Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Modular TM$_1$ mixing in light of precision measurement in JUNO

Wen-Hao Jiang, Ruiwen Ouyang, Ye-Ling Zhou

TL;DR

This work assesses TM$_1$ leptonic mixing in the context of modular $S_4$ flavor symmetry, constrained by JUNO’s high-precision measurements of $\Delta m^2_{21}$ and $\sin^2\theta_{12}$. It develops three distinct modular-$S_4$ constructions (Models A–C) that realize TM$_1$ via different residual-symmetry realizations and analyzes their parameter spaces under JUNO/NuFIT inputs. While Model A is found over-constrained and excluded, Models B and C remain viable, yielding analytic relations among mixing angles and phases (e.g., $\sin\theta_{13}=\sin\theta_R/\sqrt{3}$, $\tan\theta_{12}=\cos\theta_R/\sqrt{2}$) and predictive $m_{ee}$ correlations with the lightest mass. The study demonstrates that TM$_1$ in modular $S_4$ can be tested through forthcoming measurements of the Dirac CP phase and neutrinoless double-beta decay, with JUNO- and KamLAND-Zen-like experiments providing critical probes.

Abstract

This paper investigates the landscape of models based on modular $S_4$ symmetry that predicts the trimaximal TM$_1$ mixing pattern for leptonic flavor mixing, and explores their parameter spaces with constraints from the latest high-precision measurement on $θ_{12}$ and $Δm^2_{21}$ given by JUNO experiment. We review on how the mixing pattern arises from residual symmetries after the spontaneous breaking of a flavor symmetry, via an appropriate vacuum alignment of modular fields and flavon fields. We show three different models that realize the TM$_1$ in three approaches with the same symmetry structure. Due to different model building strategies used, predictions on the CP-violating phase and the effective mass in neutrinoless double beta decay are different, making them distinguishable.

Modular TM$_1$ mixing in light of precision measurement in JUNO

TL;DR

This work assesses TM leptonic mixing in the context of modular flavor symmetry, constrained by JUNO’s high-precision measurements of and . It develops three distinct modular- constructions (Models A–C) that realize TM via different residual-symmetry realizations and analyzes their parameter spaces under JUNO/NuFIT inputs. While Model A is found over-constrained and excluded, Models B and C remain viable, yielding analytic relations among mixing angles and phases (e.g., , ) and predictive correlations with the lightest mass. The study demonstrates that TM in modular can be tested through forthcoming measurements of the Dirac CP phase and neutrinoless double-beta decay, with JUNO- and KamLAND-Zen-like experiments providing critical probes.

Abstract

This paper investigates the landscape of models based on modular symmetry that predicts the trimaximal TM mixing pattern for leptonic flavor mixing, and explores their parameter spaces with constraints from the latest high-precision measurement on and given by JUNO experiment. We review on how the mixing pattern arises from residual symmetries after the spontaneous breaking of a flavor symmetry, via an appropriate vacuum alignment of modular fields and flavon fields. We show three different models that realize the TM in three approaches with the same symmetry structure. Due to different model building strategies used, predictions on the CP-violating phase and the effective mass in neutrinoless double beta decay are different, making them distinguishable.

Paper Structure

This paper contains 13 sections, 58 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Trimaximal TM$_1$ mixing
  3. TM$_1$ mixing in light of recent data
  4. TM$_1$ mixing predicted in flavor symmetries
  5. Models based on modular $S_4$ symmetry
  6. Model A
  7. Model B
  8. Model C
  9. Fit with JUNO Data
  10. Parameterization
  11. Predictions of observables and sum rules
  12. Numerical Result
  13. Conclusions

Figures (3)

  • Figure 1: A few approaches to realise TM$_1$ mixing in modular flavour models.caption
  • Figure 2: Sum rules between $\theta_{12}$ and $\theta_{13}$ in TM$_1$ and TM$_2$ mixing. best-fits, $1\sigma$ and $1\sigma$ ranges from NuFIT 6.0 (green) Esteban:2024eli and the first run of JUNO (red) JUNO:2025gmd are shown as comparison.
  • Figure 3: $m_{\rm lightest}$ vs $m_{ee}$ predicted in Models B and C. Current experimental upper bound and future sensitivities on $m_{ee}$ are shown as references.