Decay $\phi\to Z \gamma\gamma$ ($\phi=h, H,A$) in the minimal supersymmetric standard model

The decays of the CP-even ($h,\,H$) and the CP-odd ($A$) Higgs bosons $h,\,H,\,A\to Z\gamma\gamma$ are calculated in the context of the minimal supersymmetric standard model (MSSM), where they are induced at the one-loop level via box and reducible Feynman diagrams. For the numerical evaluation of the branching ratios we employ the decoupling limit and consider values for the MSSM parameters still consistent with the current experimental data. We consider a particular scenario for the radiative corrections to the Higgs boson masses, dubbed hMSSM, which leads to only two free parameters, namely $m_A$ and $\tan\beta$. We found that the branching ratio of the $CP$-odd Higgs boson decay $A\to Z\gamma\gamma$ can reach values up to $10^{-8}$ for $m_A=750$ GeV, which is three order of magnitude smaller than that of the $A\to\gamma\gamma$ channel. On the other hand, the branching ratio of the $H\to Z\gamma\gamma$ decay is of the order of $10^{-7}$ for large values of $m_H$ and small values of $\tan\beta$, which is comparable with the branching ratio of the $H\to Z\gamma$ channel. As far as the branching ratio of the SM-like Higgs boson decay $h\to Z\gamma\gamma$ is concerned, it is considerably suppressed, of the order of $10^{-11}$.
Comment: 21 pages, 8 figures