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Quarks in QLF — colour, charge, flavour, and confinement

What the Quantum Logical Framework (QLF) can and cannot say about quarks, read off the nucleon knot of Atomic_Structure_QLF.md §7: a baryon is a 3-axis Borromean closure whose three internal qubits are the three colour directions, threaded by charge. This doc collects the proven core, the dynamical reading, the open frontier, and the predictions — with the standard three-tier scope (✓ proven / ⚠ structural reading / ✗ open).

A quark in QLF is not a standalone particle — only hadrons are closure observables (QLF_QuarkMass, quark_not_closed). In the knot picture a quark is a junction where two internal colour dimensions meet and the closure turns — interior to one closure, with no free end. That single fact is most of confinement.

1. Colour — the three axes (essentially complete ✓)

  • Colour = the three spatial axes. axOf (QLF_BaryonWinding): <>→x, ^v→y, /\→z; gauge +− carries no axis. R/G/B = (x,y,z).
  • SU(3) = the traceless 3-axis directional tensor (QLF_StrongAlgebra: trace_commutator_zero, gluon_commutator_nonzero); the eight gluons are its off-diagonal couplings — i.e. the connectors where the closure hops between colour axes.
  • The Borromean three-colour necessity (QLF_QuarkStructure, baryon_needs_all_three_axes): B ≠ 0 requires a twist on every colour axis; remove any one colour and B = 0. So a baryon needs all three quarks/axes — no one- or two-colour baryon. The minimal baryon >^/ carries exactly one twist per axis (minimal_baryon_one_per_axis): three quarks = three axes.

This is a genuine proof of the colour structure (three colours, SU(3), Borromean closure, singlets).

2. Confinement — the singlet-closure obstruction (proven ✓)

Confinement is proven, as the closure obstruction already established for charge, applied to colour (QLF_Confinement):

  • charged_not_closed — a state carrying a net annihilation-odd charge (electric, or the strong instance colour) is not a ZFA closure. A lone quark carries net colour ⟹ it cannot close ⟹ it is not a physical state.
  • singlet_closure — every ZFA closure has zero net charge/colour: only singlets close.
  • baryon_needs_all_three_axes — and the only nonzero-baryon closure is the three-axis Borromean triple. single_colour_not_baryon — a history on a single colour axis has B = 0: a lone quark's colour content is not a baryon. Together: physical hadrons are colour-neutral, and a baryon is exactly the three-colour lock — no lone or two-colour baryon.

The dynamical reading — confinement as the 3-body threshold (⚠ cited dynamics, QLF-native bridge). The closure ladder is the n-body integrability ladder:

internal dimensions n-body behaviour
1 (neutrino) 1-body trivially closes
2 (electron, positronium, muonium) 2-body, integrable always closes — leptons are free, no confinement
3 (baryon) 3-body, chaotic (Poincaré) closes only in the special Borromean lock

A generic 3-axis history is chaotic ⇒ non-terminating ⇒ pruned (full_zeno_prune; a terminating computation is exactly a ZFA closure, qlf_universality). So a lone or perturbed quark configuration is chaotic and never closes — you cannot pull a quark out. Confinement = the onset of three-body chaos; the Borromean triple is the integrable island (the prime-3 lock, QLF_PrimeResonance, "balanced and prime"). The flux tube / linear potential V(r) ∝ r is the structural reading (the closure cost grows with separation); its value and the asymptotic-freedom→confinement RG flow stay open (confinement_in_progress).

3. Charge — conservation, neutrality, quantisation

  • Proven ✓: electric charge = signed gauge-phase count (chargeWeight, QLF_BMinusL); conserved (signed_count_conserved); zero on every closure (wcount_zero_on_ZFA) — global neutrality; annihilation-odd; charged_not_closed (a bare charge needs its completer — the proton needs its electron, Weak_Force.md §4a).
  • Quantisation in thirds, from colour (✓ proven). The charge quantum is 1/n for n colours: charge_quantum_from_colours (QLF_QuarkStructure) — tracelessness n·q + L = 0 with an integer-charge remainder L forces q = −L/n. With QLF's n = 3 colours (= 3 spatial axes) and the SU(5) 5̄ (three d^c colour copies + a lepton doublet of net charge −1), down_quark_charge_third gives 3q − 1 = 0 ⟹ q = 1/3 — the down quark is −1/3. So the thirds are forced by the three colours (the SU(5) multiplet content, QLF_SU5, is the input; the thirds are the theorem). The absolute up/down value is then the §4 split.

4. Flavour — the settled bookkeeping vs the mass puzzle

Flavour is the label for which of the six quark fields an excitation is. As in the SM it splits cleanly into a settled gauge-quantum-number bookkeeping and the open mass/Yukawa puzzle — and QLF reproduces the first (some of it now proven) and reframes the second. diagrams/flavor_grid.svg shows the 3×2 grid with the CKM transitions.

Settled — the gauge bookkeeping (QLF reproduces; some proven ✓).

  • Charge: up-type +2/3, down-type −1/3 — proven thirds from the three colours (§3).
  • Weak isospin T₃ = ±1/2 within a generation = the weak SU(2) doublet (the 2-state "bit"; weak_isospin_su2 in BraKetRhoQuCalc; u,d doublet in QLF_QuarkMass). u↔d is one gauge-fold pair-flip — charge changes by 1 (uud=+1, udd=0, §7).
  • Three generations = the three axes (num_generations_eq_three, QLF_Generations).
  • CKM: flavour changes only via the W charged current; unitarity = closure, near-diagonal (Cabibbo), 3 angles + 1 CP phase, CP needing ≥3 generations (Kobayashi–Maskawa) — QLF_CKM, QLF_FlavorMixing. The angle values stay open. (GIM / no tree-level FCNC is consistent-with, not derived.)

The puzzle — mass / Yukawa. In the SM each quark's mass is a free Yukawa coupling to the Higgs, and the "flavor puzzle" is why three tiers spanning five orders of magnitude. This is the genuinely open part — and the one place QLF goes past "free input."

Folds demystify mass, so QLF can go further. In QLF mass is not a coupling but the gauge-fold delay m = 1/R — the constructing delay of the closure (mass_is_gauge_fold_delay, QLF_HiggsMechanism; m=1/R in QLF_QuantumBlackHole). So the SM's free Yukawa is a closure depth — structural, not dialled. The flavour mass puzzle becomes "why these fold depths," and QLF has partial answers:

  • The three generations = three fold-depth tiers, and the charged-lepton tier is Koide-constrained: Q = 2/3 from N=3 ∧ A²=2, predicting m_τ to 0.006% (koide_two_thirds, QLF_Koide) — a real relation among the three masses the SM has no handle on.
  • One scale. Every mass is the proton scale times a ratio, m = m_p · (ratio) (spectrum_one_scale, QLF_MassSpectrum) — the SM's ~13 mass parameters collapse to one absolute input, m_p. (diagrams/flavor_grid.svg gives the six quark masses in m_p units.) And that one ratio span is exponentially natural, not fine-tuned: dimensional transmutation gives ln R = 14π = 2π·b₀ (QLF_AlphaS) — the huge hierarchy is e^{14π} from a single integer, not a tuned coupling.
  • For quarks specifically, confinement intervenes: bare quark masses are not closure observables (quark_not_closed); the observable is the hadron-mass splitting m_n−m_p (the d↔u step), the well-posed target (the down is less charged yet heavier — mass ≠ charge, Weak_Force.md §5e).

Quark masses in proton-mass units (m_p = 938.27 MeV, the single QLF scale):

Quark Gen Charge Mass Mass / m_p
u (up) 1 +2/3 2.16 MeV 0.0023
d (down) 1 −1/3 4.67 MeV 0.0050
s (strange) 2 −1/3 93.4 MeV 0.100
c (charm) 2 +2/3 1.27 GeV 1.35
b (bottom) 3 −1/3 4.18 GeV 4.45
t (top) 3 +2/3 172.7 GeV 184

Values are PDG (MS-bar for u,d,s,c,b; pole mass for t). These are running, scale- and scheme-dependent numbers extracted from high-energy data (there is no free quark to weigh): a quark mass is defined at a reference scale and decreases toward higher energy (RG running), and it shifts with scheme — the top alone moves ~6% between pole (≈173 GeV) and MS-bar (≈163 GeV). Mass ratios are nearly RG-invariant, so the relative pattern is robust; but a bare-quark mass being tied to the extraction scale is exactly why it is not a QLF observable (quark_not_closed: the closure observable is the hadron, not the bare quark). The m_p column is the QLF reading: every mass = m_p × (a ratio) (spectrum_one_scale, QLF_MassSpectrum); and since m = 1/R, it is the inverse fold-depth ratio (lighter = deeper closure). The ~5-orders-of-magnitude span 0.0023 → 184 is the flavor puzzle — exponentially natural in the closure-depth picture, not six independently tuned couplings.

Charged leptons in proton-mass units (the clean Koide tier — the sharp example):

Lepton Gen Charge Mass Mass / m_p
e (electron) 1 −1 0.511 MeV 0.000545
μ (muon) 2 −1 105.66 MeV 0.1126
τ (tau) 3 −1 1776.86 MeV 1.894

Unlike quarks, charged-lepton masses are clean closure observables, and the three obey Koide exactly: Q = (Σm) / (Σ√m)² = 0.6667 = 2/3 (koide_two_thirds, QLF_Koide), which predicts m_τ to 0.006% from m_e, m_μ — the sharpest case of the depth-ratio reduction (the tier collapses to {m_p, δ}, with the Koide angle δ the one open input). Neutrinos are Majorana with sub-eV masses (open; QLF_NeutrinoMass).

Honest residual (still open ✗): the Koide angle δ (which fixes the individual masses within a tier), the absolute scale, the per-flavour twist signature, and the quark CKM/Yukawa angle values. "Flavour = the Yukawa structure" — and in QLF that structure is fold depth: demystified, partly derived (Koide tier relation + exponential hierarchy), not yet fully.

5. Predictions

Graded honestly — what is a genuine/falsifiable prediction vs a reproduction with a new reason.

  1. Dimensional confinement — the 3-body threshold (falsifiable). No confined sub-three-colour state (no lone-quark or diquark baryon); confinement turns on at exactly three axes = three spatial dimensions. Skeleton proven (baryon_needs_all_three_axes; single_colour_not_baryon and baryon_zero_of_missing: fewer than three colours ⟹ B=0); the chaos cause is cited. Falsifier: a stable two-colour bound state, or confinement in a genuinely 2D system.
  2. Exotic hadrons are molecular, not fundamental (falsifiable). The only nonzero-B Borromean closure is the three-axis triple, so tetra-/penta-quark states must be two colour-singlets loosely bound, not new fundamental closures — matching the emerging experimental "molecular" reading. Falsifier: a compact, deeply-bound exotic with no two-singlet substructure.
  3. No fourth generation — exactly three (proven prediction). Three axes ⟹ three generations (QLF_Generations, num_generations_eq_three) — the same "3" as colour.
  4. The charge quantum is 1/n for n colours (proven). charge_quantum_from_colours: tracelessness n·q + L = 0 ⟹ q = −L/n, so the charge quantum is exactly 1/(number of colours); QLF's three colours give the thirds (down_quark_charge_third: q = 1/3). The sharp counterfactual ("1/d in d spatial dimensions, since colours = spatial axes") is the one speculative step; the 1/3-from-3 itself is now a theorem.

The strongest new ones are 1 (proven skeleton + falsifiable) and 2 (current experimental relevance). 3 and the 1/3-from-three-colours of 4 are proven; the dimensional counterfactual in 4 is the soft part.

Honest scope

  • ✓ Proven: colour = 3 axes + SU(3); the Borromean three-colour necessity; confinement (only singlets close, charged_not_closed/singlet_closure; no lone-quark baryon, single_colour_not_baryon); charge conservation, neutrality, charged_not_closed, and quantisation in thirds from the three colours (charge_quantum_from_colours, down_quark_charge_third); three generations.
  • ⚠ Structural reading: the integrability/chaos cause of confinement (the bridge chaotic ⇒ non-terminating ⇒ pruned is QLF-native; 3-body chaos itself is cited Poincaré); the flux-tube linear potential; the quark-as-junction picture; the 1/d-in-d-dimensions counterfactual.
  • ✗ Open: the per-flavour (u/d) twist signature and quark masses; the string-tension value and the asymptotic-freedom→confinement RG flow.

References

Internal (QLF)

External

  • Gell-Mann, M. (1964). A schematic model of baryons and mesons. Phys. Lett. 8, 214 — quarks.
  • Greenberg, O. W. (1964). Spin and unitary-spin independence in a paraquark model. Phys. Rev. Lett. 13, 598 — colour.
  • Fritzsch, H., Gell-Mann, M., Leutwyler, H. (1973). Advantages of the color octet gluon picture. Phys. Lett. B 47, 365 — QCD / SU(3) colour, the eight gluons.
  • Gross, D. J., Wilczek, F. (1973); Politzer, H. D. (1973). Asymptotic freedom — the high-energy vanishing of the strong coupling (the deconfined limit).
  • Wilson, K. G. (1974). Confinement of quarks. Phys. Rev. D 10, 2445 — the Wilson loop and the linear (flux-tube) potential V(r) ∝ r.
  • Georgi, H., Glashow, S. L. (1974). Unity of all elementary-particle forces. Phys. Rev. Lett. 32, 438 — SU(5); the tracelessness charge-quantisation argument behind the thirds-from-three-colours (§3).
  • Skyrme, T. H. R. (1962). A unified field theory of mesons and baryons. Nucl. Phys. 31, 556 — baryon number as a topological winding (QLF's baryonNumber).
  • Poincaré, H. (1890). Sur le problème des trois corps et les équations de la dynamique. Acta Math. 13, 1 — non-integrability of the three-body problem (the chaos behind the 3-axis confinement threshold, §2).
  • Zhukov, M. V. et al. (1993). Bound state properties of Borromean halo nuclei. Phys. Rep. 231, 151 — Borromean three-body binding (bound only as a triple, no two-body sub-bound state).
  • Chen, H.-X., Chen, W., Liu, X., Zhu, S.-L. (2016). The hidden-charm pentaquark and tetraquark states. Phys. Rep. 639, 1 — the multiquark / molecular-vs-compact debate (Prediction 2).