The Strong CP Problem and Discrete Symmetries

Abstract: We discuss a possible solution to the strong CP problem which is based on spontaneous CP violation and discrete symmetries. At the same time we predict in a simple way the almost right-angled quark unitarity triangle angle ($\alpha \simeq 90^\circ$) by making the entries of the quark mass matrices either real or imaginary. To prove the viability of our strategy we present a toy flavour model for the quark sector.