180 research outputs found
Are neutrino masses modular forms?
We explore a new class of supersymmetric models for lepton masses and mixing
angles where the role of flavour symmetry is played by modular invariance. The
building blocks are modular forms of level N and matter supermultiplets, both
transforming in representations of a finite discrete group Gamma_N. In the
simplest version of these models, Yukawa couplings are just modular forms and
the only source of flavour symmetry breaking is the vacuum expectation value of
a single complex field, the modulus. In the special case where modular forms
are constant functions the whole construction collapses to a supersymmetric
flavour model invariant under Gamma_N, the case treated so far in the
literature. The framework has a number of appealing features. Flavon fields
other than the modulus might not be needed. Neutrino masses and mixing angles
are simultaneously constrained by the modular symmetry. As long as
supersymmetry is exact, modular invariance determines all higher-dimensional
operators in the superpotential. We discuss the general framework and we
provide complete examples of the new construction. The most economical model
predicts neutrino mass ratios, lepton mixing angles, Dirac and Majorana phases
uniquely in terms of the modulus vacuum expectation value, with all the
parameters except one within the experimentally allowed range. As a byproduct
of the general formalism we extend the notion of non-linearly realised
symmetries to the discrete case.Comment: 40 pages, 3 figures; added comments and a new section with an example
of normal ordering of neutrino masses; to appear in the book "From my vast
repertoire: the legacy of Guido Altarelli", S. Forte, A. Levy and G. Ridolfi,
ed
Maximal Neutrino Mixing from Discrete Symmetry in Extra Dimensions
I review the construction of a model for lepton masses based on the flavour
symmetry group A4 x U(1) reproducing the so-called tri-bimaximal lepton mixing
scheme, in eccelent agreement with current data. The model predicts a neutrino
spectrum of normal hierarchy type, not far from degenerate. A testable relation
between neutrino masses is obtained. I shortly discuss also general
requirements for models based on spontaneously broken flavour symmetries, in
order to get a maximal atmospheric mixing angle.Comment: 3 pages, 1 figure, contribution to proc. of the Int. Europhysics
Conf. on High Energy Physics (HEP2005) July 21th-27th 2005, Lisboa, Portuga
Pieces of the Flavour Puzzle
An overview of the flavour problem is presented, with emphasis on the
theoretical efforts to find a satisfactory description of fermion masses and
mixing angles.Comment: 26 pages, 7 figure
Neutrino Masses and Mixings: a Theoretical Perspective
We briefly review the recent activity on neutrino masses and mixings which
was prompted by the confirmation of neutrino oscillations by the
Superkamiokande experiment.Comment: 30 pages, LATEX, no figures, uses procsla.sty; corrected miss-print
in Table 1. Version to appear on Physics Report
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