[Paper Review] Zee and Zee-Babu mechanisms in the minimal 331 model

A. C. B. Machado, Pedro Pasquini+1 more|arXiv (Cornell University)|Oct 5, 2018

Stochastic processes and financial applicationsEconomics, Econometrics and Finance3 citations

TL;DR

This paper demonstrates that the minimal 3-3-1 model naturally implements the Zee and Zee-Babu mechanisms for generating neutrino masses at one-loop and two-loop levels, respectively, without adding new particles. It presents a systematic method to fit charged and neutral lepton masses and the PMNS mixing matrix using the 1-loop modified Zee mechanism, showing that tree-level neutrino masses are inconsistent with current data, but one-loop contributions successfully accommodate oscillation data.

ABSTRACT

We show that the minimal 3-3-1 model cannot accommodate the neutrino masses at tree level using present experimental data. Nevertheless, a modified Zee and the Zee-Babu mechanisms for generating neutrino masses at 1-loop and 2-loop, respectively, are automatically implemented in the minimal 3-3-1 model, without introducing new degrees of freedom to the model. We also present a systematic method for finding solutions to the leptonic sector masses and mixing. As a case study, we accommodate the charged and neutral leptons masses and the PMNS matrix in the 1-loop modified Zee mechanism contained in the minimal 3-3-1 model.

Motivation & Objective

• To investigate whether the minimal 3-3-1 model can generate neutrino masses at tree level using current experimental data.
• To show that the Zee and Zee-Babu mechanisms are naturally embedded in the model's particle content without introducing new degrees of freedom.
• To develop a systematic method for solving the leptonic sector, including charged and neutral lepton masses and PMNS mixing matrix.
• To demonstrate that the 1-loop modified Zee mechanism in the model can successfully reproduce neutrino oscillation data.

Proposed method

• The model uses the leptonic triplet structure ΨaL = (νa, la, lc a)T ~ (3,0) and scalar triplets η, ρ, χ to define Yukawa interactions with symmetric and antisymmetric flavor matrices G^S and G^η.
• The neutrino mass matrix is derived from one-loop and two-loop diagrams involving the scalar fields η and S, with the Zee and Zee-Babu mechanisms implemented via the model’s existing scalar content.
• A general basis is used where both the charged lepton and neutrino mass matrices are fully general, and unitary rotations V^ν, V^l_L, V^l_R are applied to diagonalize them.
• An auxiliary basis is introduced where the symmetric matrix G^S is diagonalized via a transformation A, enabling a systematic solution for the PMNS matrix in terms of A, V^l_L, and V^ν.
• The PMNS matrix is reconstructed as V_PMNS = A* V^l†_L,2 A U_2, linking the flavor and mass eigenstate bases.
• The method allows fitting the full leptonic spectrum, including masses and mixing, within the 1-loop Zee framework.

Experimental results

Research questions

• RQ1 Can the minimal 3-3-1 model generate neutrino masses at tree level while satisfying current neutrino oscillation data?
• RQ2 Are the Zee and Zee-Babu mechanisms naturally realized in the minimal 3-3-1 model without adding new particles?
• RQ3 Can the full leptonic sector—charged lepton masses, neutrino masses, and PMNS mixing—be consistently fitted within the 1-loop modified Zee mechanism in this model?
• RQ4 What is the role of the symmetric and antisymmetric Yukawa matrices in generating the observed lepton masses and mixing?
• RQ5 How can a systematic method be constructed to solve for the PMNS matrix and lepton masses in the context of the 1-loop Zee mechanism in the m331 model?

Key findings

• Tree-level neutrino masses in the minimal 3-3-1 model are inconsistent with current neutrino oscillation data.
• The 1-loop Zee mechanism is naturally implemented in the model via the existing scalar and fermion content, without introducing new fields.
• The 2-loop Zee-Babu mechanism is also automatically realized in the model due to its representation structure.
• A systematic method is developed to solve for the PMNS matrix and lepton masses using the 1-loop modified Zee mechanism.
• The 1-loop contributions successfully reproduce the observed neutrino masses and mixing angles, while tree-level contributions alone fail to do so.
• Right-handed neutrinos are not required in this framework; the observed neutrino masses can arise entirely from loop mechanisms, potentially allowing for light sterile neutrinos if needed for dark matter or anomalies.