Are neutrino masses modular forms?
By F. Feruglio. From My Vast Repertoire ..., 2017
265 citations recorded by the source corpus.
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 ΓN. 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 ΓN, 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.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/ac0d155b30f5c3917ab6870bdc0cf1caf319c6e3
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In Nuclear and High Energy Physics
Citations in the corpus
- Modular A5 symmetry for flavour model building (2018, background): “In the case of Γ3, the corresponding set of four seed functions η̃i reads [14]:”
- Flavor structures of charged fermions and massive neutrinos (2019, background): “They transform in the threedimensional representation of A4 and can be explicitly written out in terms of the Dedekind ηfunction η(τ) and its derivative η̇(τ) [776]:”
- Lepton masses and mixing from modular S4 symmetry (2018, methodology): “ (11) indicates a sum (with independent coecients) of all possible singlets one can extract from this product. The eects of enforcing invariance under N for N= 2 and N= 3 have been studied in Refs. [3,4]. The group 2 is isomorphic to S 3 while 3 ’A 4. In what follows we consider invariance under the”
- Modular invariance faces precision neutrino data (2018, background): “[20] where the same models considered here were analyzed in a particular limit.”
- Generalised CP symmetry in modular-invariant models of flavour (2019, background): “The lowest weight modular multiplet of Γ3 can be written in terms of the above vectors, namely (see also [21]):”
- Modular S4 models of lepton masses and mixing (2018, methodology): “[7] where also models based on the finite modular group Γ3 ' A4 have been constructed.”
- Neutrino masses and mixing from double covering of finite modular groups (2019, background): “In the modular symmetry approach to neutrino masses and mixing [15], only even weight modular forms are considered in the literature at present.”