Two-gluon exchange contribution to elastic $\gamma \gamma \to \gamma \gamma$ scattering and production of two-photons in ultraperipheral ultrarelativistic heavy ion and proton-proton collisions

TL;DR

This paper analyzes the two-gluon exchange contribution to elastic photon-photon scattering at high energies, highlighting its significance relative to other mechanisms and exploring its observability in ultraperipheral heavy ion and proton-proton collisions.

Contribution

It provides a detailed impact-factor representation of the two-gluon exchange amplitude, including all helicity states and finite quark masses, and assesses its importance compared to other known contributions.

Findings

Charm quark enhances the cross section significantly.

Helicity-flip contributions are negligible compared to helicity-conserving ones.

Two-gluon exchange can be comparable to box contributions under specific cuts, but the cross section remains small.

Abstract

We discuss the two-gluon exchange contribution (formally three-loops) to elastic photon-photon scattering in the high-energy approximation. The elastic $\gamma\gamma \to \gamma \gamma$ amplitude is given in the impact-factor representation for all helicity configurations and finite quark masses. We discuss the importance of including the charm quark, which contribution, due to interference, can enhance the cross section considerably. We investigate the contribution to the $\gamma \gamma \to \gamma \gamma$ amplitude from the soft region, by studying its dependence on nonperturbative gluon mass. Helicity-flip contributions are shown to be much smaller than helicity-conserving ones. We identify region(s) of phase space where the two-gluon exchange contribution becomes important ingredient compared to box and nonperturbative VDM-Regge mechanisms considered in the literature. Consequences for the $A A \to A A \gamma \gamma$ reaction are discussed. Several differential distributions are shown. A feasibility study to observe the effect of two-gluon exchange is presented. We perform a similar analysis for the $p p \to p p \gamma \gamma$ reaction. Only by imposing severe cuts on $M_{\gamma \gamma}$ and a narrow window on photon transverse momenta the two gluon contribution becomes comparable to the box contribution but the corresponding cross section is rather small.