Optimal observables for $Z^{\prime }$ 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 $Z^{\prime }$ 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 $Z^{\prime }$ mass and the $Z$--$Z^{\prime }$ mixing angle as well as to the exclusion reach and statistical efficiency of the signal is investigated in details.

Comments: 13 pages, 8 figures, 8 tables