Contribution of scalar loops to the three-photon decay of theZ

I present the contribution of scalar particles to the decay of the ${\mathit{Z}}^0$ gauge boson into three photons, if their masses are larger than the ${\mathit{Z}}^0$ mass. As an underlying theory I take the two Higgs doublet model and the minimal supersymmetric standard model. I show that the amplitude is identical to 0 up to the second order in the expansion of the Higgs boson mass squared. The maximal contribution to the partial decay width of the ${\mathit{Z}}^0$ to three photons via a charged Higgs scalar loop is therefore about 4×${10}^{\mathrm{-}16}$(${\mathit{m}}_{\mathit{Z}}^0$/${\mathit{m}}_{\mathit{H}}^{+}$ ${)}^8$ GeV, which is more than a factor of 5×${10}^4$ less than the W boson contribution and so more than 6 orders of magnitude less than the fermionic contribution. If we take into account all families of the scalar partners of the leptons and quarks this value is enhanced by a factor of about 8 and therefore still much less as the W boson contribution and the fermionic one.