# Neutrino Mass Sum Rules and Symmetries of the Mass Matrix

## TL;DR

This paper investigates the origin of neutrino mass sum rules, concluding they arise from parameter reduction in models rather than residual symmetries, clarifying their theoretical basis.

## Contribution

It systematically analyzes the relationship between neutrino mass sum rules and symmetries, confirming that sum rules result from model parameter constraints, not residual symmetries.

## Key findings

- Sum rules are not linked to residual symmetries.
- Sum rules result from parameter reduction in models.
- Confirmed previous statements about the origin of sum rules.

## Abstract

Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which was not yet discussed fully satisfactorily was the origin of these sum rules and if they are related to any residual or accidental symmetry. We will address this open issue here systematically and find previous statements confirmed. Namely, that the sum rules are not related to any enhanced symmetry of the Lagrangian after family symmetry breaking but that they are simply the result of a reduction of free parameters due to skillful model building.