Seiberg-Witten map Invariant Scatterings

Abstract

We investigate Scattering amplitudes of the reversible $\theta$-exact Seiberg-Witten (SW) map based noncommutative (NC) quantum electrodynamics, and show explicitly the SW map invariance for all tree-level NCQED $2\to2$ proceses, including M\"oller, Bhabha, Compton, pair annihilation, pair production and light-by-light $(\gamma\gamma\to\gamma\gamma)$ scatterings. We apply our NCQED results to the $\gamma\gamma\to\gamma\gamma$ and $\gamma\gamma\to\ell^+\ell^-$ exclusive processes, convoluted to the ultraperipheral lead $^{208}$Pb ion-ion collisions, recently measured by the ATLAS collaboration at LHC. We demonstrate that $\gamma\gamma\to\gamma\gamma$ is the more appropriate channel to probe NC scale $\Lambda_{\rm NC}$ while both are less efficient than some other probes.