Another relation among the neutrino mass-squared differences?

TL;DR

This paper proposes a simple algebraic relation between neutrino mass-squared differences, potentially aiding in determining absolute neutrino masses and providing insights into the mass-generation mechanism, with implications for a vanishing $ u_1$ mass.

Contribution

It introduces a novel algebraic relation between neutrino mass-squared differences inspired by recent global fits, offering a new analytical framework and physical interpretations.

Findings

Relation suggests a possible zero mass for $ u_1$

Framework facilitates analytical manipulation of neutrino parameters

Provides insights into neutrino mass-generation mechanisms

Abstract

Determining absolute neutrino masses remains a central challenge in particle physics. Relations among the neutrino mass-squared differences could facilitate this determination and shed additional light on the underlying mass-generation mechanism. Inspired by recent global fits of neutrino oscillation parameters, we propose a simple algebraic relation between $\Delta m^2_{21}$ and $\Delta m^2_{31}$. It provides a framework to analytically manipulate these parameters and admits specific physical interpretations. In particular, the results may point toward a vanishing $\nu_1$ mass.