Measurement of Deeply Virtual Compton Scattering Beam-Spin Asymmetries

The beam-spin asymmetries in the hard exclusive electroproduction of photons on the proton ($\overrightarrow{e}p\to ep\gamma$) were measured over a wide kinematic range and with high statistical accuracy. These asymmetries result from the interference of the Bethe-Heitler process and of deeply virtual Compton scattering. Over the whole kinematic range ($x_B$ from 0.11 to 0.58, $Q^2$ from 1 to $4.8{\mathrm{GeV}}^2$, $-t$ from 0.09 to $1.8{\mathrm{GeV}}^2$), the azimuthal dependence of the asymmetries is compatible with expectations from leading-twist dominance, $A\simeq a\sin \varphi /(1+c\cos \varphi )$. This extensive set of data can thus be used to constrain significantly the generalized parton distributions of the nucleon in the valence quark sector.

Figure 1

Schematic representation of the leading-order handbag diagram contribution to DVCS, where $x$ is the average longitudinal momentum fraction of the active quark in the initial and final states [measured in terms of the average hadron momentum $(p+p^{\prime })/2$], while $2\xi$ is their difference; it is related to the Bjorken scaling variable by $\xi \simeq x_B/(2-x_B)$. The squared four-momentum transfer to the target is $t=(p^{\prime }-p{)}^2$, and the squared four-momentum of the virtual photon is $-Q^2$.

Figure 2

Distributions in cone angle ${\theta }_{\gamma Y}$ for the $ep\to epY$ reaction (left) and in missing energy $E_X$ for the $ep\to ep\gamma X$ reaction (right), before (black dotted curve) and after (red solid) all kinematic cuts discussed in the text but the one on the histogrammed variable, given by the location of the arrow. The thin solid black line represents the physical background, calculated from measured $ep\to ep{\pi }^0$ events. The distributions are integrated over all kinematic variables and apply to the case where the photon is detected in the IC.

Figure 3

Left: kinematic coverage and binning in the ($x_B$, $Q^2$) space. Right: $A(\varphi )$ for 2 of the 62 ($x_B$, $Q^2$, $t$) bins, corresponding to $⟨x_B⟩=0.249$, $⟨Q^2⟩=1.95{\mathrm{GeV}}^2$, and two values of $⟨t⟩$. The red long-dashed curves correspond to fits with Eq. (2) (with $d=0$). The black dashed curves correspond to a Regge calculation [27]. The blue curves correspond to the GPD calculation described in the text, at twist-2 (solid) and twist-3 (dot-dashed) levels, with $H$ contribution only.

Figure 4

$a=A(90°)$ as a function of $-t$. Each individual plot corresponds to a bin in ($x_B$, $Q^2$). Systematic uncertainties and bin limits are illustrated by the gray band in the lower left plot. Black circles are from this work. Previous results are from Ref. [12] (red square) or extracted from cross section measurements [17] (green triangles), at similar—but not equal—values of $⟨x_B⟩$ and $⟨Q^2⟩$. See Fig. 3 caption for curve legend.