Laboratory frame analysis of $e^+ e^- \to \mu^+ \mu^-$ scattering in the Noncommutative Standard Model

TL;DR

This paper investigates how noncommutative geometry modifies muon pair production in electron-positron collisions, revealing distinctive angular distributions and time-dependent effects that could be tested at future colliders.

Contribution

It provides a detailed analysis of second-order noncommutative effects on e+e- to mu+mu- scattering, including earth's rotation impacts, which are novel in this context.

Findings

Significant deviation in angular distributions from the Standard Model.

Strong dependence of cross section on noncommutative electric vector orientation.

Periodic variation of total cross section over a day, detectable at future colliders.

Abstract

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 $\Theta_{\mu\nu}$. 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 earth's 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).