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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 ofthe ILC. In this work we investigate these rare decays in several new physicsmodels, namely the type-II two Higgs doublet model (type-II 2HDM), thelepton-specific two Higgs doublet model (L2HDM), the nearly minimalsupersymetric standard model (nMSSM) and the next-to-minimal supersymmetricstandard model (NMSSM). We find that in the parameter space allowed by currentexperiments, 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 $Z\to aaa$, whichimplies that the decays $Z \to \bar{f} f a$ and $Z \to a a a$ may be accessibleat the GigaZ option. Moreover, since different models predict differentpatterns of the branching ratios, the measurement of these rare decays at theGigaZ may be utilized to distinguish the models.

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