[Paper Review] A see-saw scenario of an $A_4$ flavour symmetric standard model

Dinh Nguyen Dinh, N. Anh Ky+2 more|arXiv (Cornell University)|Feb 24, 2016

Neutrino Physics Research31 references3 citations

TL;DR

This paper proposes a type-I seesaw mechanism within an A₄ flavour-symmetric extension of the Standard Model, introducing three Higgs doublets as an A₄ triplet and three singlets, along with four right-handed neutrinos (one triplet and three singlets) to generate small neutrino masses. The model successfully predicts neutrino mixing parameters, CP-violating phases, and the effective Majoron mass for neutrinoless double beta decay, with results consistent with current experimental data and the T2K collaboration's recent findings on δCP.

ABSTRACT

A see-saw scenario for an $A_4$ flavour symmetric standard model is presented. The latter, compared with the standard model, has an extended field content adopting now an additional $A_4$ symmetry structure (along with the standard model symmetry). As before, the see-saw mechanism can be realized in several models of different types depending on different ways of neutrino mass generation corresponding to the introduction of new (heavy in general) fields with different symmetry structures. In the present paper, a general description of all these see-saw types is made with a more detailed investigation on type-I models, while for type-II and type-III models a similar strategy can be followed. As within the original see-saw mechanism, the symmetry structure of the standard model fields decides the number and the symmetry structure of the new fields. In a model considered here, the scalar sector consists of three standard-model-Higgs-like iso-doublets ($SU_L(2)$-doublets) forming together an $A_4$-triplet, and three iso-singlets transforming as three singlets (1,$1^{'}$ and $1^{''}$) of $A_4$. In the lepton sector, the three left-handed lepton iso-doublets form an $A_4$-triplet, while the three right-handed charged leptons are either $A_4$-singlets in one version of the model, or components of an $A_4$-triplet in another version. To generate neutrino masses through, say, the type-I see-saw mechanism, it is natural to add four right-handed neutrino multiplets, including one $A_4$-triplet and three $A_4$-singlets. For an interpretation, the model is applied to deriving some physics quantities such as neutrinoless double beta decay effective mass $|\langle m_{ee} angle|$, CP violation phase $δ_{CP}$ and Jarlskog parameter $J_{CP}$, which can be verified experimentally.

Motivation & Objective

• To extend the Standard Model with an A₄ family symmetry to explain small neutrino masses and mixing patterns.
• To implement a type-I seesaw mechanism using A₄ multiplets for right-handed neutrinos to generate Majorana masses.
• To predict observable quantities such as the effective mass for neutrinoless double beta decay, CP-violating phase δCP, and Jarlskog invariant.
• To achieve consistency with experimental data, including recent T2K results on δCP, without requiring additional discrete symmetries like Z₃×Z₄.

Proposed method

• The scalar sector includes three SU(2)L doublets forming an A₄ triplet and three singlets transforming as 1, 1′, and 1″ under A₄.
• The lepton sector assigns left-handed charged leptons to an A₄ triplet and right-handed charged leptons to either A₄ singlets or an A₄ triplet.
• Four right-handed neutrinos are introduced: one A₄ triplet and three A₄ singlets, enabling the type-I seesaw mechanism.
• A perturbative expansion is applied to the Yukawa and mass terms to derive the light neutrino mass matrix and mixing structure.
• The PMNS mixing matrix is reconstructed from the model’s mass eigenstates, allowing extraction of δCP, JCP, and |⟨mee⟩|.
• The model’s predictions are compared with global fits of neutrino oscillation data and the T2K collaboration’s δCP measurements.

Experimental results

Research questions

• RQ1 How can the A₄ family symmetry be consistently embedded in a seesaw model to generate small neutrino masses?
• RQ2 What are the implications of the A₄ structure on the neutrino mixing angles and CP-violating phases?
• RQ3 Can the model predict the effective Majoron mass |⟨mee⟩| for neutrinoless double beta decay that matches current experimental bounds?
• RQ4 How do the predicted values of δCP and JCP compare with recent experimental data, particularly from T2K?
• RQ5 Can the model reproduce the observed deviation from tri-bimaximal mixing without introducing additional discrete symmetries?

Key findings

• The model predicts a neutrino mixing pattern consistent with global fits of neutrino oscillation data, including deviations from tri-bimaximal mixing.
• The predicted value of the CP-violating phase δCP is in excellent agreement with the T2K collaboration’s recent measurement, both in normal and inverse neutrino mass ordering.
• The effective Majoron mass |⟨mee⟩| is predicted to be within the sensitivity range of ongoing and future neutrinoless double beta decay experiments.
• The Jarlskog invariant JCP is non-zero, confirming the presence of CP violation in the lepton sector within the model.
• The model achieves a consistent seesaw mechanism without requiring additional symmetries such as Z₃×Z₄, simplifying the model structure.
• The perturbative analysis of the Yukawa and mass terms successfully reproduces the observed neutrino mass splittings and mixing angles.