Another relation among the neutrino mass-squared differences?

TL;DR

The paper addresses the challenge of determining absolute neutrino masses from oscillation data by proposing a simple algebraic relation between the mass-squared differences $\Delta m^2_{21}$ and $\Delta m^2_{31}$, encapsulated in a ratio $\lambda$ that numerically approximates $\sqrt{2}$. Using recent global fits, the authors argue that this near-$\sqrt{2}$ value persists across analyses, enabling an analytic framework to manipulate the spectrum. Under the assumption $\lambda = \sqrt{2}$ and the standard relation $\Delta m^2_{31}-\Delta m^2_{21}=\Delta m^2_{32}$, the entire mass spectrum can be reconstructed from two masses, implying $m_1\approx 0$ with $m_2=\sqrt{\Delta m^2_{21}}$ and $m_3=\sqrt{\Delta m^2_{31}}$, and yielding concrete predictions for $\sum_i m_i$, $m_{\nu_e}$, and $m_{\beta\beta}$ compatible with current constraints. The approach exhibits a Koide-like structure and offers testable predictions, particularly through JUNO and forthcoming oscillation measurements, while remaining perturbatively robust to small deviations from $\sqrt{2}$. This framework, if validated, could significantly constrain the absolute neutrino mass scale and illuminate the underlying mass-generation mechanism.

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 $Δm^2_{21}$ and $Δm^2_{31}$. It provides a framework to analytically manipulate these parameters and admits specific physical interpretations. In particular, the results may point toward a vanishing $ν_1$ mass.