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We study muon pair production $ e^+ e^- \to \mu^+ \mu^-$ in thenoncommutative(NC) extension of the standard model using the Seiberg-Wittenmaps of this to the second order of the noncommutative parameter $\Theta_{\mu\nu}$. Using $\mathcal{O}(\Theta^2)$ Feynman rules, we find the$\mathcal{O}(\Theta^4)$ cross section(with all other lower order contributionssimply cancelled) for the pair production. The momentum dependent$\mathcal{O}(\Theta^2)$ NC interaction significantly modifies the cross sectionand angular distributions which are different from the commuting standardmodel. We study the collider signatures of the space-time noncommutativity atthe International Linear Collider(ILC) and find that the process $ e^+ e^- \to\mu^+ \mu^-$ can probe the NC scale $\Lambda$ in the range $0.8 - 1.0$ TeV fortypical ILC energy ranges.

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