Decay $\varphi \to Z\gamma \gamma$ ($\varphi =h$, $H$, $A$) 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 $m_A=750\mathrm{GeV}$, 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 ${10}^{-11}$.

Figure 1

Box diagrams that contribute to the $A\to Z\gamma \gamma$ decay in the MSSM, with $f$ standing for any charged SM fermion and ${\tilde{\chi }}_i^{+}$ ($i=1$, 2) for the charginos. The crossed diagrams in which the photons are exchanged are not shown. The box diagrams for the process $\varphi \to Z\gamma \gamma$ ($\varphi =h$, $H$) are obtained by replacing $A$ by $\varphi$.

Figure 2

Reducible Feynman diagrams for the $A\to Z\gamma \gamma$ process in the MSSM. There are additional triangle diagrams that can be obtained by exchanging the photons in the triangle diagrams. Here ${\overline{q}}_i^{+}$ stands for the squarks.

Figure 3

Extra reducible Feynman diagram that contribute to the $\varphi \to Z\gamma \gamma$ ($\varphi =h$, $H$) decay in the MSSM. The diagram obtained by exchanging the photons is not shown.

Figure 4

Branching ratio for the $A\to Z\gamma \gamma$ decay in the hMSSM as a function of $m_A$ for two values of $t_{\beta }$ (top plots) and as a function of $t_{\beta }$ for two values of $m_A$ (bottom plots). We also include the dominant decay channels of the $CP$-odd scalar boson. The neutralino mass $m_{{\chi }_1^0}$ is about 230 GeV.

Figure 5

The same as in Fig. 4 but for the CP-even Higgs boson $H$ decays.

Figure 6

Feynman rules involving only SM particles. All the 4-momenta are incoming and the Lorentz structures are given by ${\mathrm{\Gamma }}^{\alpha \mu \nu }(k_1,k_2,k_3)=(k_1-k_2{)}^{\nu }{g}^{\alpha \mu }+(k_2-k_3{)}^{\alpha }{g}^{\mu \nu }+(k_3-k_1{)}^{\mu }{g}^{\alpha \nu }$ and ${\mathrm{\Sigma }}^{\alpha \beta \mu \nu }=2g^{\alpha \beta }{g}^{\mu \nu }-g^{\alpha \mu }{g}^{\beta \nu }-g^{\alpha \nu }{g}^{\beta \mu }$. The coupling constants read $g_{VWW}=1$ ($-\frac{c_W}{s_W}$) for $V=\gamma$ ($Z$) as well as $g_A^f=\frac{1}{2}{T}_f^3$ and $g_V^f=T_3^f-2Q_f{s}_W^2$, with $Q_f$ the fermion charge and $T_f^3=1/2$ ($-1/2$) for up quarks (down quarks and charged leptons).

Figure 7

Feynman rules for the couplings of the scalar bosons to fermions and charginos in the MSSM. In the lower diagram $\varphi =h$, $H$, $A$, and the corresponding coupling constants are shown in Tables 1 and 2.

Figure 8

Feynman rules for the couplings of scalar bosons and squarks to the gauge bosons in the MSSM. In the top-left plot $V=Z$, $W$ and in the top-right diagram $\varphi =h$, $H$. All the four-momenta are incoming, and the corresponding coupling constants are shown in Table 2.