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

A new possibility for solving the strong CP-problem is suggested,which assumes that apart of the ordinary world of observable particles described by standard model, there exits a mirror sector of particles and two sectors share the same Peccei-Quinn symmetry realized {\it a l\`a} Weinberg-Wilczek model. The mirror gauge group is completely analogous to that of the standard model for ordinary particles but having somewhat larger electroweak scale,which in turn implies the infrared scale $\Lambda'$ of the mirror strong interactions has to be larger than the ordinary QCD scale $\Lambda$. In this way, the axion mass and interaction constants are actually determined by mirror sector scales $v'$ and $\Lambda'$, while the $\theta$ terms are simultaneously cancelled in both sectors due to mirror symmetry. The experimental and astrophysical limits on such an axion is discussed. An interesting parameter window is found where $f_a \sim {\rm few}\times 10^4$ GeV whereas the axion mass is $\sim 1$ MeV