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}}. $
Highlights
In the following we shall employ Monte-Carlo techniques to study quantitatively the dependence of yet undetermined, but soon testable parameters of the neutrino sector on the unknown O(1) factors of the mass matrices
Using the already measured neutrino masses and mixings as input, we find surprisingly sharp predictions which indicate a large value for the smallest mixing angle θ13 in accordance with recent results from T2K [13], Minos [14] and Double Chooz [15], a value for the lightest neutrino mass of O(10−3) eV and one Majorana phase in the mixing matrix peaked at α21 = π
In the following we study the impact of the unspecified O(1) factors in the lepton mass matrices on the various parameters of the neutrino sector by using a Monte Carlo method, taking present knowledge on neutrino masses and mixings into account
Summary
As far as orders of magnitude are concerned, the masses of quarks and charged leptons approximately satisfy the relations mt : mc : mu ∼ 1 : η2 : η4 , mb : ms : md ∼ mτ : mμ : me ∼ 1 : η : η3 ,. Hd and S are the Higgs fields for electroweak and B − L symmetry breaking, i.e., their vacuum expectation values generate the Dirac masses of quarks and leptons and the Majorana masses for the right-handed neutrinos, respectively. In this setup, the Yukawa couplings are determined up to complex O(1) factors by assigning U(1) charges to the fermion and Higgs fields in eq (2.2), hij ∼ ηQi+Qj. With the charge assignment given in table 1 the mass relations in eq (2.1) are reproduced. Carrying out the analysis described below and calculating the 68% confidence intervals, we find that in many cases our results are sharply peaked, yielding a higher precision than only an order-of-magnitude estimate
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