAID03 (dashed dotted), and MAID00 (long-dashed-dotted) calculations.

Figure 12

$A_{\mathrm{et}}$ as a function of the photon virtuality $Q^2$, integrated over the whole range in $\cos {\theta }^{*},60{}^{\circ }<{\varphi }^{*}<156{}^{\circ }$, and 12 invariant mass regions from 1.1 to 1.7 GeV in steps of 0.05 GeV. The curves correspond to the MAID07 (solid), DMT (dotted), Sato and Lee (dashed), and MAID03 (dashed dotted) calculations.

Figure 13

$A_t$ as a function of the photon virtuality $Q^2$, integrated over the whole range in $\cos {\theta }^{*},60{}^{\circ }<{\varphi }^{*}<156{}^{\circ }$, and 12 invariant mass regions from 1.1 to 1.7 GeV in steps of 0.05 GeV. The curves correspond to the MAID07 (solid), DMT (dotted), Sato and Lee (dashed), and MAID03 (dashed dotted) calculations.