Rare Z-decay into light pseudoscalar bosons in the simplest little Higgs model

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The simplest little Higgs model predicts a light pseudoscalar boson η and opens up some new decay modes for Z-boson, such as Z → f f η, Z→ ηηη, Z→ ηγ and Z→ ηgg. We examine these decay modes in the parameter space allowed by current experiments, and find that the branching ratios can reach 10⁻⁷ for Z→ bbη, 10⁻⁸ for Z→ ττη, and 10⁻⁸ for Z→ ηγ, which should be accessible at the GigaZ option of the ILC. However, the branching ratios can reach 10⁻¹² for Z→ ηηη, and 10⁻¹¹ for Z→ ηgg, which are hardly accessible at the GigaZ option.