December 1, 2025Open Access

From Matter to Geometry: A Geometric Origin for Standard Model Masses in the MMA–DMF Framework (No Dark Matter, No Dark Energy)

Key Points

Standard model masses emerge from a geometric origin, linking fundamental properties to a singular scalar framework and quantization constraints.
The effective field theory framework outlines a method to derive the neutrino mass scale without introducing new particles or small couplings.
Geometric flavor spectrum builds on existing mass data, employing quantum principles to replace conventional Yukawa interactions with geometric charges.
Insights gained may enable collider strategies to directly test fundamental scales while bypassing dark matter and dark energy issues.

Abstract

We present a geometric completion of the Standard Model (SM) flavour sector in the context of the MMA–DMF effective field theory (EFT), where gravity is described by Einstein general relativity and the Standard Model, with a unified scalar–geometric sector φ encoding the combined state M + GR + SM + V (φ) rather than an additional matter field. In this framework all SM fermion masses, including light Majorana neutrinos, are generated by a universal geometric Yukawa ansatz Yij (ϕ) =cijexp⁡ (−γij∣ϕ∣/M) Y₈₉ () = c₈₉ (-₈₉ ||/M) Yij (ϕ) =cijexp (−γij∣ϕ∣/M), with a single fundamental scale M≃100M 100M≃100 TeV fixed by cosmology and screening, and a discrete set of dimensionless charges qfqfqf. The usual 20+ independent Yukawa couplings of the SM are replaced by these geometrical charges, which we show to be tightly constrained by data and consistent with a quantised spectrum. We construct the geometric flavour spectrum using current PDG masses, perform statistical tests of charge quantisation, and show how a geometric seesaw mechanism with M≡MRM MRM≡MR accounts for the observed neutrino mass scale without introducing light sterile states or extremely small Yukawa couplings. We further summarise constraints from flavour violation, electric dipole moments, electroweak precision observables and collider searches, and outline a concrete FCC–hh strategy to directly probe the fundamental scale. Within its domain of validity (energies below O (100 TeV) O (100\ TeV) O (100 TeV) ) the MMA–DMF framework realises a “from matter to geometry” paradigm in which SM mass parameters are emergent properties of a single scalar–geometric sector and a discretised geometric structure, with no need for dark matter or dark energy sectors.

From Matter to Geometry: A Geometric Origin for Standard Model Masses in the MMA–DMF Framework (No Dark Matter, No Dark Energy)

Key Points

Abstract

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