We study the muon pair production $ e^+ e^- to mu^+ mu^-$ in the framework of the non-minimal noncommutative(NC) standard model to the second order of the NC parameter $Theta_{mu u}$. The $mathcal{O}(Theta^2)$ momentum dependent NC interaction significantly modifies the cross section and angular distributions which are different from the standard model. After including the effects of earths rotation we analyse the time-averaged and time dependent observables in detail. The time-averaged azimuthal distribution of the cross section shows siginificant departure from the standard model. We find strong dependence of the total cross section(time- averaged) and their distributions on the orientation of the noncommutative electric vector (${vec{Theta}}_E$). The periodic variation of the total cross-section with time over a day seems to be startling and can be thoroughly probed at the upcoming Linear Collider(LC).
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