A Solution to the Strong CP Problem

One may argue that QCD solves the strong CP problem by itself, without having to introduce new symmetries and particles. To test this idea, a lattice simulation is performed. The problem is investigated in the CP$^3$ model first. It is found that the model has a first order phase transition in $\theta$ from a confining phase at small $\theta$ to a deconfining phase at large $\theta$, and that the critical value of $\theta$ decreases towards zero as $\beta$ is taken to infinity. This suggests that $\theta$ is tuned to zero in the continuum limit. Preliminary studies of the SU(2) Yang-Mills theory in four dimensions show a phase transition in $\theta$ as well, so that it is quite likely that the strong CP problem in QCD is solved along the same line.