Probing $e^{+}e^{-}$ annihilation in noncommutative electroweak model

TL;DR

This paper investigates how noncommutative spacetime affects $e^{+}e^{-}$ annihilation into two photons, revealing parity violation and analyzing helicity states due to spin and magnetic field effects within a modified Lorentz framework.

Contribution

It provides a detailed analysis of parity violation and helicity behavior in noncommutative electroweak theory, highlighting the role of spin and magnetic fields in these phenomena.

Findings

Parity violation occurs in $e^{+}e^{-} o\gamma ext{ } ext{ } ext{ } ext{ }$ in noncommutative spacetime.

Helicity states show distinct behaviors influenced by spin and magnetic fields.

Energy-momentum conservation holds, but electric fields modify particle energy spectra without causing symmetry violation.

Abstract

If the twist $Poincar\acute{e}$ transformation is imposed on the noncommutative spacetime, then $Lorentz$ invariance cannot be applied on QFT. To data, noncommutative theory is one of the best candidates to modify $Lorentz$ transformation. In this paper, we argue parity violation under the process of $e^{+}e^{-}\to\gamma \gamma$ and make a detailed analysis of the difference behavior of each helicity state on noncommutative spacetime. The effect arises from the production of spin and magnetic fields. We check the energy momentum conservation for all used couplings and discover that if the electric field changes particle energy spectrum, there is no symmetry violation as the field produces a longitudinal state on the finial triple boson couplings.