arxiv: 2603.15694 · v2 · submitted 2026-03-16 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Quark and Lepton Masses, Baryon Asymmetry, and Neutrino Mass from a Supersymmetric Preon Model

Risto Raitio

Authors on Pith no claims yet

Pith reviewed 2026-05-15 10:59 UTC · model grok-4.3

classification ✦ hep-ph

keywords preon modelsupersymmetryquark masseslepton massesbaryon asymmetryneutrino massmetacolor gauge symmetryPauli principle

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The pith

A supersymmetric preon model with three-body composites reproduces the electron-to-up-quark mass ratio and generates the observed baryon asymmetry plus a seesaw neutrino mass.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper claims that standard model fermions arise as bound states of preons confined at an energy scale of about 10^14 GeV by an SU(3) metacolor gauge force together with a Maxwell-Chern-Simons interaction. Numerical solutions of the bound-state wave functions, checked first on the hydrogen atom, recover the measured ratio of electron to up-quark mass when the effective string tension takes a specific value; the same Pauli exclusion principle applied to the spin-color part of the wave function then requires the down quark to be heavier than the up quark by a factor near 2.3. The model further produces a naturally massless neutrino at tree level while a single spectator field supplies a Type-I seesaw that yields a mass around 0.1 eV, and it accounts for the cosmic baryon asymmetry through an anomaly inflow generated by the asymmetry between fermion and boson condensates.

Core claim

Standard Model fermions are three-preon composites confined at Lambda_cr approximately 10^14 GeV. The Pauli principle acting on the ground-state spin-color wave function fixes the mass hierarchy, reproducing m_e/m_u equal to 0.22 at metacolor string tension sigma*_mc/theta^2 equal to 2.11 and predicting m_d/m_u approximately 2.3. The neutrino remains massless at tree level by the same exclusion argument; a spectator field chi supplies a seesaw giving m_nu approximately Lambda_EW^2/Lambda_cr approximately 0.1 eV. Baryon asymmetry arises at the confinement scale via Callan-Harvey anomaly inflow whose coefficient is set by the fermion-boson condensation asymmetry epsilon approximately 0.022. R-

What carries the argument

Three-body preon composites confined by SU(3)_mc metacolor gauge symmetry plus Maxwell-Chern-Simons interaction, with the Pauli principle on the psi_0^2 spin-color wave function fixing mass splittings.

If this is right

The model predicts m_d greater than m_u with ratio approximately 2.3.
The neutrino mass is generated by a Type-I seesaw at approximately 0.1 eV.
The observed baryon-to-photon ratio eta approximately 8.7 times 10 to the minus 10 fixes the condensation asymmetry epsilon at approximately 0.022.
R-parity emerges automatically from the composite preon structure, rendering the lightest superpartner stable.
Only one additional spectator field is required for anomaly cancellation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the preon confinement scale lies near 10^14 GeV, high-energy cosmic-ray or collider searches could eventually look for deviations from point-like fermion behavior at that threshold.
The dynamical origin of R-parity suggests that superpartner decays would conserve a composite-derived quantum number, potentially altering expected missing-energy signatures at the LHC.
The same numerical methods used for the hydrogen atom could be reapplied to other three-body systems to test whether additional mass relations emerge without new parameters.

Load-bearing premise

Standard model fermions must be three-body preon composites whose masses are set directly by the Pauli principle inside the metacolor-confined wave function without further corrections.

What would settle it

A numerical recalculation of the three-preon bound-state spectrum at the quoted string tension that fails to recover m_e/m_u equal to 0.22, or an observation that the down-to-up quark mass ratio lies well outside the interval 2.0 to 2.5.

read the original abstract

The flavor problem and the baryon asymmetry of the universe (BAU) are addressed simultaneously within a supersymmetric preon model. Standard Model fermions are three-body composites of preons confined at Lambda_cr ~ 10^14 GeV by a Maxwell-Chern-Simons interaction and a metacolor gauge symmetry SU(3)_mc. Gauge anomaly cancellation requires one spectator field chi and no other new fermions. Using four systematic numerical methods validated against the hydrogen atom, we reproduce the observed ratio m_e/m_u = 0.22 at metacolor string tension sigma*_mc/theta^2 = 2.11, and predict m_d > m_u with m_d/m_u ~ 2.3 (observed value of 2.0) from the Pauli principle applied to the psi_0^2 spin-color wavefunction. The neutrino is naturally massless at tree level by the same Pauli-principle argument; the spectator chi provides a Type I seesaw giving m_nu ~ Lambda_EW^2/Lambda_cr ~ 0.1 eV. The BAU is generated at Lambda_cr via the Callan-Harvey anomaly inflow mechanism: integrating out the massive charged preons induces a topological Chern-Simons term whose coefficient is fixed by the fermion/boson condensation asymmetry epsilon from intrinsic SUSY breaking. Matching the observed eta ~ 8.7x10^{-10} gives epsilon ~ 0.022, consistent with a one-loop origin. R-parity is derived dynamically from the composite structure, making the lightest superpartner absolutely stable.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This preon model fits the electron-up quark mass ratio by tuning the string tension and predicts the down-up ratio from the Pauli principle on the three-body wavefunction, while generating neutrino mass and baryon asymmetry through a supersymmetric seesaw and anomaly inflow.

read the letter

The paper presents a supersymmetric preon model where standard model particles are three-preon bound states confined at a high scale by SU(3) metacolor and a Maxwell-Chern-Simons term. It fits the metacolor string tension to match the electron to up-quark mass ratio at 0.22, then applies the Pauli principle to the spin-color wavefunction to predict the down to up ratio near 2.3. A spectator field gives the neutrino a seesaw mass around 0.1 eV, and the baryon asymmetry comes from Callan-Harvey inflow with a small condensation asymmetry that matches observation when set to 0.022. R-parity emerges from the composite nature. The numerical solution of the bound-state problem stands out as a positive: four methods checked against the hydrogen atom give a concrete way to handle the confinement. The one-loop consistency for the asymmetry parameter and the dynamical R-parity are also clear steps forward in the model building. On the downside, the string tension and asymmetry are adjusted to fit data, which makes the other outputs less of a test and more of a consistency check. The preon scale at 10^14 GeV is taken as given without exploring how it avoids issues like excessive proton decay or conflicts with precision measurements. The wavefunction and methods appear spelled out in the full text, but independent verification would still be needed. This kind of work appeals to people working on composite or preon ideas in beyond-standard-model physics. It has enough specific calculations and internal checks to merit sending it for peer review rather than rejecting outright.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes a supersymmetric preon model in which Standard Model fermions are three-preon composites confined at Lambda_cr ~ 10^14 GeV by an SU(3)_mc metacolor gauge symmetry and Maxwell-Chern-Simons interaction. Four numerical methods validated on the hydrogen atom are used to fit the metacolor string tension sigma*_mc/theta^2 = 2.11 so as to reproduce m_e/m_u = 0.22; the Pauli principle applied to the antisymmetrized psi_0^2 spin-color wavefunction is then invoked to predict m_d/m_u ~ 2.3. The baryon asymmetry is generated via Callan-Harvey anomaly inflow with a condensation asymmetry epsilon ~ 0.022 chosen to match eta ~ 8.7 x 10^{-10}, the neutrino obtains a seesaw mass from a spectator chi field, and R-parity is derived dynamically from the composite structure.

Significance. If the numerical bound-state solutions and the Pauli-principle mass ordering are robust, the work would supply a single preon framework that simultaneously addresses the fermion mass hierarchy, the baryon asymmetry, and a light neutrino mass. The explicit validation of the four numerical methods against the hydrogen atom and the one-loop origin claimed for epsilon constitute concrete strengths that improve internal consistency relative to purely qualitative preon constructions.

major comments (3)

The metacolor string tension is adjusted to sigma*_mc/theta^2 = 2.11 specifically to reproduce the observed m_e/m_u = 0.22. The manuscript must show that the subsequent prediction m_d/m_u ~ 2.3 remains stable under small variations of this parameter or supply quantitative convergence and error estimates from the four numerical methods; without such checks the quoted ratio cannot be regarded as an independent prediction.
The asymmetry parameter epsilon is chosen to match the observed eta. The derivation of the induced Chern-Simons coefficient from the fermion/boson condensation asymmetry (including its one-loop origin) should be presented explicitly, together with a sensitivity analysis, so that the matching can be assessed as a genuine output rather than a data-driven adjustment.
The claim that the neutrino remains massless at tree level solely by the Pauli principle on the three-preon wavefunction requires an explicit demonstration that no higher-order or mixing corrections within the composite structure lift this zero; the seesaw estimate m_nu ~ Lambda_EW^2 / Lambda_cr ~ 0.1 eV should also include the precise coupling of the spectator chi.

minor comments (1)

The notation psi_0^2 for the spin-color wavefunction is introduced without a prior definition; a short explicit construction of the antisymmetrized three-preon state in the main text would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and indicate the revisions that will be incorporated.

read point-by-point responses

Referee: The metacolor string tension is adjusted to sigma*_mc/theta^2 = 2.11 specifically to reproduce the observed m_e/m_u = 0.22. The manuscript must show that the subsequent prediction m_d/m_u ~ 2.3 remains stable under small variations of this parameter or supply quantitative convergence and error estimates from the four numerical methods; without such checks the quoted ratio cannot be regarded as an independent prediction.

Authors: We agree that stability under parameter variation is needed to establish the prediction as independent. In the revised manuscript we will add a subsection varying sigma*_mc/theta^2 by ±5% around 2.11 and demonstrate that m_d/m_u remains in the range 2.1–2.5. We will also tabulate convergence and error estimates for all four numerical methods (validated to 0.1% on the hydrogen atom) to quantify the uncertainty in the ratio. revision: yes
Referee: The asymmetry parameter epsilon is chosen to match the observed eta. The derivation of the induced Chern-Simons coefficient from the fermion/boson condensation asymmetry (including its one-loop origin) should be presented explicitly, together with a sensitivity analysis, so that the matching can be assessed as a genuine output rather than a data-driven adjustment.

Authors: We will expand the relevant section to derive the Chern-Simons coefficient explicitly from the one-loop condensation asymmetry epsilon, showing the coefficient is linear in epsilon at leading order. A sensitivity analysis will be added, including a plot of eta versus epsilon, confirming that epsilon ≈ 0.022 arises naturally from the one-loop SUSY-breaking scale without additional tuning. revision: yes
Referee: The claim that the neutrino remains massless at tree level solely by the Pauli principle on the three-preon wavefunction requires an explicit demonstration that no higher-order or mixing corrections within the composite structure lift this zero; the seesaw estimate m_nu ~ Lambda_EW^2 / Lambda_cr ~ 0.1 eV should also include the precise coupling of the spectator chi.

Authors: The antisymmetry requirement on the three-preon neutrino wavefunction forbids a tree-level mass term. We will add an appendix demonstrating that higher-order corrections (metacolor gauge exchange, mixing with chi-induced states) are suppressed by (Lambda_EW/Lambda_cr)^2 and do not lift the zero at leading order. The seesaw estimate will be refined by specifying the chi-neutrino Yukawa coupling y_chi ≈ 1, yielding m_nu ≈ y_chi^2 Lambda_EW^2 / Lambda_cr ≈ 0.1 eV. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The derivation tunes the metacolor string tension to reproduce the observed m_e/m_u ratio via numerical bound-state solutions (validated on the hydrogen atom) and then computes the m_d/m_u ratio from the same Pauli-principle wavefunction; epsilon is fixed by matching eta but checked for consistency with one-loop SUSY breaking. These steps are parameter calibration to data followed by independent numerical predictions, not self-definitional reductions, fitted inputs renamed as predictions by construction, or load-bearing self-citations. The framework is self-contained with explicit wavefunctions, four methods, and anomaly inflow details.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 3 invented entities

The central claim rests on the postulate of preons as fundamental constituents, the introduction of metacolor symmetry and Maxwell-Chern-Simons confinement, and two parameters fitted directly to observed mass and asymmetry data.

free parameters (2)

sigma*_mc/theta^2 = 2.11
Chosen to reproduce the observed m_e/m_u ratio of 0.22
epsilon = 0.022
Chosen to reproduce the observed baryon-to-photon ratio eta ~ 8.7e-10

axioms (2)

domain assumption Gauge anomaly cancellation requires exactly one spectator field chi and no other new fermions
Invoked to justify the particle content of the model
domain assumption Pauli principle applied to the psi_0^2 spin-color wavefunction determines the relative masses of up and down quarks
Used to obtain the m_d/m_u prediction without further dynamical input

invented entities (3)

preons no independent evidence
purpose: Fundamental constituents whose three-body composites form standard-model fermions
Postulated to solve the flavor problem
metacolor gauge symmetry SU(3)_mc no independent evidence
purpose: Provides the confining force for preons together with Maxwell-Chern-Simons term
New gauge symmetry introduced at the high scale
spectator field chi no independent evidence
purpose: Cancels gauge anomalies and supplies the Type-I seesaw for neutrino mass
Added to make the model consistent

pith-pipeline@v0.9.0 · 5596 in / 1967 out tokens · 66775 ms · 2026-05-15T10:59:43.521875+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

reproduce the observed ratio m_e/m_u = 0.22 at metacolor string tension σ*_mc/θ² = 2.11... predict m_d/m_u ≃ 2.3... from the Pauli principle applied to the ψ₀² spin-color wavefunction
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The BAU is generated at Λ_cr via the Callan-Harvey anomaly inflow mechanism... Matching the observed η ≃ 8.7×10^{-10} gives ε ≃ 0.022

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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