Using an intense laser beam in interaction with muon/electron beam to probe the Noncommutative QED

It is known that the linearly polarized photons can partly transform to circularly polarized ones via forward Compton scattering in a background such as the external magnetic field or noncommutative space time. Based on this fact we explore the effects of the NC-background on the scattering of a linearly polarized laser beam from an intense beam of charged leptons. We show that for a muon/electron beam flux $\bar\varepsilon_{\mu,e}\sim 10^{12}/10^{10}\,{\rm TeV}\,{\rm cm}^{-2}\,{\rm sec}^{-1}$ and a linearly polarized laser beam with energy $k^0\sim$1 eV and average power $\bar{P}_{\rm laser}\simeq$1 MW, the generation rate of circularly polarized photons is about $R_{_V} \sim 10^4/{\rm sec}$ for Noncommutative energy scale $\Lambda_{\tiny{NC}}\sim 10$TeV. This is fairly large and can grow for more intense beams in near future.