Landau-Yang Theorem and Decays of a Z' Boson into Two Z Bosons

We study the decay of a Z' boson into two Z bosons by extending the Landau-Yang theorem to a parent particle decaying into two Z bosons. For a spin-1 parent the theorem predicts: 1) there are only two possible couplings and 2) the normalized differential cross-section depends on kinematics only through a phase shift in the azimuthal angle between the two decay planes of the Z boson. When the parent is a Z' the two possible couplings are anomaly-induced and CP-violating, respectively. At the Large Hadron Collider (LHC) effects of the two couplings could be disentangled when both Z bosons decay leptonically.