Some phenomenological consequences of the time-ordered perturbation theory of QED on non-commutative spacetime
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A framework was recently proposed for doing perturbation theory on non-commutative (NC) spacetime. It preserves the unitarity of the S matrix and differs from the naive, popular approach already at the lowest order in perturbation when time does not commute with space. In this work, we investigate its phenomenological implications at linear colliders, especially the TESLA at DESY, through the processes of \(e^+e^-\to\mu^+\mu^-,H^+H^-,H^0H^0\). We find that some NC effects computed previously are now modified and that there are new processes which now exhibit NC effects. Indeed, the first two processes get corrected at tree level as opposed to the null result in the naive approach, while the third one coincides with the naive result only in the low energy limit. The impact of the earth's rotation is incorporated. The NC signals are generally significant when the NC scale is comparable to the collider energy. If this is not the case, the non-trivial azimuthal angle distribution and day-night asymmetry of events due to Lorentz violation and the earth's rotation will be useful in identifying signals. We also comment briefly on the high energy behavior of the cross section that grows linearly in the center of mass energy squared and argue that it does not necessarily contradict some statements, e.g., the Froissart-Martin bound, achieved in ordinary theory.
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