Higgs boson decay into Z bosons and a photon

We have performed a one-loop calculation of the width of the rare decay H -> Z Z \gamma in the standard model for Higgs boson masses 190 GeV \leq m_H \leq 250 GeV. We find that the most dominant helicity combinations for the Z bosons and the photon is when one of the Z bosons is longitudinally polarized and the other Z boson and the photon have the same helicity. A comparison of the decay width \Gamma(H->Z Z \gamma) to those of H->\gamma \gamma and H->\gamma Z shows that the ratios of the decay widths are \Gamma(H->Z Z \gamma) / \Gamma(H->\gamma\gamma) ~ \Gamma(H->Z Z \gamma) / \Gamma(H->\gamma Z) ~ 10^{-7}.