Leptophobic $Z'$ in Models with Multiple Higgs Doublet Fields

We study the collider phenomenology of the leptophobic $Z'$ boson from an extra $U(1)'$ gauge symmetry in models with $N$-Higgs doublet fields. We assume that the $Z'$ boson at tree level has (i) no $Z$-$Z'$ mixing, (ii) no interaction with charged leptons, and (iii) no flavour-changing neutral current. Under such a setup, it is shown that in the $N=1$ case, all the $U(1)'$ charges of left-handed quark doublets and right-handed up- and down-type quarks are required to be the same, while in the $N \ge 3$ case one can take different charges for the three types of quarks. The $N=2$ case is not well-defined under the above three requirements. We study the $pp\to Z'V\to b\bar{b}V$ processes ($V=\gamma,~Z$ and $W^\pm$) with the leptonic decays of $Z$ and $W^\pm$ at the LHC. The most promising discovery channel or the most stringent constraint on the $U(1)'$ gauge coupling constant comes from the $Z'\gamma$ process below the $t\bar{t}$ threshold and from the $t\bar{t}$ process above the threshold. Assuming the collision energy of 8 TeV and the integrated luminosity of 19.6 fb$^{-1}$, we find that the constraint from the $Z'\gamma$ search in the lower mass regime can be stronger than that from the UA2 experiment. In the $N \ge 3$ case, we consider four benchmark points for the $Z'$ couplings with quarks. It is noted that if such a $Z'$ is discovered, a careful comparison between the $Z'\gamma$ and $Z'W$ signals is crucial to reveal the nature of $Z'$ couplings with quarks. We also present the discovery reach of the $Z'$ boson at the 14-TeV LHC in both $N=1$ and $N\geq 3$ cases.