Rare Z-decay into light CP-odd Higgs bosons: a comparative study in different new physics models

Various new physics models predict a light CP-odd Higgs boson (labeled as $a$) and open up new decay modes for Z-boson, such as $Z \to \bar{f} f a$, $Z\to a\gamma$ and $Z\to aaa$, which could be explored at the GigaZ option of the ILC. In this work we investigate these rare decays in several new physics models, namely the type-II two Higgs doublet model (type-II 2HDM), the lepton-specific two Higgs doublet model (L2HDM), the nearly minimal supersymetric standard model (nMSSM) and the next-to-minimal supersymmetric standard model (NMSSM). We find that in the parameter space allowed by current experiments, the branching ratios can reach $10^{-4}$ for $Z \to \bar{f} f a $ ($f=b,\tau$), $10^{-9}$ for $Z\to a\gamma$ and $10^{-3}$ for $Z\to aaa$, which implies that the decays $Z \to \bar{f} f a$ and $Z \to a a a$ may be accessible at the GigaZ option. Moreover, since different models predict different patterns of the branching ratios, the measurement of these rare decays at the GigaZ may be utilized to distinguish the models.