E00-110 experiment at Jefferson Lab Hall A: Deeply virtual Compton scattering off the proton at 6 GeV

We present final results on the photon electroproduction $\left(\vec{e}p\to ep\gamma \right)$ cross section in the deeply virtual Compton scattering (DVCS) regime and the valence quark region from Jefferson Lab experiment E00-110. Results from an analysis of a subset of these data were published before, but the analysis has been improved, which is described here at length, together with details on the experimental setup. Furthermore, additional data have been analyzed, resulting in photon electroproduction cross sections at new kinematic settings for a total of 588 experimental bins. Results of the $Q^2$ and $x_B$ dependencies of both the helicity-dependent and the helicity-independent cross sections are discussed. The $Q^2$ dependence illustrates the dominance of the twist-2 handbag amplitude in the kinematics of the experiment, as previously noted. Thanks to the excellent accuracy of this high-luminosity experiment, it becomes clear that the unpolarized cross section shows a significant deviation from the Bethe-Heitler process in our kinematics, compatible with a large contribution from the leading twist-2 ${\mathrm{DVCS}}^2$ term to the photon electroproduction cross section. The necessity to include higher-twist corrections to fully reproduce the shape of the data is also discussed. The DVCS cross sections in this paper represent the final set of experimental results from E00-110, superseding the previous publication.

Figure 1

Lowest-order QED amplitude for the $ep\to ep\gamma$ reaction including its decomposition. The momentum four-vectors of all external particles are labeled at left. The net four-momentum transfer to the proton is ${\mathrm{\Delta }}_{\mu }={(q-q^{\prime })}_{\mu }={(p^{\prime }-p)}_{\mu }$. In the virtual Compton scattering (VCS) amplitude, the (spacelike) virtuality of the incident photon is $Q^2=-q^2=-{(k-k^{\prime })}^2$. In the Bethe-Heitler (BH) amplitude, the virtuality of the incident photon is $-{\mathrm{\Delta }}^2=-t$. Standard $(e,e^{\prime })$ invariants are $s_e={(k+p)}^2$, $x_B=Q^2/\left(2qp\right)$, and $W^2={(q+p)}^2$.

Figure 2

The leading-order virtual Compton scattering (VCS) amplitude in the limit of large $Q^2$, fixed $x_B$, and small $t={\mathrm{\Delta }}^2$. The kinematic variable $\xi =-{(q+q^{\prime })}^2/\left[2(q+q^{\prime })P\right]$, with $P=(p+p^{\prime })/2$. In the aforementioned limit $\xi \to x_B/(2-x_B)$ and $2\xi \to {\mathrm{\Delta }}^{+}/P^{+}=({\mathrm{\Delta }}^0+{\mathrm{\Delta }}^z)/(P^0+P^z)$, with the $z$ direction parallel to $\mathbf{P}$ in the $\mathbf{q}+\mathbf{P}=0$ center-of-mass frame. Similarly, in the middle diagram, the quark and proton lines are labeled by their “+” momentum fractions and “+” momentum components, respectively.

Figure 3

Distribution of $H(e,e^{\prime }\gamma )X$ events in the $[x_B$, $Q^2]$ plane, for Kin2 ($x_B=0.36$, $Q^2=1.9{\mathrm{GeV}}^2$) and Kin3 ($x_B=0.36$, $Q^2=2.3{\mathrm{GeV}}^2$). Events for KinX2 ($x_B=0.39$, $Q^2=2.06{\mathrm{GeV}}^2$) and KinX3 ($x_B=0.34$, $Q^2=2.17{\mathrm{GeV}}^2$) are bounded by the two horizontal lines at $Q^2=1.95{\mathrm{GeV}}^2$ and $Q^2=2.30{\mathrm{GeV}}^2$.

Figure 4

Setup of the E00-110 experiment in Hall A of Jefferson Lab. The photon calorimeter as well as the proton array were centered on the virtual photon direction $\mathbf{q}$, then shifted sideways by half a calorimeter block away from the beam to limit the singles rate on the detector elements close to the beamline.

Figure 5

Perspective view of the downstream face of electromagnetic calorimeter. The virtual photon (${\gamma }^{*}$) acceptance is shown projected on the calorimeter plane. The distance (black line) between the “impact” of the virtual photon and the detected real photon ($\gamma$) position is roughly proportional to $\sqrt{t-t_{\text{min}}}$ for the small $t_{\text{min}}-t$ values of this experiment. The angle $\varphi$ is the azimuthal angle of the photon with respect to the plane formed by the incident beam and the virtual photon. For the central $(e,e^{\prime })$ kinematics indicated by ${\gamma }^{*}$, $\varphi$ is measured counterclockwise from the horizontal (to the right) direction.

Figure 6

Signal and background rates (normalized to the electron beam current) in one of the planes of the electron detector as a function of strip number (top) and asymmetry measured for each of the laser polarization states and the background as a function of strip number (bottom).

Figure 7

Compton polarimeter results, using only the electron detector. Beam polarization is shown in the top plot. The bottom plot shows the signal-to-background ratio. The first three points in the beginning of the experiment correspond to a nonoptimal Wien angle setting.

Figure 8

Longitudinal shower profile for different incoming particles into the DVCS calorimeter, obtained from the Monte Carlo simulation. The aluminum shielding corresponds to the total thickness of material between the target and the calorimeter crystals, and includes both the scattering chamber and some additional Al shielding in front of the calorimeter front face.

Figure 9

Energy measured in the calorimeter minus energy expected from elastic kinematics during elastic calibrations runs. In both elastic calibration periods, we obtained 2.4% energy resolution at an elastic energy of 4.2 GeV. The results of the second calibration when first calibration coefficients are used are also plotted to show the necessity of a careful monitoring of the coefficients between these two calibration points.

Figure 10

($\gamma \gamma$) invariant mass for Kin2.

Figure 11

Flash ADC value as a function of time recorded by the ARS system for a typical calorimeter pulse.

Figure 12

Distribution of the sum of all ten Čerenkov PMT ADC values for each kinematic setting. The cut applied to remove the one-photoelectron signal from data is also shown.

Figure 13

Reaction point along the beam reconstructed by the HRS. The cut on the target length applied is shown by the vertical lines. The 7.8-mm downstream shift of the target observed during the experiment is also evident.

Figure 14

(Top) Resolution of the vertex reconstruction from a multifoil target. (Bottom) Closeup of the central foil fit, which results in a $\sigma =1.9$-mm resolution. The foil thickness is 1 mm and the HRS was at $37.{69}^{\circ }$ during this run.

Figure 15

Squared missing mass $M_X^2$ associated with the reaction $ep\to e\gamma X$ for Kin2. Total events for Kin2 are represented as inverted black triangles, the estimated ${\pi }^0$ contamination is represented as green diamonds, the distribution after the subtraction of accidentals and ${\pi }^0$'s is shown as blue open circles. Finally, it is compared with the normalized DVCS Monte Carlo (described in Sec. 4e) shown as a red solid line. To remove unnecessary uncertainties owing to low-missing-mass-squared accidental events, we apply a cut requiring a missing-mass squared higher than 0.5 ${\mathrm{GeV}}^2/c^4$ for all kinematics.

Figure 16

Time spectrum of blocks with $E>300$ MeV in the Kin3 setting. It shows the 45-ns time window of the wave-form analysis. The 2-ns Continuous electron beam accelerator facility (CEBAF) beam structure is clearly visible. The coincidence $[-3,3]$-ns window used for clustering is shown by the solid line. Dashed lines show windows used for the HRS-calorimeter accidental subtraction.

Figure 17

Estimated efficiency (color scale) of the ${\pi }^0$ subtraction using a Monte Carlo simulation as a function of the photon cluster position in the calorimeter ($x_{\mathrm{clus}}$ and $y_{\mathrm{clus}}$). An octagonal cut on the front face of the calorimeter applied to all events was used to ascertain a nearly full efficiency of the ${\pi }^0$ subtraction; it is shown as a black line. The general shape and size of the cut can be understood from the size of the front face and the width of the shower profile (Fig. 8).

Figure 18

Total counts (top) and difference of counts for opposite helicities (bottom) as a function of $\varphi$ for the Kin3 bin $x_B=0.37$, $Q^2=2.36{\mathrm{GeV}}^2$, and $-t=0.32{\mathrm{GeV}}^2$. The solid curve histogram in black corresponds to the distribution of events after all analysis cuts have been applied. The estimated remaining contribution corresponding to accidental events is shown as a dashed green histogram. The estimated ${\pi }^0$ contribution is represented as a red dotted histogram.

Figure 19

Mean $\mu$ (top) and standard deviation $\sigma$ (bottom) of the Gaussian distribution used to smear the simulated photon data of Kin3 viewed on the calorimeter surface $y_{\text{clus}}$ vs $x_{\text{clus}}$ (beam on the right side).

Figure 20

(Top) Variation of the $ep\to ep\gamma$ cross section for Kin2, $-t=0.17{\mathrm{GeV}}^2$, as a function of the missing-mass-squared cut, for $\varphi =0^{\circ }$ (upper blue points) and $\varphi ={180}^{\circ }$ (lower black points). The dotted vertical line corresponds to the nominal cut. The systematic uncertainties are evaluated bin by bin in $\varphi$ and $t$ for each kinematic setting by studying the variation of the cross section between the nominal and the lower missing-mass-squared cut (dashed line). The inset represents the same cuts on the missing-mass plot, along with the normalized Monte Carlo distribution. (Bottom) Ratio of the running integrals of the experimental and Monte Carlo missing-mass spectra as a function of the upper limit on the squared missing mass.

Figure 21

Difference in % between the cross section extracted with the squared DVCS amplitude term and with the $\mathrm{Re}{\mathcal{C}}^{\mathcal{I},V}$ term for $x_B=0.37$, $Q^2=2.36{\mathrm{GeV}}^2$, and $-t=0.33{\mathrm{GeV}}^2$. The $\varphi$ profile of the difference is a consequence of the small $cos\varphi$ and $cos2\varphi$ dependencies of the $\mathrm{Re}{\mathcal{C}}^{\mathcal{I},V}$ kinematic coefficient. Both extractions give almost the same reduced ${\chi }^2/\text{DOF}=0.94$ (nominal) and 0.93 (alternate) for the entire Kin2 setting.

Figure 22

Unpolarized (top) and helicity-dependent (bottom) cross-section extraction for the Kin3 bin $-t=0.32{\mathrm{GeV}}^2$. The error bars on the data points are statistical only. The shaded areas represent the statistical uncertainty for each contribution.

Figure 23

Combinations of effective CFFs extracted from the fitting procedure described in Sec. 4f using the formalism developed in Ref. [41], integrated over $t$ and plotted as a function of $Q^2$. The top three plots show the effective CFFs resulting from the unpolarized cross-section fit (Kin2 and Kin3), whereas the bottom plots show the effective CFFs resulting from the helicity-dependent cross-section fit (Kin1–3). The shaded areas represent systematic uncertainties.

Figure 24

Unpolarized cross sections for Kin2. Each $t$-bin corresponds to slightly different average $(x_B,Q^2)$ values; their range is indicated in the legend, their specific values are listed in the data tables. Error bars are statistical only. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The KM10a model along with its modified version (including the TMC effects) are shown as dotted blue and solid green curves, respectively. The BH contribution is represented as a dashed red line.

Figure 25

Unpolarized cross sections for Kin3. Error bars are statistical only. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The KM10a model along with its modified version (including the TMC effects) are shown as dotted blue and solid green curves, respectively. The BH contribution is represented as a dashed red line.

Figure 26

Cross-section differences for opposite beam helicities for Kin1. Error bars are statistical only. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The KM10a model along with its modified version (including the TMC effects) are shown as dotted blue and solid green curves, respectively, except for the first $t$ bin, which is outside the prescribed range of this model.

Figure 27

Cross-section differences for opposite beam helicities for Kin2. Error bars are statistical only. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The KM10a model along with its modified version (including the TMC effects) are shown as dotted blue and solid green curves, respectively.

Figure 28

Cross-section differences for opposite beam helicities for Kin3. Error bars are statistical only. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The KM10a model along with its modified version (including the TMC effects) are shown as dotted blue and solid green curves, respectively.

Figure 29

Unpolarized cross sections for KinX2. Error bars are statistical only. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The KM10a model along with its modified version (including the TMC effects) are shown as dotted blue and solid green curves, respectively. The BH contribution is represented as a dashed red line.

Figure 30

Unpolarized cross sections for KinX3. Error bars are statistical only. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The KM10a model along with its modified version (including the TMC effects) are shown as dotted blue and solid green curves, respectively. The BH contribution is represented as a dashed red line.

Figure 31

Cross-section differences for opposite beam helicities for KinX2. Error bars are statistical only. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The KM10a model along with its modified version (including the TMC effects) are shown as dotted blue and solid green curves, respectively.

Figure 32

Cross-section differences for opposite beam helicities for KinX3. Error bars are statistical only. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The KM10a model along with its modified version (including the TMC effects) are shown as dotted blue and solid green curves, respectively.

Figure 33

Unpolarized (top) and helicity-dependent (bottom) cross sections for the Kin2 bin $-t=0.23{\mathrm{GeV}}^2$. The light blue area represents the point-to-point systematic uncertainties added linearly to the normalization error. The predictions from the distribution-based models KMS12 and VGG are shown as the dashed green and solid red curves, respectively. The KM10a fit is represented as the solid blue line. The target-mass and finite-$t$ corrections are included in the KMS12 model and shown as the dot-dashed curve. The correction is then applied to the KM10a model shown as the dotted blue line.