Moller And Bhabha Scattering In The Noncommutative Standard Model

This paper concerns about the Moller and Bhabha scattering in the non-commutative extension of the standard model using the Seiberg-Witten maps consideringθ-exact solution, i.e. considering the impact of both Z boson and photon exchange. The non-commutativity of coordinate means that special vectors exit in the world. If we can detect this phenomenon, thus we can determine the direction and quantity, i.e. ANC (just like the plank constant h) ofθE andθB, so a primary coordinate exists. Thus a primary coordinate is assumed existing around the universe, so we should take into account the apparent time variation ofθμv in the lab frame due to the earth’s rotation when we discuss phenomenology for any experiment on the earth. Since both of the Moller and Bhabha scattering are two important, elementary processes in detecting the possible NC signal. From the phenomenological view point, it is necessary to examine the contribution of higherθorder NC correction and give aθ-exact solution since in the future colliders the collision energy may be comparable or even exceed the TeV NC scale. In this work, the calculation is completed with theθ-exact formation of Feynman rules. We may consider that the measured value for observable by collider experiments is usually given as a mean value, so we take any physical results(e.g. total cross section or angular distribution) a full-day averaged before analyzed with experiment. In particular, it is found in previous work that for each collision process there is always exists an optimal collision energy Eoc for achieving the greatest NC correction, and varies linearly with NC scale ANC. This feature can help us indirectly estimate the ANC value through determining the EOC in future collision experiment. In the paper, the same relationship is found too.