In this review phenomenological consequences of the Standard Model extension by means of new spin-1 chiral fields with the internal quantum numbers of the electroweak Higgs doublets are summarized. The prospects for resonance production and detection
of the chiral vector $Z^*$ and $W^{*pm}$ bosons at the LHC energies are considered. The $Z^*$ boson can be observed as a Breit-Wigner resonance peak in the invariant dilepton mass distributions in the same way as the well-known extra gauge $Z$ bosons. However, the $Z^*$ bosons have unique signatures in transverse momentum, angular and pseudorapidity distributions of the final leptons, which allow one to distinguish them from other heavy neutral resonances. In 2010, with 40 pb$^{-1}$ of the LHC proton-proton data at the energy 7 TeV, the ATLAS detector was used to search for narrow resonances in the invariant mass spectrum of $e^+e^-$ and $mu^+mu^-$ final states and high-mass charged states decaying to a charged lepton and a neutrino. No statistically significant excess above the Standard Model expectation was observed. The exclusion mass limits of 1.15 TeV$/c^2$ and 1.35 TeV$/c^2$ were obtained for the chiral neutral $Z^*$ and charged $W^*$ bosons, respectively. These are the first direct limits on the $W^*$ and $Z^*$ boson production. For almost all currently considered exotic models the relevant signal is expected in the central dijet rapidity region. On the contrary, the chiral bosons do not contribute to this region but produce an excess of dijet events far away from it. For these bosons the appropriate kinematic restrictions lead to a dip in the centrality ratio distribution over the dijet invariant mass instead of a bump expected in the most exotic models.
