Signatures of noncommutative QED at photon colliders

In this paper we study noncommutative (NC) quantum electrodynamics (QED) signatures at photon colliders through pair production of charged leptons ${(l}^{+}{l}^{-})$ and charged scalars ${(H}^{+}{H}^{-}).\mathrm{}$ The NC corrections for the fermion pair production can be easily obtained since NC QED with fermions has been extensively studied in the literature. NC QED with scalars is less studied. To obtain the cross section for $H^{+}{H}^{-}$ production, we first investigate the structure of NC QED with scalars, and then study the corrections due to the NC geometry to the ordinary QED cross sections. Finally by folding in the photon spectra for a $\gamma \gamma$ collider with laser backscattered photons from the $e^{+}{e}^{-}$ machine, we obtain a $95\%$ C.L. lower bound on the NC scale using the above two processes. We find that, with $\sqrt{s}=0.5,\hspace{0.5em}1.0,$ and $1.5$ TeV and integrated luminosity $L=500\mathrm{}\hspace{0.5em}\left({\mathrm{fb}}^{-1}\right),$ the NC scale up to 0.7, 1.2, and 1.6 TeV can be probed, respectively, while, for monochromatic photon beams, these numbers become 1.1, 1.7, 2.6 TeV, respectively.