Cross Sections for the Exclusive Photon Electroproduction on the Proton and Generalized Parton Distributions

Unpolarized and beam-polarized fourfold cross sections $(d^4\sigma /d{Q}^{2}d{x}_{B}dtd\varphi )$ for the $ep\to e^{\prime }{p}^{\prime }\gamma$ reaction were measured using the CLAS detector and the 5.75-GeV polarized electron beam of the Jefferson Lab accelerator, for 110 ($Q^2,x_B,t$) bins over the widest phase space ever explored in the valence-quark region. Several models of generalized parton distributions (GPDs) describe the data well at most of our kinematics. This increases our confidence that we understand the GPD $H$, expected to be the dominant contributor to these observables. Through a leading-twist extraction of Compton form factors, these results support the model predictions of a larger nucleon size at lower quark-momentum fraction $x_B$.

Figure 1

Left: The dominant mechanism for the DVCS process at large $Q^2$ and small $|t|$, as predicted by the QCD factorization theorem. Right: The Bethe-Heitler (BH) process.

Figure 2

Two of the four variables on which $3\sigma$ exclusivity cuts (vertical lines) were applied to select the $ep\to e^{\prime }{p}^{\prime }\gamma$ reaction: $\mathrm{\Delta }\varphi$ and ${\theta }_{\gamma X}$. Black solid distributions show the events with at least one electron, one proton, and one photon, after applying the cuts on $M{M}_{e^{\prime }{p}^{\prime }}^2$. Each blue shaded distribution shows the events remaining after applying the cuts on all the variables except the plotted one.

Figure 3

($Q^2,x_B$) and ($-t,x_B$) kinematic coverages, with the corresponding binning.

Figure 4

Top six plots: Unpolarized cross section $(d^4{\sigma }_{ep\to e^{\prime }{p}^{\prime }\gamma }/d{Q}^{2}d{x}_{B}dtd\varphi )$ and beam-polarized cross-section difference $\mathrm{\Delta }(d^4\sigma )$ for the $ep\to e^{\prime }{p}^{\prime }\gamma$ reaction, as a function of $\varphi$, for $(Q^2,x_B)=(1.63{\mathrm{GeV}}^2,0.185)$ and three $-t$ values. Bottom six plots: The same observables for $(Q^2,x_B)=(2.78{\mathrm{GeV}}^2,0.335)$ and three $-t$ values. The green long-dashed curves show the BH contribution only. The other curves are the predictions of four GPD models from three groups: VGG [6, 22, 23] (blue solid curves), KMS [24] (cyan dash-dotted curves), and two versions of the KM model [25, 26], KM10 (red dotted curves) and KM10a (red short-dashed curves). The blue bands show the systematic uncertainties.

Figure 5

Results of the CFF fit of our data for $H_{\mathrm{Im}}$ and $H_{\mathrm{Re}}$, for three ($Q^2,x_B$) bins, as a function of $t$. The blue solid curves are the VGG predictions. The black dashed curves show the fit of the results by the function $A{e}^{bt}$.