Minimal spontaneous CP-violating GUT and predictions for leptonic CP phases

A non-supersymmetric renormalizable $SO(10)$ model, with CP invariant Yukawa sector consisting of Lorentz scalars in $10$ and $\overline{126}$ dimensional representations, is proposed. The elemental Yukawa couplings are real due to CP symmetry. The latter is broken in the low energy effective theory through the standard model Higgs which is a complex linear combination of electroweak doublets residing in $10$ and $\overline{126}$ scalars. As a result, the mass matrices in the quark and lepton sectors, including those of heavy and light neutrinos, depend only on three phases which in turn determine CP violation in both sectors. The model is comprehensively analysed for its viability and predictions including the possibility to generate baryon asymmetry through thermal leptogenesis. It predicts relatively small values for CP phases in the lepton sector. Successful leptogenesis further restricts the ranges to $-0.4 \le \sin\delta \le 0.4$ for the Dirac phase and $-0.3 \le \sin \eta_1 \le 0.2$, $-0.5 \le \sin \eta_2 \le 0.5$ for the Majorana phases.