# Modular Invariance Faces Precision Neutrino Data

### Submission summary

 As Contributors: Juan Carlos Criado · Ferruccio Feruglio Arxiv Link: https://arxiv.org/abs/1807.01125v3 (pdf) Date accepted: 2018-10-23 Date submitted: 2018-09-26 02:00 Submitted by: Feruglio, Ferruccio Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory High-Energy Physics - Phenomenology Approach: Theoretical

### 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.

### Ontology / Topics

See full Ontology or Topics database.

Published as SciPost Phys. 5, 042 (2018)

Dear Editor and Referees, we have modified our text following your suggestions. In particular

• In section 3, second paragraph, we have hopefully better clarified what results of reference [20] we are using and the role played by the reactor angle in our analysis. This part has been completely rewritten aiming to a more transparent presentation.
• In section 3, at the end, we have added a paragraph where we briefly mention the implications of modular invariance for the quark sector, as requested.
• Finally we have corrected the grammatical errors/typos.

We hope that the present version fulfills your requirements.

                       Kind regards,           Juan Carlos Criado and Ferruccio Feruglio


### List of changes

- In section 3, second paragraph, we have hopefully better clarified what results of reference [20] we
are using and the role played by the reactor angle in our analysis. This part has been completely rewritten
aiming to a more transparent presentation.
- In section 3, at the end, we have added a paragraph where we briefly mention the implications of modular
invariance for the quark sector, as requested.
- Finally we have corrected the grammatical errors/typos.

### Submission & Refereeing History

#### Published as SciPost Phys. 5, 042 (2018)

Resubmission 1807.01125v3 on 26 September 2018
Submission 1807.01125v2 on 17 July 2018

## Reports on this Submission

### Report

The authors answered satisfactory to my question. I am therefore pleased to propose the paper for publication in the current form.

• validity: top
• significance: top
• originality: high
• clarity: top
• formatting: excellent
• grammar: excellent

### Report 1 by George Leontaris on 2018-9-27 (Invited Report)

• Cite as: George Leontaris, Report on arXiv:1807.01125v3, delivered 2018-09-27, doi: 10.21468/SciPost.Report.595

### Report

The present version of the paper clarifies all the points required in my report,
in particular those regarding theta_13 angle and quark sector.
In my opinion it is now suitable for publication.

• validity: good
• significance: good
• originality: high
• clarity: good
• formatting: good
• grammar: good