A geometrical approach to neutrino oscillation parameters

Abstract

We propose a geometric hypothesis for neutrino mixing: twice the sum of the three mixing angles equals $180^{\circ }$, forming a Euclidean triangle. This condition leads to a predictive relation among the mixing angles and, through trigonometric constraints, enables reconstruction of the mass-squared splittings. The hypothesis offers a phenomenological resolution to the ${\theta }_{23}$ octant ambiguity, reproduces the known mass hierarchy patterns, and suggests a normalized geometric structure underlying the PMNS mixing. We show that while an order-of-magnitude scale mismatch remains (the absolute splittings are underestimated by $\sim 10\times$), the triangle reproduces mixing ratios with notable accuracy, hinting at deeper structural or symmetry-based origins. We emphasize that the triangle relation is advanced as an empirical, phenomenological organizing principle rather than a result derived from a specific underlying symmetry or dynamics. It is testable and falsifiable: current global-fit values already lie close to satisfying the condition, and improved precision will confirm or refute it. We also outline and implement a simple ${\chi }^2$ consistency check against global-fit inputs to quantify agreement within present uncertainties.

arXiv comment14 pages, 2 figures

References in corpus (7)

• Tri-Bimaximal Mixing and the Neutrino Oscillation Data
• Neutrino Physics with JUNO
• 2020 Global reassessment of the neutrino oscillation picture
• NuFit-6.0: Updated global analysis of three-flavor neutrino oscillations
• Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing
• Sub-percent Precision Measurement of Neutrino Oscillation Parameters with JUNO
• Resolving the octant of theta23 with T2K and NOvA

Cited by in corpus (1)

• Predictions of the neutrino oscillations parameters