The resonance production of new chiral spin-1 bosons and their detection through the Drell--Yan process at the CERN LHC is considered. Quantitative evaluations of various differential cross-sections of the chiral bosons production are made within the CalcHEP package. The new neutral chiral bosons can be observed as a Breit--Wigner resonance peak in the invariant dilepton mass distribution, as usual. However, unique new signatures of the chiral bosons exist. First, there is no Jacobian peak in the lepton transverse momentum distribution. Second, the lepton angular distribution in the Collins-Soper frame for the high on-peak invariant masses of the lepton pairs has a peculiar swallowtail shape.
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