Two-parametric model-independent observables for $Z^{\mathrm{\prime }}$ searching at the Tevatron

We propose a scheme of searches for the $Z^{\mathrm{\prime }}$ gauge boson as a virtual state in scattering processes at the Tevatron taking into account model-independent relations between the $Z^{\mathrm{\prime }}$ couplings to fermions. We integrate the Drell-Yan process cross setion to construct two-parametric observables, which are suitable for $Z^{\mathrm{\prime }}$ searches in the $p\bar{p}\to l^{+}{l}^{-}$ process. The observables allow to constrain the $Z^{\mathrm{\prime }}$ vector and axial-vector couplings to SM fermions in a general parameterization with non-universal $Z^{\mathrm{\prime }}$ interactions with fermion generations. Also a one-parametric observable for searching for the popular leptophobic $Z^{\mathrm{\prime }}$ boson is proposed.