Neutrino mass hierarchy from a geometric progression and a spectral hypothesis for the hyperbolic 3-manifold m003
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2026
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| _version_ | 1866901377587871744 |
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| author | Borisson Andrew |
| author_facet | Borisson Andrew |
| contents | <p> We propose a minimal hypothesis for the neutrino mass hierarchy: the three active neutrino masses follow a geometric progression m2 = km1, m3 = k^2m1. Using the experimentally measured values (∆m21)^2 and (∆m31)^2 from neutrino oscillations, we obtain k = 5.7347. From this we derive the absolute masses m1 = 0.001501 eV, m2 = 0.008608 eV, m3 = 0.04937 eV, and their sum mν = 0.0594 ± 0.002 eV, a sharp prediction testable by upcoming cosmological surveys such as DESI, Euclid and the Simons Observatory. We suggest that the factor k = 5.7347 may have a spectral origin, namely the ratio of the first two eigenvalues of the Dirac operator on the Gieseking manifold m003 with a suitable spin structure. Notably, the Koide relation 2/3 appears as (3−1)/(4−1), possibly related to the Z/4 symmetry of m003.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18903431 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Neutrino mass hierarchy from a geometric progression and a spectral hypothesis for the hyperbolic 3-manifold m003 Borisson Andrew Hyperbolic 3-manifold, Neutrino masses, Spectral geometry, m003, Dirac operator, Koide relation <p> We propose a minimal hypothesis for the neutrino mass hierarchy: the three active neutrino masses follow a geometric progression m2 = km1, m3 = k^2m1. Using the experimentally measured values (∆m21)^2 and (∆m31)^2 from neutrino oscillations, we obtain k = 5.7347. From this we derive the absolute masses m1 = 0.001501 eV, m2 = 0.008608 eV, m3 = 0.04937 eV, and their sum mν = 0.0594 ± 0.002 eV, a sharp prediction testable by upcoming cosmological surveys such as DESI, Euclid and the Simons Observatory. We suggest that the factor k = 5.7347 may have a spectral origin, namely the ratio of the first two eigenvalues of the Dirac operator on the Gieseking manifold m003 with a suitable spin structure. Notably, the Koide relation 2/3 appears as (3−1)/(4−1), possibly related to the Z/4 symmetry of m003.</p> |
| title | Neutrino mass hierarchy from a geometric progression and a spectral hypothesis for the hyperbolic 3-manifold m003 |
| topic | Hyperbolic 3-manifold, Neutrino masses, Spectral geometry, m003, Dirac operator, Koide relation |
| url | https://doi.org/10.5281/zenodo.18903431 |