# Discrete symmetries for electroweak natural type-I seesaw mechanism

## TL;DR

This paper explores how discrete symmetries can naturally produce the cancellations needed for TeV-scale fermion singlets in type-I seesaw models, addressing neutrino mass generation without fine-tuning.

## Contribution

It demonstrates that discrete symmetries can enforce exact cancellations in the seesaw formula, resulting in degenerate fermion singlets and decoupling, with specific models based on $A_4$ and $\\Sigma(81)$.

## Key findings

- Discrete symmetries lead to degenerate fermion singlets.
- Exact cancellations require two fermion singlets to be degenerate.
- Perturbations can generate viable neutrino masses.

## Abstract

The naturalness of electroweak scale in the models of type-I seesaw mechanism with ${\cal O}(1)$ Yukawa couplings requires TeV scale masses for the fermion singlets. In this case, the tiny neutrino masses have to arise from the cancellations within the seesaw formula which are arranged by fine-tuned correlations between the Yukawa couplings and the masses of fermion singlets. We motivate such correlations through the framework of discrete symmetries. In the case of three Majorana fermion singlets, it is shown that the exact cancellation arranged by the discrete symmetries in seesaw formula necessarily leads to two mass degenerate fermion singlets. The remaining fermion singlet decouples completely from the standard model. We provide two candidate models based on the groups $A_4$ and $\Sigma(81)$ and discuss the generic perturbations to this approach which can lead to the viable neutrino masses.