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

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.