Longitudinal Target-Spin Asymmetries for Deeply Virtual Compton Scattering

A measurement of the electroproduction of photons off protons in the deeply inelastic regime was performed at Jefferson Lab using a nearly 6 GeV electron beam, a longitudinally polarized proton target, and the CEBAF Large Acceptance Spectrometer. Target-spin asymmetries for $ep\to e^{\prime }{p}^{\prime }\gamma$ events, which arise from the interference of the deeply virtual Compton scattering and the Bethe-Heitler processes, were extracted over the widest kinematics in $Q^2$, $x_B$, $t$, and $\varphi$, for 166 four-dimensional bins. In the framework of generalized parton distributions, at leading twist the $t$ dependence of these asymmetries provides insight into the spatial distribution of the axial charge of the proton, which appears to be concentrated in its center. These results also bring important and necessary constraints for the existing parametrizations of chiral-even generalized parton distributions.

Figure 1

The “handbag” diagram for the DVCS process on the proton $ep\to e^{\prime }{p}^{\prime }\gamma$. $t=(p-p^{\prime }{)}^2$ is the squared four-momentum transfer between the initial and final protons. $\xi$ is proportional to the Bjorken variable $x_B$ [$\xi \simeq x_B/(2-x_B)$, where $x_B=Q^2/2M\nu$, $M$ is the proton mass, and $\nu =E_e-E_{e^{\prime }}$]. $x$ is not accessible experimentally in the DVCS process.

Figure 2

Left: Squared missing mass of $X$ in the $ep\to e^{\prime }{p}^{\prime }X$ reaction; right: $\mathrm{\Delta }\varphi$. The dot-dashed and solid lines show the events before exclusivity cuts for, respectively, ${}^{14}{\mathrm{NH}}_3$ and ${}^{12}\mathrm{C}$ data; the gray shaded and black shaded plots are the events after all cuts but the one on the plotted variable were applied for, respectively, ${}^{14}{\mathrm{NH}}_3$ and ${}^{12}\mathrm{C}$ data. The lines and arrows show the limits of the cuts. The plots for ${}^{14}{\mathrm{NH}}_3$ and ${}^{12}\mathrm{C}$ data are normalized to each other via their relative luminosities.

Figure 3

Target-spin asymmetry ($A_{\mathrm{UL}}$) for DVCS-BH events as a function of $\varphi$ for each three-dimensional bin in $Q^2\text{−}{x}_B$ (rows) and $-t$ (columns) (the bin limits are shown on the top axis). The shaded bands are the systematic uncertainties. The thin black line is the fit to $A_{\mathrm{UL}}$ with the function $\alpha \sin \varphi /(1+\beta \cos \varphi )$ [for all bins but those marked with $(*)$, which were fitted with $\alpha \sin \varphi$ due to the limited $\varphi$ coverage]. The dashed red lines are the predictions of the VGG model [20].

Figure 4

Plots (a)–(e): $-t$ dependence of the $\sin \varphi$ amplitude of $A_{\mathrm{UL}}$ for each $Q^2\text{−}{x}_B$ bin. The shaded bands represent the systematic uncertainties. The curves show the predictions of four GPD models: (i) VGG [20] (red dashed line), (ii) GK [24] (black dotted line), KMM12 [25] (blue thick solid line), GGL [26] (black solid line). Plot (f): Comparison of the $\sin \varphi$ amplitude of $A_{\mathrm{UL}}$ as a function of $-t$ for the results of this work (black dots) integrated over all $Q^2$ and $x_B$ values [$⟨Q^2⟩=2.4(\mathrm{GeV}/c{)}^2$, $⟨x_B⟩=0.31$], the HERMES results [14] (green squares) at $⟨Q^2⟩=2.459(\mathrm{GeV}/c{)}^2$, $⟨x_B⟩=0.096$, and the previously published CLAS results [13] (pink triangles), at $⟨Q^2⟩=1.82(\mathrm{GeV}/c{)}^2$, $⟨x_B⟩=0.28$.