A Solution to the Strong CP Problem

Abstract

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 $θ$ from a confining phase at small $θ$ to a deconfining phase at large $θ$, and that the critical value of $θ$ decreases towards zero as $β$ is taken to infinity. This suggests that $θ$ 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 $θ$ as well, so that it is quite likely that the strong CP problem in QCD is solved along the same line.