Decays Z ′ → γ γ γ and Z → γ γ γ in the minimal 331 model

The possibility of a significant effect of exotic particles on the ${Z}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}$ and $Z\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}$ decays is investigated in the context of the minimal 331 model. This model, which is based in the $S{U}_{C}(3)\ifmmode\times\else\texttimes\fi{}S{U}_{L}(3)\ifmmode\times\else\texttimes\fi{}{U}_{X}(1)$ gauge group, predicts the existence of many exotic charged particles that can significantly enhance the decay widths. It is found that the standard model prediction for the $Z\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}$ decay remains essentially unchanged, as the new physics effects quickly decouple. On the other hand, it is found that the contributions of the new exotic quarks and gauge bosons predicted by this model lead to a branching fraction for the ${Z}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}$ decay of about ${10}^{\ensuremath{-}6}$, which is about 3 orders of magnitude larger than that of the $Z\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}$ decay.