Strong CP Problem and the Natural Hierarchy of Yukawa Couplings
  A possible solution to the strong CP problem is presented without using an axion. The model is based on the framework of the supersymmetric vectorlike theory with the spontaneous breakdown of the P-C-T-invariance. It is shown that the characteristic structure of the Yukawa coupling matrices that results from the spontaneous P-C-T-breaking plays the essential role in naturally realizing $\theta=0$ at the tree level. It is argued that $\theta=0$ will not be affected by the radiative corrections. 
Kenzo Inoue, Naoki Yamatsu