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Abstract We consider $$Z'$$ Z ′ s in heterotic string derived models and study $$Z'$$ Z ′ resonant production at the TeV scale at the Large Hadron Collider (LHC). We use various kinematic differential distributions for the Drell–Yan process at NNLO in QCD to explore the parameter space of such models and investigate $$Z'$$ Z ′ couplings. In particular, we study the impact of Z- $$Z'$$ Z ′ kinetic-mixing interactions on forward-backward asymmetry ( $$A_{FB}$$ A FB ) and other distributions at the LHC.