  So far the null results from axion searches have enforced a huge hierarchy
between the Peccei-Quinn and electroweak symmetry breaking scales. Then the
inevitable Higgs portal poses a large fine tuning on the standard model Higgs
scalar. Now we find if the Peccei-Quinn global symmetry has a set of residually
discrete symmetries, these global and discrete symmetries can achieve a chain
breaking at low scales such as the accessible TeV scale. This novel mechanism
can accommodate some new phenomena including a sizable coupling of the standard
model Higgs boson to the axion.
