Radiative effects in deep virtual Compton scattering

Radiative corrections to the cross sections of photon electroproduction and the single spin asymmetries induced by the interference between the Bethe-Heitler and deep virtual Compton scattering amplitudes are calculated within the leading log approximation. The deep virtual Compton scattering amplitude is presented in the Belitsky-Müller-Kirchner (BMK) approximation for the polarized initial particles. The Fortran code for estimation of the radiative effects in a given kinematic point and Monte Carlo generator for simulation of one or two photons are developed. Numerical results are performed for beam-spin asymmetries in kinematical conditions of current experiments in the Jefferson Laboratory.

Figure 1

Feynman graphs of BH (a) and (b) and DVCS process (c).

Figure 2

Feynman graphs with two real photons in the final state: both photons produced by leptons (a), (b), and (c) and by leptons and hadrons (d) and (e).

Figure 3

The dependence of $z_1$ and $z_2$ on $V^2$ for $\cos (\varphi )>0$ (a) and $\cos (\varphi )<0$ (b). Other kinematical variables used for this example were $x=0.175$, $Q^2=1{\mathrm{GeV}}^2$, $t=-0.1{\mathrm{GeV}}^2$, and $E_{\text{beam}}=5.75\mathrm{GeV}$. In plot (b), the curves $z_{1,2}(V^2)$ cross the lines $z_{1,2}=z_{1,2}^m$ at $V^2=V_{1s,p}^2$ and reach their minimum values at $V^2=V_{2s,p}^2$ such that $V_{1s,p}^2<V_{2s,p}^2<V_{\max }^2$. The explicit expressions for $z_{1,2}^p$ and $V_{1,2s,p}^2$ are given in the Appendix.

Figure 4

The one-loop Feynman graphs for the BH (a-h) and DVCS (k) amplitudes containing the infrared divergence and the graphs for the vacuum polarization (i), (j), and (l).

Figure 5

The $\varphi$-dependence of the asymmetry (upper) and RC factors (lower plots). The dashed curve at the upper plots gives the ${\sigma }_{1\gamma }$ and the solid curve shows the observed cross sections with $V_{\mathrm{cut}}^2=0.3{\mathrm{GeV}}^2$ (the curve closer to dashed curve) and without cuts. Dashed and solid curves at the bottom plots show ${\delta }_{u,p}$ with and without the cut, respectively. The curves with higher values corresponds to ${\delta }_p$, i.e., ${\delta }_p>{\delta }_u$. Kinematical variables used for this example were $x=0.1$, $Q^2=2{\mathrm{GeV}}^2$, and $E_{\text{beam}}=11\mathrm{GeV}$.

Figure 6

The $t$-dependence of the asymmetry (upper left), RC to asymmetry (upper right), and RC factors (lower plots). Dashed curve for $A$ gives the ${\sigma }_{1\gamma }$ and solid curved show the observed cross sections with $V_{\mathrm{cut}}^2=0.3{\mathrm{GeV}}^2$ (the curve closer to dashed curve) and without cuts. Dashed and solid curves at the other three plots show ${\delta }_{A,u,p}$ with and without the cut, respectively. Kinematical variables used for this example were $x=0.1$, $Q^2=2{\mathrm{GeV}}^2$, and $E_{\text{beam}}=11\mathrm{GeV}$.