Seiberg-Witten map invariant scatterings

We investigate scattering amplitudes of the reversible.-exact Seiberg-Witten map-based noncommutative (NC) quantum electrodynamics and show explicitly the SW map invariance for all types of tree-level NCQED two-by-two processes, including Moller, Bhabha, Compton, pair annihilation, pair production, and light-by-light (LbyL: gamma gamma -> gamma gamma) scatterings. We apply our NCQED results to the gamma gamma -> gamma gamma and gamma gamma -> l(+)l(-) exclusive channels, convoluted to the ultraperipheral lead Pb-208 ion-ion collisions, where LbyL scattering was recently measured by the ATLAS Collaboration at the LHC. We have demonstrated that gamma gamma -> gamma gamma is the more appropriate channel to probe scale Lambda(NC). We also find that the transverse (phi) dependence of the NC PbPb(gamma gamma) -> Pb*Pb*gamma gamma differential cross section shows large anisotropy near the peak NC contribution for a pure spacelike NC parameter. So the phi variation of the differential cross section is likely an appropriate signature for the NCQED contributions with the pure space-space noncommutative parameter, given that enough events could be available for determining the anisotropy.

Automated summary

The study investigated scattering amplitudes of noncommutative quantum electrodynamics based on the reversible-exact Seiberg-Witten map and demonstrated the SW map invariance. The results suggest that the gamma gamma -> gamma gamma channel is more suitable for probing the scale Lambda(NC), and the transverse (phi) dependence may serve as an appropriate signature for NCQED contributions.