Optimal observables for $Z'$ models in annihilation leptonic processes

Abstract: The optimal observables with the best ratio of signal to statistical uncertainty are proposed for a bunch of popular models of the $Z'$ boson. They are the cross sections integrated over the phase space of the final particles with proper weight functions. It is shown that the proposed observables are completely equivalent to the $\chi^2$ fit of the differential cross section, so they could be used as an alternative of aggregating events into bins with further minimization of the $\chi^2$ function, especially in preliminary analysis of experimental data. Application of the observables to the maximum likelihood estimate of the $Z'$ mass and the $Z$--$Z'$ mixing angle as well as to the exclusion reach and statistical efficiency of the signal is investigated in details.