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$e^+ e^- \to μ^+ μ^-$ scattering in the Noncommutative standard model

We study muon pair production $ e^+ e^- \to μ^+ μ^-$ in the noncommutative(NC) extension of the standard model using the Seiberg-Witten maps of this to the second order of the noncommutative parameter $Θ_{μν}$. Using $\mathcal{O}(Θ^2)$ Feynman rules, we find the $\mathcal{O}(Θ^4)$ cross section(with all other lower order contributions simply cancelled) for the pair production. The momentum dependent $\mathcal{O}(Θ^2)$ NC interaction significantly modifies the cross section and angular distributions which are different from the commuting standard model. We study the collider signatures of the space-time noncommutativity at the International Linear Collider(ILC) and find that the process $ e^+ e^- \to μ^+ μ^-$ can probe the NC scale $Λ$ in the range $0.8 - 1.0$ TeV for typical ILC energy ranges.