Seiberg-Witten map invariant scatterings

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