Search for HZZ′ couplings at the LHC

New physics models predict the possibility of extra neutral gauge bosons $(Z')$ associated with an extra $U(1)'$ gauge symmetry. We study the couplings of the Higgs boson to the Z boson and Z′ boson predicted by the new physics models. Since there is stringent limit on the Z′ boson mass from the $Z'\to l^+ l^-$ channel at the LHC experiments, we use two benchmark models: the leptophobic $Z'_{LP}$ which has no couplings with leptons and the eta $Z'_{\eta}$ which has small couplings with fermions. The couplings of the Z′ boson to quarks can also be investigated through the $Z'q\bar{q}$ interactions. The accessible ranges of the parameter space have been searched for processes $pp\rightarrow HZX$ and $pp\rightarrow HHZX$ at the LHC with $\sqrt{s}=14\ \text{TeV}$