Figure 1

The one-photon exchange diagram of the resonance electroproduction process, where, for example, $k_i$ is the four-momentum vector of the incoming electron composed of energy $E$ and momentum ${\overrightarrow{k}}_i$.Reuse & Permissions

Figure 2

The scattering and reaction plane coordinate systems.Reuse & Permissions

Figure 3

A plan view of Hall C showing the beamline, target, and the SOS and HMS spectrometers that detected electrons and protons, respectively. Figure from Ref. [2].Reuse & Permissions

Figure 4

A side view of the HMS detector stack, which is also representative of the SOS. The detected particles travel from left to right, encountering first the two drift chambers (DC) then the first two arrays of scintillators (S1) oriented in the X and Y directions, then the gas Čerenkov detector, the third and fourth scintillator arrays and finally the calorimeter. Figure from Ref. [2]Reuse & Permissions

Figure 5

The $W$ acceptance of the detector pair for the $e(p,e^{\text{'}}p)\eta$ reaction, in the lower-$Q^2$ configuration, as a function of the laboratory scattering angle and momentum of the proton. The contours are constant $W$ of the hadronic system, for an electron at $47.5^{°}$ and momentum of 1.74 GeV/$c$, for the full range of ${\theta }^{*}$ and $\varphi =0^{°}$ and ${180}^{°}$. The solid central contour is $W=1.5$ GeV, from which they increase in steps of 100 MeV to the outermost at $W=1.9$ GeV. In practice, the angle and momentum bite of the SOS causes the contours to be much broader. Each black box is the acceptance of a particular HMS setting (${}^{†}$Table ). The alternate settings are offset by $1.5^{°}$ and are a 4.7% increase in momentum, so that they are approximately centered on the points where the boxes join.Reuse & Permissions

Figure 6

The correlation between $E_{\mathrm{norm}}$ and $N_{\mathrm{p}.\mathrm{e}.}$ for all the lower-$Q^2$ data. The particle ID cuts to select electrons, $N_{\mathrm{p}.\mathrm{e}.}>0.5$ and $E_{\mathrm{norm}}>0.7$, are visible as dashed lines in the figure. All other cuts listed in Table have already been applied to the data.Reuse & Permissions

Figure 7

Coincidence time spectrum for the lower-$Q^2$ data with all of the “standard” cuts except the coincidence time cut. The dark-gray shaded region represents the 3-ns-wide proton cut. The 2-ns beam structure is clear in the accidental background. Data from the light-gray shaded regions was used to estimate the amount of accidentals in each ($W$, $\cos {\theta }_{\eta }^{*}$, ${\varphi }_{\eta }^{*}$ and $m_x^2$) bin under the proton peak.Reuse & Permissions

Figure 8

Missing-mass-squared, $m_x^2$, from Eq. (1), for all the lower-$Q^2$ data.Reuse & Permissions

Figure 9

The ${\varphi }_{\eta }$ dependence of missing-mass-squared distributions for $W=1.5$ GeV and $\cos {\theta }_{\eta }^{*}=-0.916$. The (green) points are the data while the solid fill is the sum of the simulations. The multipion background component is the light-gray filled area and $\eta$ production simulation component has the darker gray fill. The dot-dashed lines shows the region within which the background fit is done while the dashed lines show the region within which the $\eta$ cross section is extracted.Reuse & Permissions

Figure 10

The ${\varphi }_{\eta }$ dependence of missing-mass-squared distributions for $W=1.5$ GeV and $\cos {\theta }_{\eta }^{*}=0.416$. Symbols as in Fig. 9. Panels with ${\varphi }_{\eta }=1.178$, 1.963, 4.320, and 5.105 are the out-of-plane ϕ bins where the simulations of the signal and background are sufficiently similar to make a two-parameter bin-by-bin fit unreliable.Reuse & Permissions

Figure 11

The $W$ dependence of missing-mass-squared distributions for $\cos {\theta }_{\eta }^{*}=-0.916$ and $\varphi =3.534$ radians. Symbols as in Fig. 9.Reuse & Permissions

Figure 12

The $\cos {\theta }_{\eta }^{*}$ dependence of missing-mass-squared distributions for $W=1.5$ GeV and $\varphi =3.534$ radians. Symbols as in Fig. 9. The vertical dashed lines, which show the region within which the $\eta$ cross section is extracted, vary with $\cos {\theta }_{\eta }^{*}$ to accommodate the changing resolution.Reuse & Permissions

Figure 13

The $W$ dependence of the normalization coefficient of the multipion background simulation.Reuse & Permissions

Figure 14

The $\cos {\theta }^{*}$ dependence of the normalization coefficient of the multipion background simulation.Reuse & Permissions

Figure 15

The (green) points are the $m_x^2$ distribution of the full set of data off the “dummy” target cell, and the gray filled histogram is the simulation of multipion background from hydrogen. The simulation is arbitrarily normalized to match the data, with the same factor in all three panels. Note the similarity in shape.Reuse & Permissions

Figure 16

Radiative corrections for $-1<\cos {\theta }_{\eta }<-\frac{1}{3}$. Uncertainty is due to Monte Carlo statistics only.Reuse & Permissions

Figure 17

Radiative corrections for $-\frac{1}{3}<\cos {\theta }_{\eta }<\frac{1}{3}$. Uncertainty is due to Monte Carlo statistics only. Symbols as in Fig. 16.Reuse & Permissions

Figure 18

Radiative corrections for ⅓ < $\cos {\theta }_{\eta }$ < 1. Uncertainty is due to Monte Carlo statistics only. Symbols as in Fig. 16.Reuse & Permissions

Figure 19

Ratio of yield of elastic $\mathit{ep}$ coincidence events to predicted yield from Monte Carlo (Yield Data/Yield MC) plotted versus ${\theta }_e$ for ${\theta }_{\mathrm{SOS}}=47.5^{°}$ and three different combinations of ${\theta }_{\mathrm{HMS}}$ and $p_{\mathrm{HMS}}$. The solid line is the average ratio $=0.95\pm 0.01$, of all points between ${\theta }_e=45.5{}^{\circ }$ to $49.5^{°}$. The corresponding value of electron δ for a given ${\theta }_e$ is given by the upper $x$ axis.Reuse & Permissions

Figure 20

Inclusive inelastic differential cross sections as measured by the SOS spectrometer centered at $47.5^{°}$ and ${70}^{°}$, as a function of $W$, with the angular cut $-30<\mathit{dy}/\mathit{dz}<30$ mr. The curves are from a fit to world data [24].Reuse & Permissions

Figure 21

Extracted $\mathit{ep}\to \mathit{ep}\eta$ differential cross sections for the lower-$Q^2$ setting. The solid (blue) curve is a fit of Eq. (8) to each $W$ bin. The dashed curve is the ETA-MAID [34] isobar model for $\eta$ electroproduction from the nucleon at $Q^2=5$ ${\mathrm{GeV}}^2$, projected to the appropriate $Q^2$ for each $W$ bin by the factor $[5\hspace{0.5em}{\mathrm{GeV}}^2/Q^2(W)]{}^3$. The inner error bars are statistical and the outer error bars are the quadrature sum of the statistical and systematic errors.Reuse & Permissions

Figure 22

Extracted parameters from fits of Eq. (8) to the lower-$Q^2$ differential cross section, shown as curves in Fig. 21.Reuse & Permissions

Figure 23

The result of fits to the differential cross section, plotted as the ratio of the linear $\cos {\theta }_{\eta }^{*}$ term to the isotropic component, for the present work and other $\eta$-electroproduction data [2, 5, 6]. The black dotted line is drawn at $W=1.535$ GeV, the nominal mass for the $S_{11}$ resonance.Reuse & Permissions

Figure 24

Extracted $\mathit{ep}\to \mathit{ep}\eta$ differential cross sections for the higher-$Q^2$ setting. The (blue) solid curve is a fit to the data of the form $d\sigma /d{\Omega }^{*}=A+B\cos {\theta }^{*}$. The dashed curve is the ETA-MAID model [34] at $Q^2=5\hspace{0.5em}{\mathrm{GeV}}^2$, projected to the appropriate $Q^2$ for each $W$ bin by the factor $[5\hspace{0.5em}{\mathrm{GeV}}^2/Q^2(W)]{}^3$. The inner error bars are statistical and the outer error bars, the quadrature sum of the statistical and systematic errors.Reuse & Permissions

Figure 25

The ratio of the quadratic ${\cos }^2{\theta }_{\eta }^{*}$ term to the isotropic component for fits to the $\eta$-electroproduction differential cross section for the present work and other data [2, 6]. Symbols are the same as in Fig. 23.Reuse & Permissions

Figure 26

A simultaneous fit to the lower-$Q^2$ and higher-$Q^2$ data of the sum (solid line) of a relativistic Breit-Wigner (long dash) and nonresonant background term (short dashed line). The data are the total cross section determined from $4\pi \langle d\sigma /d{\Omega }^{*}\rangle$. The background was constrained as described in the text.Reuse & Permissions

Figure 27

Plot of the 1-σ contours from the various Breit-Wigner fits to the data.Reuse & Permissions

Figure 28

Values for $A_{1/2}(Q^2)$ determined from ${\sigma }_R$ for the present and other data [2, 5, 6] (consistently with $W_R=1.53$ GeV, ${\Gamma }_R=150$ MeV, and $b_{\eta }=0.55$). The curves are from Refs. [36, 37, 38, 39, 40].Reuse & Permissions

Figure 29

The $Q^2$ dependence of $Q^3{A}_{1/2}$ for $\eta$ production. Scaling in this quantity appears to begin at a photon momentum transfer of $Q^2~5\hspace{0.5em}{\mathrm{GeV}}^2$. The dashed lines are a high $Q^2$, pQCD calculation from Carlson and Poor [4] using three different nucleon distribution amplitudes.Reuse & Permissions

Figure 30

The $Q^2$ dependence of $Q^3{A}_{1/2}(S_{11})/Q^4{G}_M^p$ for $\eta$ production.Reuse & Permissions