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Light-by-Light Scattering and Spacetime Noncommutativity

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 ($γγ\toγγ$) 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, $\rmΛ_{NC}$, 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 $\rmΛ_{NC}$, while the SM contribution is strongly suppressed in such region. Our results show that the current ATLAS $\rm\sqrt{s_{NN}} = 5.02$ TeV experiment can only probe $\rmΛ_{NC}<100$ GeV region. On the other hand, future hadron-hadron collider proposals could have the potential to extend to $\rmΛ_{NC}\lesssim 300$ GeV region, making the performance of $\rm Pb+Pb(γγ)\to Pb+Pbγγ$ scattering on testing space-time noncommutativity close to that of the previously proposed photon-photon mode of linear electron-positron collider.