Neutrinos, Dark Matter and Higgs Vacua in Parity Solutions of the strong CP problem

The strong CP problem can be solved if the laws of nature are invariant under a space-time parity exchanging the Standard Model with its mirror copy. We review and extend different realizations of this idea with the aim of discussing Dark Matter, neutrino physics, leptogenesis and collider physics within the same context. In the minimal realization of Ref. [1] the mirror world contains a massless dark photon, which leads to a rather interesting cosmology. Mirror electrons reproduce the dark matter abundance for masses between 500-1000 GeV with traces of strongly interacting dark matter. This scenario also predicts deviations from cold dark matter, sizable $\Delta N_{\rm eff}$ and colored states in the TeV range that will be tested in a variety of upcoming experiments. We also explore scenarios where the mirror photon is massive and the mirror particles are charged under ordinary electro-magnetism with very different phenomenology. We also show that, for the measured values of the SM parameters, the Higgs effective potential can give rise to a second minimum at large field value as required to break spontaneously the parity symmetry.