A note on the rare decay of a Higgs boson into photons and a $Z$ boson

Abstract

We have calculated the width of the rare decay $H\to {\hat{I}}^3{\hat{I}}^{3}Z$ at one-loop level in the standard model for Higgs boson masses in the range $115\mathrm{GeV}\le m_H\le 160\mathrm{GeV}$ . 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 $\hat{I}“(H\to {\hat{I}}^3{\hat{I}}^{3}Z)$ to those of $H\to {\hat{I}}^3{\hat{I}}^3$ and $H\to {\hat{I}}^{3}Z$ shows that, for the Higgs boson mass of $m_H\sim 135\mathrm{GeV}$, the ratios of the decay widths are $\hat{I}“(H\to {\hat{I}}^3{\hat{I}}^{3}Z)/\hat{I}“(H\to {\hat{I}}^3{\hat{I}}^3)\sim \hat{I}“(H\to {\hat{I}}^3{\hat{I}}^{3}Z)/\hat{I}“(H\to {\hat{I}}^{3}Z)\sim 10^{-5}-10^{-6}$.

4 pages, 5 figures, RevTeX