WIMP dark matter expected in the parity solution to the strong CP problem

We construct an extended Standard Model (SM), motivated by the strong CP problem and dark matter. In our model, parity symmetry is conserved at high energy by introducing a mirror sector with the extra gauge symmetry, $SU(2)_R \times U(1)_R$. The charges of $SU(2)_R \times U(1)_R$ are assigned to the mirror fields in the same way as in the SM, but the chirality of the mirror fermions is opposite to respect the parity symmetry. The strong CP problem is resolved, since the mirror quarks are also charged under the $SU(3)_c$ in the SM. In the minimal setup, the mirror gauge symmetry leads stable colored particles, so that we introduce two scalars in order to avoid the stable colored particle. Interestingly, one of the scalars becomes stable because of the gauge symmetry, so that it can be a good dark matter candidate. In this paper, we especially study the phenomenology relevant to the dark matter. We also discuss the neutrino sector and show that the right-handed neutrinos from the mirror sector can increase the effective number of neutrinos or dark radiation by $0.14$.