Note on the rare decay of a Higgs boson into photons and a Z boson

We have calculated the width of the rare decay H→γγZ at one-loop level in the standard model for Higgs boson masses in the range 115 GeV≤mH≤160 GeV . For this range of Higgs boson masses we find that Z boson is predominantly longitudinally polarized, and the photons have the same helicity. A comparison of the decay width Γ(H→γγZ) to those of H→γγ and H→γZ shows that, for the Higgs boson mass of mH∼135 GeV, the ratios of the decay widths are Γ(H→γγZ)/Γ(H→γγ)∼Γ(H→γγZ)/Γ(H→γZ)∼10-5-10-6