Predicting θ 13 and the neutrino mass scale from quark lepton mass hierarchies

Abstract

Abstract Flavour symmetries of Froggatt-Nielsen type can naturally reconcile the large quark and charged lepton mass hierarchies and the small quark mixing angles with the observed small neutrino mass hierarchies and their large mixing angles. We point out that such a flavour structure, together with the measured neutrino mass squared differences and mixing angles, strongly constrains yet undetermined parameters of the neutrino sector. Treating unknown $ \mathcal{O} $ (1) parameters as random variables, we obtain surprisingly accurate predictions for the smallest mixing angle, $ {\text{si}}{{\text{n}}^{{2}}}{2}{\theta_{{{13}}}} = 0.0{7}_{{ - 0.05}}^{{ + 0.11}} $ , the smallest neutrino mass, $ {m_{{1}}} = {2}.{2}_{{ - {1}.{4}}}^{{ + 1.7}} \times {1}{0^{{ - {3}}}}{\text{eV}} $ , and one Majorana phase, $ {\alpha_{{{21}}}}/\pi = {1}.0_{{ - 0.2}}^{{ + 0.2}}. $