Light-by-Light Scattering and Spacetime Noncommutativity

Abstract

The aim of this article is to explore a potential usability of a photon-photon self-interaction from the noncommutative quantum electrodynamics (NCQED) in the case of light-by-light scattering ($\gamma \gamma \to \gamma \gamma$) in ultraperipheral Pb+Pb collisions, a reaction measured recently by ATLAS and planned for future experiments in hadron-hadron colliders. We compute the total cross section from both, the full one-loop standard model (SM) and the tree-level NCQED amplitudes, in the equivalent photon approximation with impact parameters, for various noncommutative scales, ${\mathrm{\Lambda }}_{\mathrm{NC}}$, and incoming nuclear spin-energy combinations. We find that NCQED contribution to the cross section has considerable increase at diphoton invariant mass range higher than ${\mathrm{\Lambda }}_{\mathrm{NC}}$, while the SM contribution is strongly suppressed in such region. Our results show that the current ATLAS $\sqrt{{\mathrm{s}}_{\mathrm{NN}}}=5.02$ TeV experiment can only probe ${\mathrm{\Lambda }}_{\mathrm{NC}}<100$ GeV region. On the other hand, future hadron-hadron collider proposals could have the potential to extend to ${\mathrm{\Lambda }}_{\mathrm{NC}}\lesssim 300$ GeV region, making the performance of $\mathrm{Pb}+\mathrm{Pb}(\gamma \gamma )\to \mathrm{Pb}+\mathrm{Pb}\gamma \gamma$ scattering on testing space-time noncommutativity close to that of the previously proposed photon-photon mode of linear electron-positron collider.

Comments: 8 pages, 3 figures, version to be published in PRD