Leading twist asymmetries in deeply virtual Compton scattering

TL;DR

The paper addresses extracting skewed parton distributions (SPDs) from deeply virtual Compton scattering (DVCS) by analyzing spin, charge, and azimuthal asymmetries at leading $ ext{twist-2}$. It develops the cross-section formalism including DVCS, Bethe-Heitler, and their interference, with explicit leading-$ ext{twist-2}$ amplitudes ${\cal H}_1, {\cal E}_1, \widetilde{\cal H}_1, \widetilde{\cal E}_1$ obtained from SPD convolutions. The work examines small-$x$ and large-$|\Delta^2|$ regimes to map out extraction strategies and presents numerical estimates for HERA and HERMES using Forward Parton Distribution (FPD) and Double Distribution (DD) models, predicting sizable asymmetries sensitive to ${\cal H}_1, \widetilde{\cal H}_1, {\cal E}_1$. It cautions that twist-three and next-to-leading-order (NLO) corrections could be sizable, suggesting further work to refine the framework. Overall, the paper provides a practical framework to constrain SPDs and illuminate the quark and gluon angular momentum content of the nucleon via DVCS observables.

Abstract

We calculate spin, charge, and azimuthal asymmetries in deeply virtual Compton scattering at leading twist-two level. The measurement of these asymmetries gives an access to the imaginary and real part of all deeply virtual Compton scattering amplitudes. We note that a consistent description of this process requires taking into account twist-three contributions and give then a model dependent estimate of these asymmetries.

Figures (5)

• Figure 1: The virtual Compton scattering amplitude and the Bethe-Heitler process.
• Figure 2: The kinematics of the reaction $e (\hbox{\boldmath$k$}) N (M) \to e(\hbox{\boldmath$k$}') N (\hbox{\boldmath$P$}_2) \gamma (\hbox{\boldmath$q$}_2)$ in the rest frame of the target.
• Figure 3: (a) Ratios of different approximations of the BH cross section to the exact one in dependence of the azimuthal angle $\phi_r$ for ${\cal Q}^2 = 4 \hbox{GeV}^2$ and $x = 10^{-4}$ for the Pade-type approximation for $\Delta^2 = - 0.1 \hbox{GeV}^2$ (solid) and $\Delta^2=-0.5 \hbox{GeV}^2$ (dashed) and for the leading approximation (\ref{['cal-BH-LO-unp']}) (dash-dotted and dotted, respectively). (b) Unpolarized azimuthal angle asymmetry for $\Delta^2 = - 0.05 (- 0.25) \hbox{GeV}^2$ versus $x$. Solid (dash-dotted) and dashed (dotted) lines show the result for the Pade and leading approximation, respectively, where $\kappa_{\rm sea}$ is set to zero.
• Figure 4: Unpolarized azimuthal charge asymmetry $A_{\rm C}$ for ${\cal Q}^2 = 4 \hbox{GeV}^2$ and $x = 5\cdot 10^{-4}$ with $\kappa_{\rm sea} = - 2$ at LO for the complete expression (solid curve) and neglecting the ${\cal E}_1$ contribution (dashed curve) plotted in (a) versus $- \Delta^2$. The same asymmetry for $\Delta^2 = - 0.05 \hbox{GeV}^2$ (solid curve) and $\Delta^2 = - 0.25 \hbox{GeV}^2$ (dashed curve) at LO is shown in (b) for the region $1\cdot 10^{-4} \le x \le 2\cdot 10^{-3}$. In (c) and (d) the same is shown for the electron single spin asymmetry.
• Figure 5: Perturbative leading order results for the charge asymmetry for an unpolarized beam (a), single spin asymmetries for a polarized positron beam (b) and an unpolarized target; as well as for an unpolarized lepton beam and a longitudinally (c) (transversally (d)) polarized proton target versus $x$, for ${\cal Q}^2 = 4\ {\rm GeV}^2$. The predictions for the model specified in the text are shown as solid (dotted) curves for $\Delta^2 = -0.1 (0.5)\ {\rm GeV}^2$, respectively. The same model however with neglected spin-flip contributions are presented as dashed (dash-dotted) line for the same values of $\Delta^2$.