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 that (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 CERN Large Hadron Collider their effects could be disentangled when both Z bosons decay leptonically.