Axionless Solution to the Strong CP Problem -- two-zeros textures of the quark and lepton mass matrices and neutrino CP violation --

Abstract

CP invariance is a very attractive solution to the strong CP problem in QCD. This solution requires the vanishing ${\rm arg}\,[{\rm det}\, M_d\, {\rm det} M_u]$, where the $M_d$ and $M_u$ are the mass matrices for the down- and up-type quarks. It happens if we have several zeros in the quark mass matrices. We proceed a systematic construction, in this paper, of two zeros textures for the down-type quark mass matrix while the mass matrix for the up-type quarks is always diagonal. We find only three types of the mass matrices can explain the observed CKM matrix, the masses of the quarks and the charged leptons and the small enough vacuum angle $\theta < 10^{-10}$. We extend the mass construction to the neutrino sector and derive predictions on the CP violating parameter $\delta_{CP}$ in the neutrino oscillation and the mass parameter $m_{\beta\beta}$. It is extremely remarkable that the normal (NH) and inverted (IH) hierarchies in the neutrino masses are equally possible in the case where we introduce only two right-handed neutrinos $N$s. Furthermore, we have a strict prediction on the $\delta_{CP} \simeq 200^\circ$ or $250^\circ$ in the NH case. If it is the case we can naturally explain the positive sign of the baryon asymmetry in the present universe.