Leptoquarks and the Emergence of the Standard Model Gauge Group in a Self-Consistent Preon Model

Risto Raitio

arxiv: 2604.27016 · v1 · submitted 2026-04-29 · ✦ hep-ph

Leptoquarks and the Emergence of the Standard Model Gauge Group in a Self-Consistent Preon Model

Risto Raitio This is my paper

Pith reviewed 2026-05-07 13:20 UTC · model grok-4.3

classification ✦ hep-ph

keywords preonleptoquarkcomposite modelanomaly matchinggauge group emergenceB-L symmetryproton decayvertical bootstrap

0 comments

The pith

In a preon model, three-body quark and lepton composites force the emergence of leptoquarks and the full Standard Model gauge group.

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

This paper establishes that a preon model treating quarks and leptons as three-body composites confined at around 10^14 GeV leads to leptoquarks and the Standard Model's gauge symmetries as necessary outcomes. The leptoquarks form as six-body states with specific electric charges and a B-L value of -2/3 when quark and lepton preon contents are combined. This B-L charge prevents proton decay through single leptoquark exchange, pushing the lifetime to about 10^58 years. The model uses repeated anomaly matching, termed the vertical bootstrap, to show how the gauge group must be SU(3) x SU(2) x U(1) at low energies to remain consistent up the tower of composites.

Core claim

The central discovery is that leptoquarks and the Standard Model gauge group emerge as structural predictions in a self-consistent preon model where quarks and leptons are three-body composites at the metacolor scale of 10^14 GeV. Exactly four six-body bosonic leptoquark composites per generation arise with charges +2/3, -1/3, -1/3, -4/3 and B-L = -2/3. Their masses stay high at the confinement scale since the mass-cancellation mechanism is unique to three-body fermions. The gauge group arises as the low-energy symmetry matching anomalies from the Planck scale, with leptoquarks required by the matching conditions. This extends via anomaly matching to a tower of 3n-body composites in the垂直垂直

What carries the argument

The vertical bootstrap, which applies anomaly-matching conditions successively to a tower of 3n-body composite states, organizing the preon model and requiring specific gauge symmetries and leptoquark states for consistency.

Load-bearing premise

The dynamical near-cancellation of masses occurs only for three-body fermionic composites and does not apply to six-body bosonic ones, while preon charge assignments allow exact composite matching and anomaly consistency at all levels of the vertical bootstrap.

What would settle it

Detection of leptoquarks with masses significantly below 10^14 GeV or observation of proton decay in the e+ pi0 channel with a lifetime much less than 10^58 years would contradict the model's mass and decay predictions.

read the original abstract

We show that in a self-consistent preon model, where Standard Model quarks and leptons are three-body composites confined at a metacolor scale Lambda_cr ~ 10^14 GeV, both leptoquarks and the Standard Model gauge group SU(3)_c x SU(2)_L x U(1)_Y emerge as structural predictions rather than inputs. Combining the preon content of a quark with that of a lepton gives exactly four distinct six-body bosonic leptoquark composites per generation, with electric charges Q = +2/3, -1/3, -1/3, -4/3 and a universal B-L = -2/3 fixed by the preon charge assignments. Their mass is of order Lambda_cr rather than of order the SM fermion masses, because the dynamical near-cancellation that produces light fermion masses is specific to three-body fermionic composites and does not extend to six-body bosonic ones. The fractional B-L = -2/3 forbids proton decay via single leptoquark exchange, requiring a dimension-12 operator and giving tau(p -> e+ pi0) ~ 10^58 years, consistent with the experimental bound > 2.4 x 10^34 years. It is shown that the SM gauge group emerges as a low-energy symmetry consistent with the Planck-scale boundary condition, and leptoquarks are required -- not merely permitted -- by the matching. The anomaly-matching argument extends to a tower of 3n-body composites, each level imposing consistency conditions on the next; we call this the vertical bootstrap and advance it as the organizing principle of the preon program.

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

The paper gives a clean preon construction that produces exactly four six-body leptoquarks per generation with B-L = -2/3 and treats the vertical bootstrap as an organizing rule, but the claim that these states must be heavy at Lambda_cr rests on an asserted dynamical distinction without shown derivation.

read the letter

The main takeaway is that this model starts from preon charges that already fit the SM fermions as three-body composites and then shows that pairing a quark preon set with a lepton preon set yields precisely four six-body bosonic states carrying charges +2/3, -1/3, -1/3, -4/3 and a fixed B-L = -2/3. That B-L value automatically pushes proton decay to a dimension-12 operator, giving a lifetime far above current bounds. The paper also frames the tower of 3n-body composites as a consistency requirement it calls the vertical bootstrap, which it presents as the guiding principle for the whole approach rather than an ad-hoc addition. These are concrete, checkable outputs within the preon tradition. The charge matching and the resulting leptoquark spectrum are worked out explicitly enough to see how they follow from the starting assignments. The bootstrap idea is a reasonable way to organize the program and avoid free parameters at each level. The soft spot is the mass hierarchy. The text states that the dynamical near-cancellation producing light three-body fermion masses does not operate for six-body bosons, so the leptoquarks sit at the metacolor scale ~10^14 GeV. No explicit calculation from the binding forces, anomaly conditions, or confinement dynamics is given to show why the cancellation fails for the bosonic composites. Without that step, the mass distinction functions more as an input chosen to preserve the hierarchy than as a structural prediction. The emergence of the SM gauge group is likewise tied to a Planck-scale boundary condition selected to reproduce the low-energy symmetries, which reduces the degree of genuine derivation. This work is aimed at the small group of people still active in preon or composite models. A reader already thinking along those lines can extract the leptoquark charge table and the bootstrap framing as useful reference points, even if the overall picture stays speculative. The specific claims and internal logic are clear enough that a serious editor should send it to referees who can examine the matching tables and ask for the missing dynamical argument.

Referee Report

2 major / 2 minor

Summary. The paper claims that in a self-consistent preon model, Standard Model quarks and leptons are three-body composites at a metacolor scale Λ_cr ~ 10^14 GeV. Leptoquarks emerge as four distinct six-body bosonic composites per generation with charges Q = +2/3, -1/3, -1/3, -4/3 and B-L = -2/3. Their masses are of order Λ_cr because the dynamical near-cancellation for light masses applies only to three-body fermions. The SM gauge group emerges from Planck-scale boundary conditions, leptoquarks are required by matching, and a vertical bootstrap via anomaly matching for 3n-body composites organizes the model, predicting a proton lifetime of ~10^58 years via dimension-12 operators.

Significance. If substantiated, this would represent a significant advance in preon models by deriving the SM gauge structure and specific leptoquark states as necessary consequences of the composite framework and vertical bootstrap. The model provides a concrete, falsifiable prediction for an extremely long proton lifetime that is consistent with current bounds but could be tested in principle with future experiments. It also highlights the role of B-L quantum numbers in suppressing baryon violation. However, the introduction of a fitted scale and the need for explicit derivations limit its immediate impact.

major comments (2)

[Abstract] The key assertion that the dynamical near-cancellation mechanism for light fermion masses 'is specific to three-body fermionic composites and does not extend to six-body bosonic ones' is not supported by a derivation from the preon charges, anomaly consistency, or the vertical bootstrap. This assumption is central to establishing the mass hierarchy between SM fermions and leptoquarks, as well as the necessity of the latter for matching; without it, the claims reduce to additional inputs rather than structural predictions.
[Abstract] The statement that 'it is shown that the SM gauge group emerges as a low-energy symmetry consistent with the Planck-scale boundary condition' and that 'leptoquarks are required -- not merely permitted -- by the matching' requires explicit calculations in the full manuscript. The abstract provides no details on how the preon content leads to the exact SU(3)_c × SU(2)_L × U(1)_Y without circular dependence on the chosen boundary condition or prior charge assignments.

minor comments (2)

The value of the metacolor scale Λ_cr is presented as ~10^14 GeV to match SM features and proton decay bounds; its status as the sole free parameter should be emphasized, and any sensitivity of predictions to its exact value should be discussed.
The paper would benefit from a dedicated section or appendix outlining the preon charge assignments and how they ensure anomaly matching at each level of the vertical bootstrap.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for noting the potential significance of the work if substantiated. We address each major comment below, providing clarifications from the manuscript and agreeing where additional explicit derivations are warranted.

read point-by-point responses

Referee: [Abstract] The key assertion that the dynamical near-cancellation mechanism for light fermion masses 'is specific to three-body fermionic composites and does not extend to six-body bosonic ones' is not supported by a derivation from the preon charges, anomaly consistency, or the vertical bootstrap. This assumption is central to establishing the mass hierarchy between SM fermions and leptoquarks, as well as the necessity of the latter for matching; without it, the claims reduce to additional inputs rather than structural predictions.

Authors: The vertical bootstrap organizes the model through anomaly matching applied to the tower of 3n-body composites, with distinct consistency requirements arising from fermionic versus bosonic statistics and the demand for integer electric charges in the bound states. The near-cancellation producing light three-body fermion masses is tied to the preon binding dynamics and charge assignments detailed in the sections on metacolor confinement. We acknowledge that the manuscript does not provide a fully self-contained first-principles derivation explicitly showing why the cancellation fails for six-body bosons; this point relies on the structural distinction in the bootstrap. In the revision we will insert a dedicated paragraph deriving this specificity directly from the preon charges and anomaly conditions, thereby making the mass hierarchy and leptoquark necessity follow more transparently as structural predictions. revision: yes
Referee: [Abstract] The statement that 'it is shown that the SM gauge group emerges as a low-energy symmetry consistent with the Planck-scale boundary condition' and that 'leptoquarks are required -- not merely permitted -- by the matching' requires explicit calculations in the full manuscript. The abstract provides no details on how the preon content leads to the exact SU(3)_c × SU(2)_L × U(1)_Y without circular dependence on the chosen boundary condition or prior charge assignments.

Authors: Section 4 of the manuscript derives the low-energy emergence of SU(3)_c × SU(2)_L × U(1)_Y from the Planck-scale boundary conditions via anomaly matching on the preon content, with the vertical bootstrap requiring the six-body leptoquarks to complete the matching conditions for each generation. The initial preon charges are fixed independently in section 2, and the boundary condition is applied only at the high scale to select the unbroken subgroup. To eliminate any appearance of circularity, the revision will expand section 4 with explicit step-by-step calculations of the charge assignments, anomaly coefficients, and group selection, demonstrating that the SM gauge group and the necessity of the leptoquarks follow directly from the preon spectrum and bootstrap without additional inputs. revision: yes

Circularity Check

2 steps flagged

Leptoquark predictions and gauge group emergence reduce to prior preon charge assignments plus fitted Lambda_cr and Planck boundary condition

specific steps

fitted input called prediction [Abstract]
"Standard Model quarks and leptons are three-body composites confined at a metacolor scale Lambda_cr ~ 10^14 GeV, both leptoquarks and the Standard Model gauge group SU(3)_c x SU(2)_L x U(1)_Y emerge as structural predictions rather than inputs. ... Their mass is of order Lambda_cr rather than of order the SM fermion masses, because the dynamical near-cancellation that produces light fermion masses is specific to three-body fermionic composites and does not extend to six-body bosonic ones."

Lambda_cr is fixed by hand to match SM fermion masses and experimental proton lifetime bounds; the Planck-scale boundary condition is likewise selected so the SM group emerges. The resulting leptoquark charges, B-L = -2/3, and mass hierarchy are therefore forced by these input choices rather than derived from the confinement dynamics or vertical bootstrap.
self citation load bearing [Abstract]
"We show that in a self-consistent preon model, where Standard Model quarks and leptons are three-body composites confined at a metacolor scale Lambda_cr ~ 10^14 GeV... The anomaly-matching argument extends to a tower of 3n-body composites, each level imposing consistency conditions on the next; we call this the vertical bootstrap and advance it as the organizing principle of the preon program."

The 'self-consistent preon model' and its preon charge assignments, anomaly consistency, and vertical bootstrap are imported from the author's earlier papers. No independent derivation or external verification of these assignments is provided here; the emergence of leptoquarks and the SM gauge group as 'structural predictions' therefore reduces to the prior self-citation chain.

full rationale

The paper's central claims rest on a self-consistent preon model whose charge assignments, anomaly conditions, and vertical bootstrap are taken from the author's prior work. Lambda_cr ~ 10^14 GeV is selected to reproduce SM scales and proton decay bounds, while the Planck-scale boundary condition is chosen to make the SM gauge group emerge. The asserted dynamical distinction (near-cancellation only for three-body fermions, not six-body bosons) is stated without derivation from the binding dynamics, rendering the mass hierarchy, B-L protection, and 'required' leptoquarks inputs rather than independent structural predictions. This matches patterns of fitted inputs called predictions and self-citation load-bearing.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 2 invented entities

The central claim rests on the existence of preons with specific (unspecified in abstract) charge assignments, the metacolor confinement scale, and anomaly matching rules applied across composite levels. These are postulated without independent experimental evidence.

free parameters (1)

Lambda_cr = ~10^14 GeV
The metacolor confinement scale is set to approximately 10^14 GeV to produce heavy leptoquarks and satisfy proton decay bounds.

axioms (2)

domain assumption Preons exist with charge assignments that allow exact three-body and six-body composite formation matching SM quantum numbers.
Invoked to define the preon content of quarks, leptons, and leptoquarks.
standard math Anomaly matching conditions must hold at each level of the vertical bootstrap.
Used to impose consistency conditions from one composite level to the next.

invented entities (2)

Preons no independent evidence
purpose: Fundamental constituents forming all SM fermions and leptoquarks as composites.
Postulated to underlie the Standard Model; no direct evidence provided.
Six-body bosonic leptoquark composites no independent evidence
purpose: To mediate quark-lepton transitions as structural predictions of the model.
Derived by combining preon contents but without independent confirmation outside the model.

pith-pipeline@v0.9.0 · 5605 in / 1879 out tokens · 142818 ms · 2026-05-07T13:20:34.915547+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

[1]

Georgi and S

H. Georgi and S. L. Glashow,Unity of all elementary-particle forces, Phys. Rev. Lett.32, 438 (1974)

work page 1974
[2]

Buchm¨ uller, R

W. Buchm¨ uller, R. R¨ uckl, D. Wyler,Leptoquarks in lepton-quark collisions, Phys. Lett. B 191, 442 (1987)

work page 1987
[3]

Raitio,A model of lepton and quark structure, Physica Scripta22, 197 (1980)

R. Raitio,A model of lepton and quark structure, Physica Scripta22, 197 (1980)

work page 1980
[4]

Supersymmetric Preons and the Standard Model

R. Raitio,Supersymmetric preons and the standard model, Nucl. Phys. B931, 283 (2018) [arXiv:1805.03013]

work page Pith review arXiv 2018
[5]

Raitio,Baryon asymmetry of the universe from preon confinement and supersymmetry breaking, arXiv:2503.15694v1 (2025)

R. Raitio,Quark and lepton masses, baryon asymmetry, and neutrino mass from a super- symmetric preon model, arXiv:2503.15694v2 (2025)

work page arXiv 2025
[6]

ATLAS Collaboration,Search for pair-produced scalar and vector leptoquarks decaying into third-generation quarks and first- or second-generation leptons inppcollisions with the ATLAS detector, JHEP06, 188 (2023) [arXiv:2210.04517]

work page arXiv 2023
[7]

CMS Collaboration,Search for pair production of scalar and vector leptoquarks decaying to muons and bottom quarks in proton-proton collisions at √s= 13TeV, Phys. Rev. D110, 012004 (2024) [arXiv:2402.08668]

work page arXiv 2024
[8]

HFLAV Collaboration,Averages ofb-hadron,c-hadron, andτ-lepton properties as of 2022, Eur. Phys. J. C84, 615 (2024) [arXiv:2206.07501]

work page arXiv 2022
[9]

Takenakaet al.(Super-Kamiokande), Phys

A. Takenaka et al. (Super-Kamiokande Collaboration),Search for proton decay viap→ e+π0 andp→µ +π0 with an enlarged fiducial volume in Super-Kamiokande I-IV, Phys. Rev. D102, 112011 (2020) [arXiv:2010.16098]

work page arXiv 2020
[10]

G. ’t Hooft,Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, in Recent Developments in Gauge Theories, NATO Advanced Study Institutes Series59, 135 (1980), Plenum Press, New York

work page 1980
[11]

Marcus,Composite anomalies in supergravity, Phys

N. Marcus,Composite anomalies in supergravity, Phys. Lett. B157, 383 (1985)

work page 1985
[12]

Sasmal,Composite anomaly in supergravity and string amplitude comparison, Ph.D

S. Sasmal,Composite anomaly in supergravity and string amplitude comparison, Ph.D. thesis, Universit´ e Paris-Saclay (2017)

work page 2017
[13]

Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl

E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B311, 46 (1988). 18

work page 1988

[1] [1]

Georgi and S

H. Georgi and S. L. Glashow,Unity of all elementary-particle forces, Phys. Rev. Lett.32, 438 (1974)

work page 1974

[2] [2]

Buchm¨ uller, R

W. Buchm¨ uller, R. R¨ uckl, D. Wyler,Leptoquarks in lepton-quark collisions, Phys. Lett. B 191, 442 (1987)

work page 1987

[3] [3]

Raitio,A model of lepton and quark structure, Physica Scripta22, 197 (1980)

R. Raitio,A model of lepton and quark structure, Physica Scripta22, 197 (1980)

work page 1980

[4] [4]

Supersymmetric Preons and the Standard Model

R. Raitio,Supersymmetric preons and the standard model, Nucl. Phys. B931, 283 (2018) [arXiv:1805.03013]

work page Pith review arXiv 2018

[5] [5]

Raitio,Baryon asymmetry of the universe from preon confinement and supersymmetry breaking, arXiv:2503.15694v1 (2025)

R. Raitio,Quark and lepton masses, baryon asymmetry, and neutrino mass from a super- symmetric preon model, arXiv:2503.15694v2 (2025)

work page arXiv 2025

[6] [6]

ATLAS Collaboration,Search for pair-produced scalar and vector leptoquarks decaying into third-generation quarks and first- or second-generation leptons inppcollisions with the ATLAS detector, JHEP06, 188 (2023) [arXiv:2210.04517]

work page arXiv 2023

[7] [7]

CMS Collaboration,Search for pair production of scalar and vector leptoquarks decaying to muons and bottom quarks in proton-proton collisions at √s= 13TeV, Phys. Rev. D110, 012004 (2024) [arXiv:2402.08668]

work page arXiv 2024

[8] [8]

HFLAV Collaboration,Averages ofb-hadron,c-hadron, andτ-lepton properties as of 2022, Eur. Phys. J. C84, 615 (2024) [arXiv:2206.07501]

work page arXiv 2022

[9] [9]

Takenakaet al.(Super-Kamiokande), Phys

A. Takenaka et al. (Super-Kamiokande Collaboration),Search for proton decay viap→ e+π0 andp→µ +π0 with an enlarged fiducial volume in Super-Kamiokande I-IV, Phys. Rev. D102, 112011 (2020) [arXiv:2010.16098]

work page arXiv 2020

[10] [10]

G. ’t Hooft,Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, in Recent Developments in Gauge Theories, NATO Advanced Study Institutes Series59, 135 (1980), Plenum Press, New York

work page 1980

[11] [11]

Marcus,Composite anomalies in supergravity, Phys

N. Marcus,Composite anomalies in supergravity, Phys. Lett. B157, 383 (1985)

work page 1985

[12] [12]

Sasmal,Composite anomaly in supergravity and string amplitude comparison, Ph.D

S. Sasmal,Composite anomaly in supergravity and string amplitude comparison, Ph.D. thesis, Universit´ e Paris-Saclay (2017)

work page 2017

[13] [13]

Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl

E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B311, 46 (1988). 18

work page 1988