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UV origin of δ, ε, and κ23 (ideally from U(1)dem in E6R)

Establish a ultraviolet-complete origin for the universal Jordan spread parameter δ (with δ^2 = 3/8 used to fix charged-fermion square-root mass ratios) and for the CKM-related parameters ε (the 1–2 up-leg tilt fixing |Vus|) and κ23 (the 2–3 cross-family normalization fixing |Vcb|) within the right-handed E6^R chain, ideally arising from the dynamics of the gauged U(1)dem subgroup.

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Background

Throughout the paper, the charged-fermion mass ratios are controlled by a single spread parameter δ derived from the exceptional Jordan algebra J3(O_C), together with two minimal CKM knobs: a 1–2 up-leg tilt ε and a 2–3 cross-family normalization κ23.

While these parameters successfully reproduce observed mass ratios and CKM entries at leading order, the text explicitly identifies the lack of a UV dynamical explanation for δ, ε, and κ23, suggesting they should arise from the right-handed sector’s U(1)dem dynamics within the E6R chain. This motivates a concrete UV mechanism tying these phenomenological inputs to underlying gauge dynamics.

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