Universal Predictions of Modular Invariant Flavor Models near the Self-Dual Point

Area of Science:

• High Energy Physics
• Particle Physics
• Theoretical Physics

Background:

• Modular invariant models are crucial for understanding lepton masses and mixing angles.
• Previous studies explored various model parameters and their impact on physical observables.

Purpose of the Study:

• To analyze a large set of modular invariant models for lepton masses and mixing angles.
• To identify universal behaviors emerging in these models near the self-dual point.

Main Methods:

• Analysis of a comprehensive collection of modular invariant models.
• Investigation of model behavior in the vicinity of the self-dual point (τ=i).

Main Results:

• Many models were found to prefer the self-dual point τ=i.
• A universal behavior emerges near τ=i, independent of specific model details.
• The neutrino mass spectrum is normally ordered.
• Universal relations were derived for physical observables based on |τ-i|.

Conclusions:

• The self-dual point offers a simplifying framework for modular invariant models of lepton physics.
• Universal relations near τ=i provide testable predictions and insights into fundamental particle properties.
• This universality reduces reliance on specific theoretical details, enhancing model applicability.