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

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 $\theta_{12}$ and $\Delta m^2_{21}$ 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.