The forward-backward asymmetry with $Z'$ effects in the process $e^{+}$   $e^{-}$ $\rightarrow$ $\mu^{+}$ $\mu^{-}$
  Having taken the QED radiative correction and one-loop weak corrections into account, we have computed the unpolarized forward-backward asymmetry in the process $e^+e^- -> \mu^+\mu^-$ at a very reasonable accuracy. Special attention to the effects around the LEP 200 energy, induced by the possible $Z'$ boson of the left-right symmetric model $SU(2)_{L} \times SU(2)_{R} \times U(1)_{B-L}$, is paid. The numerical results of the directly measurable asymmetry $A_{FB}^{\mu}$ versus the CMS energies are presented in figures. One may be convinced by the results that precise measurements on the asymmetry in future colliders will possibly present some indirectly evidence of the $Z'$ boson. 
Ma Wen-Gan, Sun La-Zhen, Liu Yao-Yang, Jiang Yi and Chao-Hsi Chang