Optimal one-parameter observables for $Z^{\prime }$ searches in $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ process

Abstract

To detect off-shell Abelian $Z^{\prime }$ boson in $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$, we propose one-parameter observables with the best value-to-uncertainty ratio. The observables are constructed by angular integration of the differential cross section with smooth weight functions. The value-to-uncertainty ratio is used as a criterion to select the unique weight function leading to the observable with the best statistical power for data analysis. The observables allow to select either vector or axial-vector $Z^{\prime }$ couplings to leptons. The obtained observable can be useful in future experiments at lepton colliders such as the ILC.

Comments: 18 pages, 9 figures, 1 table