Noncommutative Effects On QED Scattering Process

Noncommutative physics based on non-commutating space-time coor-dinates is a hot topic in the recent decade. This is mainly due to that the non-commutativity of space-times was discovered in the late 1990s'as an important characteristic of D-Brane dynamics at low energy limit and that a certain class of quantum field theories on noncommutative Minkowski space-times can be obtained as a particular low energy limit of open strings in the presence of a constant NS-NS Bμv field. This significant progress in string theory which is as best candidate for quantum gravitational theory generated a flurry of enthusiasm in the study of quantum field theories in noncommu-tative spaces,the number of the relative papers has been increasing rapidly. Such interest on noncommutative field theories, on the one hand, has been aimed at getting new insights into the regularization and renormalization of quantum field theories in this novel framework, on the other hand, is that many features of ordinary commutative field theories have been found analogues in the noncommutative context. There some unique characteris-tics have also been found,such as IR/UV mixing. Non-commutativity is also studied in the quantum gravitational theory,cosmology and extra dimensions.Among the many research on the noncommutative theories, a large part is the research on noncommutative phenomenology of particle physics, which studies the characteristics of particles collision scattering in the noncommu-tative spaces different from in commutative ones. The energy level applying to the noncommutative physics is too high that it is great inconvenience to test the effects caused by noncommutative space-times, which requires peo-ple to research the theory and methods to test noncommutative effects in the laboratory experiment, thus it is to verify that the noncommutative theories establish or don't, and to test indirectly that the string theory is correct or not.The research work in this article is studying the effects on the scattering cross of the fundamental scattering processes by the noncommutative space- time with the energy provided by the next generation collider in the frame-work of noncommutative quantum electrodynamics(NCQED)established with the Weyl-Moyal correspondence. First, in the foundation of the prede-cessor works,some common electron scattering processes in QED have been studied and it is found that there is the similar relation between the NC correction of scattering sections and colliding energy. In the lower order pro-cesses of the Moller scattering,Bhabha scattering and pair annihilation, it is shown that NC correction of scattering sections is not monotonous en-hancement with total energy of colliding electrons,but displaying a kurtosis distribution. Given a noncommutative scale energy ANC, The different colli-sion energy obtains the different NC correction of scattering sections, there exists an optimum collision energy to get the greatest NC correction. More-over, there is a linear relation between NC scale energy and the optimum collision energy after fitting their datum. Second, The total cross section for process e+e-→μ+μ-γ, which is higher order 0(α3)process and must exist in scattering process of high energy particles,is computed in detail, and it is also discussed that scattering cross varies with different experiment position and time. The linear relation aforementioned between the NC correction of scattering sections and optimum colliding energy is applicable to this high order process.