Neutrino masses and mixing in A4 models with three Higgs doublets

TL;DR

This paper investigates neutrino mass models with A4 symmetry and three Higgs doublets, finding that traditional approaches fail but a modified seesaw mechanism with symmetry-breaking terms can fit experimental data.

Contribution

It demonstrates the limitations of A4-based models with three Higgs doublets and proposes a modified seesaw approach with softly broken symmetry to achieve experimental consistency.

Findings

Standard A4 models with three Higgs doublets cannot produce correct neutrino masses.

Type-I seesaw fails without additional symmetry-breaking terms.

Including softly broken heavy neutrino mass terms aligns models with experimental data.

Abstract

We study neutrino masses and mixing in the context of flavor models with A4 symmetry, three scalar doublets in the triplet representation, and three lepton families. We show that there is no representation assignment that yields a dimension-five mass operator consistent with experiment. We then consider a type-I seesaw with three heavy right-handed neutrinos, explaining in detail why it fails, and showing with a numerical example that agreement with the present neutrino oscillation data can be recovered with the inclusion of dimension-three heavy neutrino mass terms that break softly the A4 symmetry.