Solving the strong CP problem via a -characterized mirror symmetry

In the standard model QCD Lagrangian, a term of CP violating gluon density is theoretically expected to have a physical coefficient , which is typically on the order of unity. However, the upper bound on the electric dipole moment of the neutron enforces the value of to be extremely small. The significant discrepancy between theoretical expectations and experimental results in this context is widely recognized as the strong CP problem. To solve this puzzle in an appealing context of two Higgs doublets, we propose a -characterized mirror symmetry between two Higgs singlets with respective discrete symmetries. In our scenario, the parameter can completely disappear from the full Lagrangian after the standard model fermions take a proper phase rotation as well as the Higgs doublets and singlets. Moreover, all of new physics for solving the strong CP problem can be allowed near the TeV scale.