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

TL;DR

This paper explores how flavour GUT models with CSD2 can predict neutrino mixing parameters and fermion mass ratios, providing a systematic classification and future experimental tests.

Contribution

It systematically classifies supersymmetric SU(5) flavour models with CSD2, predicting key neutrino and quark CP phases and mass ratios, guiding future model building.

Findings

Predicted leptonic CP phase $ heta_{23}^ ext{PMNS}$ between 230° and 290°

Quark CP phase $ heta_{23}^ ext{PMNS}$ consistent with a 90° unitarity triangle

Predicted fermion mass ratios with less uncertainty than current measurements

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.