  In this paper we study non-commutative (NC) QED signatures at photon
colliders through pair production of charged leptons $(\ell^+ \ell^-)$ and
charged scalars $(H^+ H^-)$. 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 $H^+H^-$ productions, 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 back-scattered photons from the $e^+ e^-$
machine, we obtain 95% CL lower bound on the NC scale using the above two
processes. We find that, with $\sqrt{s} = 0.5, 1.0$, and $ 1.5$ TeV and
integrated luminosity $L = 500(fb^{-1})$, 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.

High Energy Physics - Phenomenology