Solving the strong CP problem by a $\bar{\theta}$-characterized mirror symmetry

In the standard model QCD Lagrangian, a term of CP violating gluon density is theoretically expected to have a physical coefficient $\bar{\theta}$ of the order of unity. However, the upper bound on the electric dipole moment of neutron enforces the value of $\bar{\theta}$ to be extremely small. Such a huge gap between theoretical expectation and experimental result is commonly known as the strong CP problem. To solve this puzzle in an appealing context of two Higgs doublets, we propose an economical $\bar{\theta}$-characterized mirror symmetry between two Higgs singlets with respective discrete symmetries. In our scenario, the parameter $\bar{\theta}$ 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.