Two-photon decay of the Higgs bosons in a supersymmetric model with a $CP$-violating potential

In the supersymmetric standard model which is not minimal, the Higgs potential does not conserve $CP$ symmetry generally. Assuming that there exists an SU(2)-triplet Higgs field, we discuss resultant $CP$-violating effects on the Higgs bosons. The experimentally observed Higgs boson, which should be $CP$ even in the standard model, could decay into two photons of $CP$-odd polarization state non-negligibly. For the second lightest Higgs boson, in a sizable region of parameter space, the dominant decay modes are different from those expected by the standard model. The two-photon decay could yield both even and odd $CP$ final states at a ratio of the order of unity.

Figure 1

The ratio ${\mathrm{\Gamma }}_{\mathrm{odd}}/{\mathrm{\Gamma }}_{\mathrm{even}}$ of the decay ${\tilde{H}}_2^0\to \gamma \gamma$ for $\tan \beta =2$. The horizontal axis stands for the phase ${\alpha }_3$. (a) $|{\mu }_H|=300\mathrm{GeV}$, $|{\mu }_{\varphi }|=300\mathrm{GeV}$. (b) $|{\mu }_H|=1000\mathrm{GeV}$, $|{\mu }_{\varphi }|=1000\mathrm{GeV}$.

Figure 2

The ratio ${\mathrm{\Gamma }}_{\mathrm{odd}}/{\mathrm{\Gamma }}_{\mathrm{even}}$ of the decay ${\tilde{H}}_3^0\to \gamma \gamma$ for $\tan \beta =10$. The horizontal axis stands for the phase ${\alpha }_3$. (a) $|{\mu }_H|=300\mathrm{GeV}$, $|{\mu }_{\varphi }|=300\mathrm{GeV}$. (b) $|{\mu }_H|=1000\mathrm{GeV}$, $|{\mu }_{\varphi }|=1000\mathrm{GeV}$.

Figure 3

The mass of the second lightest Higgs boson ${\tilde{H}}_3^0$ for $\tan \beta =10$ under the constraint $0.1<{\mathrm{\Gamma }}_{\mathrm{odd}}/{\mathrm{\Gamma }}_{\mathrm{even}}<10.0$.

Figure 4

The branching ratios of the second lightest Higgs boson for $\tan \beta =10$ under the constraint $0.1<{\mathrm{\Gamma }}_{\mathrm{odd}}/{\mathrm{\Gamma }}_{\mathrm{even}}<10.0$. The upper and lower dots correspond to ${\tilde{H}}_3^0\to \overline{b}b$ and ${\tilde{H}}_3^0\to \gamma \gamma$, respectively.

Figure 5

The ratios $R_t$ and $R_b$ for the interactions with the $t$ and $b$ quarks for $\tan \beta =10$ under the constraint $0.1<{\mathrm{\Gamma }}_{\mathrm{odd}}/{\mathrm{\Gamma }}_{\mathrm{even}}<10.0$. The upper and lower dots correspond to $R_b$ and $R_t$, respectively.