Seiberg-Witten map invariant scatterings

Abstract

We investigate scattering amplitudes of the reversible θ-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 Møller, Bhabha, Compton, pair annihilation, pair production, and light-by-light (LbyL: γγ→γγ) scatterings. We apply our NCQED results to the γγ→γγ and γγ→+- exclusive channels, convoluted to the ultraperipheral lead Pb208 ion-ion collisions, where LbyL scattering was recently measured by the ATLAS Collaboration at the LHC. We have demonstrated that γγ→γγ is the more appropriate channel to probe scale ΛNC. We also find that the transverse (φ) dependence of the NC PbPb(γγ)→Pb∗Pb∗γγ differential cross section shows large anisotropy near the peak NC contribution for a pure spacelike NC parameter. So the φ 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.