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

TL;DR

This paper investigates how noncommutative geometry modifies muon pair production in electron-positron collisions, revealing measurable effects at TeV-scale energies and proposing collider signatures for space-time noncommutativity.

Contribution

It provides the first detailed calculation of the $e^+ e^- o ^+ ^-$ cross section in the noncommutative standard model up to second order in the noncommutative parameter, including collider implications.

Findings

Noncommutative effects significantly alter cross sections and angular distributions.

The process can probe noncommutative scales up to 1 TeV at the ILC.

The $^+ ^-$ process is sensitive to space-time noncommutativity at collider energies.

Abstract

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.