Landau-Yang Theorem and Decays of a $Z^{\prime }$ Boson into Two $Z$ Bosons

We study the decay of a $Z^{\prime }$ 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 $Z^{\prime }$ 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.

Figure 1

Two decay planes of $Z_1\to {\ell }_1{\overline{\ell }}_1$ and $Z_2\to {\ell }_2{\overline{\ell }}_2$ define the azimuthal angle $\varphi \in [0,2\pi ]$ which rotates ${\ell }_2$ to ${\ell }_1$ in the transverse view. The polar angles ${\theta }_1$ and ${\theta }_2$ shown are defined in the rest frame of $Z_1$ and $Z_2$, respectively.