Hard photoproduction of a diphoton with a large invariant mass

The electromagnetic probe has proven to be a very efficient way to access the three-dimensional structure of the nucleon, particularly thanks to the exclusive Compton processes. We explore the hard photoproduction of a large invariant mass diphoton in the kinematical regime where the diphoton is nearly forward and its invariant mass is the hard scale enabling to factorize the scattering amplitude in terms of generalized parton distributions. We calculate unpolarized cross sections and the angular asymmetry triggered by a linearly polarized photon beam.

Figure 1

The six Feynman diagrams (a, b, c, d, e, f) contributing to the coefficient functions of the process $\gamma N\to \gamma \gamma N^{\prime }$.

Figure 2

The $u^{\prime }$ dependence of the unpolarized differential cross section $\frac{d\sigma }{d{M}_{\gamma \gamma }^{2}d{u}^{\prime }dt}$ at $t=t_{\min }$ and $S_{\gamma N}=20{\mathrm{GeV}}^2$, for $M_{\gamma \gamma }^2=4{\mathrm{GeV}}^2$ with the quark GPDs modeled as in [6] (solid curve) and in [7] (dashed curve) for a proton target.

Figure 3

The $u^{\prime }$ dependence of the unpolarized differential cross section $\frac{d\sigma }{d{M}_{\gamma \gamma }^{2}d{u}^{\prime }dt}$ at $t=t_{\min }$ and $S_{\gamma N}=20{\mathrm{GeV}}^2$, for $M_{\gamma \gamma }^2=4{\mathrm{GeV}}^2$ (blue upper curve) and for $M_{\gamma \gamma }^2=6{\mathrm{GeV}}^2$ (red lower curve), for a proton target (left panel) and a neutron target (right panel).

Figure 4

The $t$-dependence of the unpolarized differential cross section $\frac{d\sigma }{d{M}_{\gamma \gamma }^{2}d{u}^{\prime }dt}$ at $u^{\prime }=-2{\mathrm{GeV}}^2$ and $S_{\gamma N}=20{\mathrm{GeV}}^2$, for $M_{\gamma \gamma }^2=3{\mathrm{GeV}}^2$.

Figure 5

The $M_{\gamma \gamma }^2$ dependence of the unpolarized differential cross section $\frac{d\sigma }{d{M}_{\gamma \gamma }^{2}dt}$ on a proton(left panel) and on a neutron(right panel) at $t=t_{\min }$ and $S_{\gamma N}=20{\mathrm{GeV}}^2$ (full curves), $S_{\gamma N}=100{\mathrm{GeV}}^2$ (dashed curve) and $S_{\gamma N}={10}^6{\mathrm{GeV}}^2$ (dash-dotted curve, multiplied by $10^5$). The range of integration with respect to $u^{\prime }$ is explained in the text.

Figure 6

The $u^{\prime }$ dependence of the unpolarized differential cross section $\frac{d\sigma }{dtd{u}^{\prime }}$ on a proton (left panel) and on a neutron (right panel) at $t=t_{\min }$ and $S_{\gamma N}=20{\mathrm{GeV}}^2$, integrated over $M_{\gamma \gamma }^2$ as explained in the text.

Figure 7

The azimuthal dependence of the differential cross section $\frac{d\sigma }{d{M}_{\gamma \gamma }^{2}dtd{u}^{\prime }d\varphi }$ at $t=t_{\min }$ and $S_{\gamma N}=20{\mathrm{GeV}}^2$. $(M_{\gamma \gamma }^2,u^{\prime })=(3,-2){\mathrm{GeV}}^2$ (solid line), $(M_{\gamma \gamma }^2,u^{\prime })=(4,-1){\mathrm{GeV}}^2$ (dotted line) and $(M_{\gamma \gamma }^2,u^{\prime })=(4,-2){\mathrm{GeV}}^2$ (dashed line). $\varphi$ is the angle between the initial photon polarization and one of the final photon momentum in the transverse plane.