CPviolation in a minimal renormalizable supersymmetricSO(10)model and beyond

We investigate the role of $CP$ phases within the renormalizable SUSY $SO(10)$ GUT with one ${10}_H$, one ${\overline{126}}_H$ one ${126}_H$ and one ${210}_H$ Higgs representations and type II seesaw dominating the neutrino mass matrix. This framework is non trivially predictive in the fermionic sector and connects in a natural way the GUT unification of $b$ and $\tau$ Yukawa couplings with the bi-large mixing scenario for neutrinos. On the other hand, existing numerical analysis claim that consistency with quark and charged lepton data prevents the minimal setup from reproducing the observed $CP$ violation via the Cabibbo-Kobayashi-Maskawa (CKM) matrix. We re-examine the issue and find by inspection of the fermion mass sum rules and a detailed numerical scan that, even though the CKM phase preferentially takes values in the second quadrant, the agreement of the minimal model with the data is actually obtained in a non negligible fraction of the parameter space. We then consider a recently proposed renormalizable extension of the minimal model, obtained by adding one chiral 120-dimensional Higgs supermultiplet. We show that within such a setup the CKM phase falls naturally in the observed range. We emphasize the robust predictivity of both models here considered for neutrino parameters that are in the reach of ongoing and future experiments.