Abstract
We analyze a modular invariant model of lepton masses, with neutrino masses originating either from the Weinberg operator or from the seesaw. The constraint provided by modular invariance is so strong that neutrino mass ratios, lepton mixing angles and Dirac/Majorana phases do not depend on any Lagrangian parameter. They only depend on the vacuum of the theory, parametrized in terms of a complex modulus and a real field. Thus eight measurable quantities are described by the three vacuum parameters, whose optimization provides an excellent fit to data for the Weinberg operator and a good fit for the seesaw case. Neutrino masses from the Weinberg operator (seesaw) have inverted (normal) ordering. Several sources of potential corrections, such as higher dimensional operators, renormalization group evolution and supersymmetry breaking effects, are carefully discussed and shown not to affect the predictions under reasonable conditions.
Highlights
In the last few years neutrino physics has entered the era of precision, a goal that could not even be conceived when neutrino oscillations were discovered twenty years ago
As a step forward in the realization of this program, an important ingredient can be represented by modular invariance
Such a symmetry is so strong that in some cases the Yukawa interactions are completely determined in terms of a complex scalar field, the modulus
Summary
In the last few years neutrino physics has entered the era of precision, a goal that could not even be conceived when neutrino oscillations were discovered twenty years ago. Supersymmetric models with modular invariance as flavour symmetry, recently proposed in ref. At low-energy and in both variants, the superpotential depends only on one overall mass scale and 3 dimensionless parameters The latter are adjusted to reproduce the charged lepton masses, which are not predicted, but just fitted as in the Standard Model. All the remaining 8 dimensionless parameters, neutrino mass ratios, lepton mixing angles, Dirac and Majorana phases, do not depend on any Lagrangian parameter. They do depend on the vacuum structure of the model, controlled by the VEVs of a modulus field and a flavon, minimally described by a total of 3 real parameters. We estimate the impact of supersymmetry breaking terms, required in any realistic framework accounting for the existing bounds on supersymmetric particles
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