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The study of lepton pair production is a powerful test of the Standard Model(SM) and can be used to search for phenomena beyond the SM. New heavy neutralbosons $Z'$ decaying to charged lepton pairs $l^+l^-$ ($l=e, \mu$) arepredicted by many scenarios of new physics, including models with extendedgauge sector. We estimate the LHC $Z'$ discovery potential with Run 2 datacomprised of 36.1 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=13$ TeV andrecorded by ATLAS detector at the CERN LHC. The model-independent constraintson the $Z'$ fermion couplings were obtained for the first time for a selectedset of $Z'$ signal mass points of $M_{Z'}=2$, 3, and 4 TeV by using the ATLASdata collected at the LHC. The analysis is based on the derived earlier specialrelations between the $Z'$ couplings proper to the renormalizable theories.Taking into account the dependence of $Z-Z'$ mixing angle $\theta_0$ on the$Z'$ axial-vector coupling $a$, the limits on $\theta_0$ are established as$\theta_0 < 10^{-4} - 10^{-3}$ in the investigated $Z'$ mass range.

Model-independent constraints on the Abelian $Z'$ couplings within the ATLAS data on the dilepton production processes at $\sqrt{s} =$ 13 TeV