Predicting $\delta^\text{PMNS}$, $\theta_{23}^\text{PMNS}$ and fermion mass ratios from flavour GUTs with CSD2

Abstract

Constrained Sequential neutrino Dominance of type 2 (referred to as CSD2) is an attractive building block for flavour Grand Unified Theories (GUTs) because it predicts a non-zero leptonic mixing angle $\theta_{13}^\text{PMNS}$, a deviation of $\theta_{23}^\text{PMNS}$ from $\pi /4$, as well as a leptonic Dirac CP phase $\delta^\text{PMNS}$ which is directly linked to the CP violation relevant for generating the baryon asymmetry via the leptogenesis mechanism. When embedded into GUT flavour models, these predictions are modified in a specific way, depending on which GUT operators are responsible for generating the entries of fermion Yukawa matrices. In this paper, we systematically investigate and classify the resulting predictions from supersymmetric $\mathrm{SU}(5)$ based flavour models by fitting the known fermion mass and mixing data, in order to provide a roadmap for future model building. Interestingly, the promising models predict the lepton Dirac CP phase $\delta^\mathrm{PMNS}$ between $230^\circ$ and $290^\circ$, and the quark CP phase $\delta^\mathrm{CKM}$ in accordance with a right-angled unitarity triangle ($\alpha_\mathrm{UT}=90^\circ$). Also, our model setup predicts the quantities $\theta_{23}^\mathrm{PMNS}$ and $m_d/m_s$ with less uncertainty than current experimental precision, and allowing with future sensitivity to discriminate between them.