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 $2\to 2$ proceses, including Möller, 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 ${\Lambda }_{\mathrm{NC}}$ while both are less efficient than some other probes.

Comments: 55 pages, 3 tables, 15 figures; v2: added transversed ($\phi$), and longitudinal ($\vartheta$) distributions of convolouted light-by-light differential cross sections, published version; v4: many typos in text and misprints in eqs (1o1-105) of LbyL scattering corrected; numerical, computer generated results are not affected by the above corrections. No change of results and conclusions