Seiberg-Witten map Invariant Scatterings

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 $2\to 2$ 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 $\gamma \gamma \to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ 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 ${\mathrm{\Lambda }}_{\mathrm{N}\mathrm{C}}$ while both are less efficient than some other probes.