Signals for Non-Commutative QED in $e \gamma$ and $\gamma \gamma$ Collisions

We study the effects of non-commutative QED (NCQED) in fermion pair production, $\gamma + \gamma \to f + \bar{f}$ and Compton scattering, $e + \gamma \to e + \gamma$. Non-commutative geometries appear naturally in the context of string/M-theory and gives rise to 3- and 4-point photon vertices and to momentum dependent phase factors in QED vertices which will have observable effects in high energy collisions. We consider $e^+ e^-$ colliders with energies appropriate to the TeV Linear Collider proposals and the multi-TeV CLIC project operating in $\gamma \gamma$ and $e\gamma$ modes. Non-commutative scales roughly equal to the center of mass energy of the $e^+e^-$ collider can be probed, with the exact value depending on the model parameters and experimental factors. However, we found that the Compton process is sensitive to $\Lambda_{NC}$ values roughly twice as large as those accessible to the pair production process.