Heavy axions from twin dark sectors with $\bar{\theta}$-characterized mirror symmetry

Abstract

The QCD Lagrangian contains a CP violating gluon density term with a physical coefficient $\bar{\theta}$. The upper bound on the electric dipole moment of neutron implies that the value of $\bar{\theta}$ should be extremely small rather than the theoretically expected order of unity. The tiny $\bar{\theta}$ is commonly known as the strong CP problem. In order to solve this puzzle, we construct a $\bar{\theta}$-characterized mirror symmetry between a pair of twin dark sectors with respective discrete symmetries. By taking a proper phase rotation of dark fields, we can perfectly remove the parameter $\bar{\theta}$ from the full Lagrangian. In our scenario, the discrete symmetry breaking, which are responsible for the mass generation of dark colored fermions and dark matter fermions, can be allowed near the TeV scale. This means different phenomena from the popular axion models with high scale Peccei-Quinn global symmetry breaking.