Coherent deeply virtual Compton scattering off ${}^4\mathrm{He}$

Coherent deeply virtual Compton scattering off the ${}^4\mathrm{He}$ nucleus is studied in impulse approximation. A convolution formula for the nuclear generalized parton distribution (GPD) is derived in terms of the ${}^4\mathrm{He}$ one-body nondiagonal spectral function and of the GPD of the struck nucleon. A model of the nuclear nondiagonal spectral function, based on the momentum distribution corresponding to the Argonne 18 nucleon-nucleon interaction, is used in the actual calculation. Typical impulse approximation results are reproduced, in proper limits, for the nuclear form factor and for nuclear parton distributions. The nuclear generalized parton distribution and the Compton form factor are evaluated using, as a nucleonic ingredient, a well-known generalized parton distribution model. An overall very good agreement is found with the data recently published by the EG6 experiment at the Jefferson Laboratory (JLab). More refined nuclear calculations are addressed and will be necessary for the expected improved accuracy of the next generation of experiments at JLab with the 12-GeV electron beam and high luminosity.

Figure 1

The generic coherent DVCS process off a target $A$.

Figure 2

The handbag approximation to the process shown in Fig. 1.

Figure 3

The impulse approximation description of the handbag process shown in Fig. 2.

Figure 4

The ${}^4\mathrm{He}$ form factor obtained as the integral of the ${}^4\mathrm{He}$ GPDs calculated in the present approach Eq. (10) (full), compared with data at low $t$ (dots) [40], the ones relevant for the discussion presented here. The red triangles represent the one-body part of the Av18 + UIX (where UIX represents the Urbana-IX) calculation of the form factor shown in Ref. [39] (see the text).

Figure 5

The ratio Eq. (20) for the flavor $q=u$ (the result for $q=d$ is indistinguishable).

Figure 6

The light-cone momentum distribution for the nucleon $N$ in ${}^4\mathrm{He}$, Eq. (15).

Figure 7

${}^4\mathrm{He}$ azimuthal beam-spin asymmetry $A_{LU}\left(\varphi \right)$ for $\varphi ={90}^{\circ }$: Results of this approach (red stars) compared with data (black squares) [30]. From left to right, the quantity is shown in the experimental $Q^2,x_B$, and $t$ bins, respectively.

Figure 8

The imaginary part of the Compton form factor for ${}^4\mathrm{He}$: Results of this approach (red stars) compared with data (black squares) [30]. From left to right, the quantity is shown in the experimental $Q^2,x_B$, and $t$ bins, respectively.

Figure 9

The real part of the Compton form factor for ${}^4\mathrm{He}$: Results of this approach (red stars) compared with data (black squares) [30]. From left to right, the quantity is shown in the experimental $Q^2,x_B$, and $t$ bins, respectively.