Modular Invariance Faces Precision Neutrino Data

TL;DR

This paper explores a highly constrained modular invariant model of lepton masses, demonstrating that neutrino observables depend solely on vacuum parameters and fitting experimental data well.

Contribution

It introduces a modular invariant framework where neutrino parameters are determined by vacuum states, providing precise predictions independent of Lagrangian parameters.

Findings

Excellent fit to data with Weinberg operator (inverted ordering)

Good fit with seesaw mechanism (normal ordering)

Predictions robust against various corrections

Abstract

We analyze a modular invariant model of lepton masses, with neutrino masses originating either from the Weinberg operator or from the seesaw. The constraint provided by modular invariance is so strong that neutrino mass ratios, lepton mixing angles and Dirac/Majorana phases do not depend on any Lagrangian parameter. They only depend on the vacuum of the theory, parametrized in terms of a complex modulus and a real field. Thus eight measurable quantities are described by the three vacuum parameters, whose optimization provides an excellent fit to data for the Weinberg operator and a good fit for the seesaw case. Neutrino masses from the Weinberg operator (seesaw) have inverted (normal) ordering. Several sources of potential corrections, such as higher dimensional operators, renormalization group evolution and supersymmetry breaking effects, are carefully discussed and shown not to affect the predictions under reasonable conditions.