Single and double spin asymmetries for deeply virtual Compton scattering measured with CLAS and a longitudinally polarized proton target

Single-beam, single-target, and double spin asymmetries for hard exclusive electroproduction of a photon on the proton $\overrightarrow{e}\overrightarrow{p}\to e^{\prime }{p}^{\prime }\gamma$ are presented. The data were taken at Jefferson Lab using the CEBAF large acceptance spectrometer and a longitudinally polarized ${}^{14}{\mathrm{NH}}_3$ target. The three asymmetries were measured in 165 four-dimensional kinematic bins, covering the widest kinematic range ever explored simultaneously for beam and target-polarization observables in the valence quark region. The kinematic dependences of the obtained asymmetries are discussed and compared to the predictions of models of generalized parton distributions. The measurement of three DVCS spin observables at the same kinematic points allows a quasi-model-independent extraction of the imaginary parts of the $H$ and $\tilde{H}$ Compton form factors, which give insight into the electric and axial charge distributions of valence quarks in the proton.

Figure 1

The handbag diagram for the DVCS process on the proton $ep\to e^{\prime }{p}^{\prime }{\gamma }^{\prime }$.

Figure 2

Scheme to illustrate the definition of the angle $\varphi$, formed by the leptonic and hadronic planes.

Figure 3

Drawing of the experimental setup, including CLAS with its components (DC, EC, CC, TOF), the inner calorimeter and the polarized target.

Figure 4

Total energy deposited in the EC ($\text{inner}+\text{outer}$ layers), $E$, divided by the particle momentum $p$ as a function of $p$ for all the negative tracks. Top: Negative charged particles, before cuts. Bottom: After minimum-momentum, $E{C}_{\text{in}}$, fiducial and timing cuts.

Figure 5

Number of CC photoelectrons (times 10) for all negative tracks (top), after applying all PID and fiducial cuts for electrons (middle), and after $ep\gamma$ exclusivity cuts (bottom).

Figure 6

$\beta$ as a function of $p$ for positively charged particles. The black lines represent the cut applied to select protons.

Figure 7

Polar angle $\theta$ as a function of the reconstructed energy for IC hits. The red line shows the cut on the minimum energy at 0.25 GeV, as well as the “triangular” cut to remove the low-energy/low-$\theta$ accidental background, applied to select photons.

Figure 8

Distribution of $\beta$ vs energy for neutrals measured by time of flight with EC. The events for which $\beta >0.92$ (black line) were retained as photon candidates.

Figure 9

DVCS channel. Comparison of data (black lines) and Monte Carlo simulation (shaded areas). From the top left, $Q^2$, $-t$, $x_B$ and $\varphi$ are plotted. The histograms are normalized to one another via the ratio of their integrals.

Figure 10

Exclusive ${\pi }^0$ channel. Comparison of data (black lines) and Monte Carlo simulation (shaded areas). Starting from the top left, $Q^2$, $-t$, $x_B$ and $\varphi$ are plotted. The histograms are normalized to one another via the ratio of their integrals.

Figure 11

IC topology. Effects of the exclusivity cuts. Top left: Squared missing mass of the $ep$ system. Top right: the angle ${\theta }_{\gamma X}$ between the measured photon and the calculated photon from $ep\to e^{\prime }{p}^{\prime }X$. Bottom left: Difference between two ways to compute the $\varphi$ angle. Bottom right: Missing transverse momentum $p_{\text{perp}}$ calculated from $ep\to e^{\prime }{p}^{\prime }\gamma X$. The dot-dashed and solid lines show the events before exclusivity cuts for, respectively, ${}^{14}{\mathrm{NH}}_3$ and ${}^{12}\mathrm{C}$ data, while the gray and black shaded areas represent the events after all exclusivity cuts except for the one on the plotted variable for, respectively, ${}^{14}{\mathrm{NH}}_3$ and ${}^{12}\mathrm{C}$ data. The lines and arrows show the limits of the selection cuts. The plots for ${}^{14}{\mathrm{NH}}_3$ and ${}^{12}\mathrm{C}$ data are normalized to each other via their relative luminosities.

Figure 12

EC topology. See caption of Fig. 11.

Figure 13

Grid showing the binning in the $Q^2\text{−}{x}_B$ space (top) and in the $-t$-$x_B$ space (bottom).

Figure 14

Dilution factor as a function of (from left to right) $x_B$, $Q^2$, $-t$, $\varphi$, for the DVCS analysis (top) and for the $ep{\pi }^0$ analysis (bottom). Part B.

Figure 15

Exclusive ${\pi }^0$ analysis, IC-IC topology. Effects of the $ep{\pi }^0$ exclusivity cuts on ${\mathrm{MM}}^2(ep)$ (top), ${\theta }_{{\pi }^{0}X}$ (middle), and two-photon invariant mass (bottom). The dot-dashed and solid lines show the events before exclusivity cuts for, respectively, ${}^{14}{\mathrm{NH}}_3$ and ${}^{12}\mathrm{C}$ data, while the gray and black shaded plots represent the events after all exclusivity cuts but the one on the plotted variable for, respectively, ${}^{14}{\mathrm{NH}}_3$ and ${}^{12}\mathrm{C}$ data. The lines and arrows show the limits of the selection cuts.

Figure 16

Exclusive ${\pi }^0$ analysis, EC-EC topology. See caption of Fig. 15.

Figure 17

Beam-spin asymmetry for the reaction $ep\to e^{\prime }{p}^{\prime }\gamma$ as a function of $\varphi$ for the various $Q^2\text{−}{x}_B$ (rows) and $-t$ (columns) bins. The point-by-point systematic uncertainties are represented by the shaded bands. The solid black curve is the fit with the function in Eq. (42). In the highest $-t$ bin of the third ($Q^2\text{−}{x}_B$) bin, $\beta$ was set to zero due to the limited $\varphi$ coverage, while no fit is performed on the first $-t$ bin of the highest ($Q^2\text{−}{x}_B$) bin, where only one data point is present. The curves show the predictions of the VGG [23] (red-dashed) and KMM12 [26] (green-dotted) models.

Figure 18

$t$ dependence for each $Q^2\text{−}{x}_B$ bin of the ${\alpha }_{\mathrm{LU}}$ term of the beam-spin asymmetry. The curves show the predictions of four GPD models for the BSA at $\varphi =90°$: (i) VGG [23] (red dashed), (ii) KMM12 [26] (green dotted), (iii) GK [25] (blue dash-dotted), and (iv) GGL [27] (orange dashed-three-dotted). The square black points are the results obtained from the present analysis; the triangular green data come from the previous CLAS experiment with unpolarized proton target [15].

Figure 19

Target-spin asymmetry for the reaction $ep\to e^{\prime }{p}^{\prime }\gamma$ as a function of $\varphi$ for the various $Q^2\text{−}{x}_B$ (rows) and $-t$ (columns) bins. The point-by-point systematic uncertainties are represented by the shaded bands. The solid black curve is the fit with the function in Eq. (43). In the highest $-t$ bin of the third ($Q^2\text{−}{x}_B$) bin, $\beta$ was set to zero due to the limited $\varphi$ coverage, while no fit is performed on the first $-t$ bin of the highest ($Q^2\text{−}{x}_B$) bin, where only one data point is present. The curves show the predictions of the VGG [23] (red-dashed) and KMM12 [26] (green-dotted) models.

Figure 20

$t$ dependence, for each $Q^2\text{−}{x}_B$ bin, of the ${\alpha }_{\mathrm{UL}}$ term of the target-spin asymmetry. The curves show the predictions of four GPD models for the TSA at $\varphi =90°$: (i) VGG [23] (red dashed), (ii) KMM12 [26] (green dotted), (iii) GK [25] (blue dash-dotted), and (iv) GGL [27] (orange dashed-three-dotted).

Figure 21

Comparisons of the $t$ dependences of the $\sin \varphi$ term of the $ep\gamma$ target-spin asymmetries for the present data, integrated over $Q^2$ and $x_B$ (black circles), the previous CLAS experiment [13] (magenta triangles), and HERMES [16] (green squares).

Figure 22

Double spin asymmetry for the reaction $ep\to e^{\prime }{p}^{\prime }\gamma$ as a function of $\varphi$ for the various $Q^2\text{−}{x}_B$ (rows) and $-t$ (columns) bins. The point-by-point systematic uncertainties are represented by the shaded bands. The solid black curve is the fit with the function in Eq. (45). In the highest $-t$ bin of the third ($Q^2\text{−}{x}_B$) bin, $\beta$ was set to zero due to the limited $\varphi$ coverage, while no fit is performed on the first $-t$ bin of the highest ($Q^2\text{−}{x}_B$) bin, where only one data point is present. The red-dashed and green-dotted curves are predictions of the VGG and KMM12 models, respectively. The pink dashed-two-dotted curves are the calculations for the Bethe-Heitler process.

Figure 23

$t$ dependence for each $Q^2\text{−}{x}_B$ bin of the constant term ${\kappa }_{\mathrm{LL}}$ of the double spin asymmetry. The pink dashed-two-dotted curves are the calculations of the DSA for the Bethe-Heitler process alone. The curves show the predictions for the full $ep\gamma$ amplitude of four GPD models: (i) VGG [23] (red dashed), (ii) KMM12 [26] (green dotted), (iii) GK [25] (blue dash-dotted), and (iv) GGL [27] (orange dashed-three-dotted).

Figure 24

$t$ dependence for each $Q^2\text{−}{x}_B$ bin of the $\cos \varphi$ term ${\lambda }_{\mathrm{LL}}$ of the double spin asymmetry. The pink dashed-two-dotted curves are the calculations of the DSA for the Bethe-Heitler process alone. The curves show the predictions for the full $ep\gamma$ amplitude of four GPD models: (i) VGG [23] (red dashed), (ii) KMM12 [26] (green dotted), (iii) GK [25] (blue dash-dotted), and (iv) GGL [27] (orange dashed-three-dotted).

Figure 25

$t$ dependence for each $Q^2\text{−}{x}_B$ bin of $H_{\mathrm{Im}}$ (black squares) and ${\tilde{H}}_{\mathrm{Im}}$ (red circles). The full points are obtained by fitting the present data (TSA, BSA and DSA). The empty points were obtained by fitting the BSA results from [15] integrated over all values of $Q^2$ at $x_B\sim 0.25$, and the TSAs from [13].