Noncommutative QED corrections to process $e^+e^-\to\mu^+\mu^-\gamma$ at linear collider energies

TL;DR

This paper investigates how noncommutative quantum electrodynamics (NC QED) affects the process e+e- to mu+mu- gamma at linear collider energies, revealing an optimal energy for maximal NC effects and discussing experimental precision improvements.

Contribution

It introduces the relationship between NC QED scale energy and optimal collision energy, highlighting a non-monotonous correction pattern and proposing methods for precise experimental detection.

Findings

NC corrections are not monotonically increasing with energy.

There exists an optimal collision energy for maximum NC correction.

A linear relation between NC scale energy and optimal energy is established.

Abstract

The cross section for process $e^+e^-\to\mu^+\mu^-\gamma$ in the framework of noncommutative quantum electrodynamics(NC QED) is studied. It is shown that the NC correction of scattering sections is not monotonous enhancement with total energy of colliding electrons, but there is an optimal collision energy to get the greatest NC correction. Moreover, there is a linear relation between NC QED scale energy and the optimal collision energy. The experimental methods to improve the precision of determining NC effects are discussed, because this process is an ${\cal O}(\alpha^3) $ NC QED process, high precision tests are necessary.