A reappraisal of constraints on $Z'$ models from unitarity and direct searches at the LHC

Abstract: In a truly model-independent approach, we reexamine a minimal extension of the Standard Model (SM) through the introduction of an additional $U(1)$ symmetry leading to a new neutral gauge boson ($Z'$), allowing its kinetic mixing with the hypercharge gauge boson. An SM neutral scalar is used to spontaneously break this extra symmetry leading to the mass of the $Z'$. Except for three right-handed neutrinos no other fermions are added. We use the current LHC Drell-Yan data to put model-independent constraints in the parameter space of three quantities, namely, $M_{Z'}$, the $Z$-$Z'$ mixing angle ($\alpha_z$) and the extra $U(1)$ effective gauge coupling ($g'x$), which absorb all model dependence. We impose additional constraints from unitarity and low energy neutrino-electron scattering. However, limits extracted from direct searches turn out to be most stringent. We obtain $M{Z'} > 4.4$ TeV and $|\alpha_z| < 0.001$ at $95\%$ C.L., when the strength of the additional $U(1)$ gauge coupling is the same as that of the SM $SU(2)_L$.