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

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¯fη, Z→ηηηZ→ηηη, Z→ηγZ→ηγ and Z→ηggZ→ηgg. We examine these decay modes in the parameter space allowed by current experiments, and find that the branching ratios can reach 10−710−7 for Z→b¯bη, 10−810−8 for Z→τ¯τη, and 10−810−8 for Z→ηγZ→ηγ, which should be accessible at the GigaZ option of the ILC. However, the branching ratios can reach 10−1210−12 for Z→ηηηZ→ηηη, and 10−1110−11 for Z→ηggZ→ηgg, which are hardly accessible at the GigaZ option.