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Leptonic absolute mass scale and Majorana phases

Determine the absolute neutrino mass scale and the two Majorana phases within the minimal Weinberg-operator texture constructed from the J3(O_C) alignment that the paper employs for the neutrino sector.

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Background

The framework predicts Majorana neutrinos and provides leading-order expressions for PMNS angles and a maximal leptonic Dirac phase, but it does not fix the absolute neutrino mass scale or the two Majorana phases.

These quantities are essential for neutrinoless double beta decay predictions and cosmological tests, and the authors explicitly list them as an open issue to be addressed by completing the neutrino sector within their construction.

References

Open issues. (a) A UV origin of $\delta$, $\varepsilon$, and $\kappa_{23}$, ideally from the $U(1){\rm dem}$ sector of $E_6R$; (b) quantitative RG--running across sectors in the $E_6L\times E_6R$ setting; (c) leptonic absolute mass scale and Majorana phases; (d) a mechanism for $\theta{\rm QCD}\approx 0$.

— Fermion mass ratios from the exceptional Jordan algebra (2508.10131 - Singh, 13 Aug 2025) in Clarifications and limitations, Open issues paragraph