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A geometrical approach to neutrino oscillation parameters
Seikh, Mohammad Ful Hossain
Seikh, Mohammad Ful Hossain
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Abstract
We propose a geometric hypothesis for neutrino mixing: twice the sum of the three mixing angles equals 180 degrees, 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 θ23 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 ∼10×), 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 χ2 consistency check against global-fit inputs to quantify agreement within present uncertainties.
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2025-10-02
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AIP Advances
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Hossain_AIP_Advances.pdf
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Mohammad Ful Hossain Seikh; A geometrical approach to neutrino oscillation parameters. AIP Advances 1 October 2025; 15 (10): 105204. https://doi.org/10.1063/5.0292233.