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

We study muon pair production $e^+ e^- \to \mu^+ \mu^-$ in the noncommutative(NC) extension of the standard model using the Seiberg-Witten maps 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 contributions simply cancelled) for the pair production. The momentum dependent $\mathcal{O}(\Theta^2)$ 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 $e^+ e^- \to \mu^+ \mu^-$ can probe the NC scale $\Lambda$ in the range $0.8 - 1.0$ TeV for typical ILC energy ranges.