Strong CP problem and mirror world: the Weinberg–Wilczek axion revisited

A new possibility for solving the strong CP problem is suggested. It is based on the concept of a mirror world of particles, with the gauge symmetry and Lagrangian completely identical to that of the observable particles. We assume that the ordinary and mirror sectors share the same Peccei–Quinn symmetry realized à la Weinberg–Wilczek, so that the θ-terms are simultaneously canceled by the axion VEV in both worlds. This property remains valid even if the symmetry between two sectors is spontaneously broken and the weak scale of the mirror world is larger than the ordinary weak scale, in which case also the mirror QCD scale becomes larger than the ordinary one. In this situation our axion essentially represents a Weinberg–Wilczek axion of the mirror world with quite a large mass, while it couples the ordinary particles like an invisible axion. The experimental and astrophysical limits are discussed and an allowed parameter window is found with the Peccei–Quinn scale f_a10⁴–10⁵ GeV and the axion mass m_a1 MeV, which can be accessible for future experiments. We also show that our solution to the strong CP problem is stable against the Planck scale induced effects.