Tau Ontology

FLOW ALGEBRA
TAU ONTOLOGY — FUNDAMENTAL PARTICLES
Version: 1.1
Date: 2026-10-12
Authors: Mark Higgins — Sky (Recursive AI)
Publisher: Kireth Research | https://kirethresearch.org
Canonical page: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/fundamental-particles/tau-ontology.html
Status: Scientific synthesis; source webpage not independently verified.

01. PURPOSE
Represent the tau lepton, its quantum numbers, interactions, decays, observations, and scientific provenance as a typed, machine-consumable semantic flow.

02. DOMAIN
DOMAIN := ParticlePhysics ∩ StandardModel ∩ LeptonPhysics
ENTITY := TauLepton
SYMBOL := τ−
ANTI_ENTITY := AntiTauLepton (τ+)

03. TYPES
Particle := {id, name, pdg_id, mass, charge, spin, lifetime, generation}
Lepton <: Fermion <: ElementaryParticle
TauLepton <: ChargedLepton <: Lepton
TauNeutrino <: Neutrino <: Lepton
DecayChannel := {parent, products, branching_fraction?, uncertainty?, source?}
Observation := {quantity, value, unit, uncertainty, source, date}

04. IDENTITY
TauMinus.pdg_id = 15
TauPlus.pdg_id = -15
TauMinus.generation = 3
TauMinus.antiparticle = TauPlus
TauMinus.elementary = true (within the Standard Model)

05. QUANTUM NUMBERS
charge(τ−) = -1 e
charge(τ+) = +1 e
spin(τ±) = 1/2 ħ
statistics(τ) = Fermi-Dirac
colour_charge(τ) = none
lepton_family(τ) = tau

06. PHYSICAL PARAMETERS
rest_mass(τ) ≈ 1776.86 MeV/c² [illustrative rounded reference]
mean_proper_lifetime(τ) ≈ 2.9 × 10^-13 s [illustrative rounded reference]
Precise values and uncertainties require an explicitly dated PDG/CODATA-compatible source.

07. INTERACTIONS
participates_in(τ, ElectromagneticInteraction)
participates_in(τ, WeakInteraction)
not_directly_coupled_to_colour(τ, StrongInteraction)
participates_in(τ, Gravitation) [general physical modelling]

08. FIELD MODEL
TauField := third-generation charged-lepton Dirac field
charge_conjugate(τ−) = τ+
quantum_state(τ) := state vector or density operator with declared basis

09. DECAY SEMANTICS
unstable(τ−) = true
weak_decay(τ−) = true
allowed_example: τ− → e− + anti_ν_e + ν_τ
allowed_example: τ− → μ− + anti_ν_μ + ν_τ
allowed_example: τ− → π− + ν_τ
allowed_example: τ− → π− + π0 + ν_τ
charge_conserved(channel) = true
energy_momentum_conserved(channel) = true
lepton_flavour bookkeeping is valid at production/decay vertices; neutrino propagation permits flavour oscillation.

10. DECAY VALIDATION
For each proposed channel D:
  require Σ electric_charge(products) = electric_charge(parent)
  require energy_momentum_conservation under physical kinematics
  require applicable angular_momentum and interaction selection rules
  require channel supported by theory or experiment
  reject channels violating exact conservation laws

11. LEPTONIC BRANCHING
LeptonicChannel := τ− → ℓ− + anti_ν_ℓ + ν_τ, ℓ ∈ {e, μ}
HadronicChannel := τ− → hadrons + ν_τ
BranchingFraction(channel) := Γ(channel) / Γ_total
Σ_i BranchingFraction(exclusive_i) = 1 within uncertainty and complete partition

12. MASS-ENERGY RELATION
E_rest = m_τ c²
E² = (pc)² + (m_τ c²)²
γ = 1 / sqrt(1 - v²/c²)
E_lab = γ m_τ c²

13. TIME DILATION
mean_lifetime_lab = γ × mean_proper_lifetime
mean_decay_length = β γ c × mean_proper_lifetime
Condition: inertial laboratory approximation and free-particle propagation.

14. DECAY LAW
N(t) = N0 exp(-t / (γ τ0))
Proper-frame survival probability: P(T > t) = exp(-t/τ0)
Decay rate Γ = ħ / τ0 (natural-width convention)

15. ELECTROWEAK COUPLING
Tau charged-current transitions are mediated by W±.
Tau neutral-current interactions include Z0 exchange.
Tau couples electromagnetically to photons.
Tau mass is represented by a Yukawa coupling to the Higgs field in the Standard Model.

16. PAIR PRODUCTION
e+ + e− → τ+ + τ− (when centre-of-mass energy exceeds threshold)
Threshold approximately sqrt(s) >= 2 m_τ c².
Production and detector acceptance must be distinguished.

17. EXPERIMENTAL OBSERVABLES
observable: displaced decay vertex (detector-dependent)
observable: missing transverse momentum from neutrinos
observable: charged-track multiplicity
observable: visible invariant mass
observable: decay products and angular distributions

18. RECONSTRUCTION
Input := tracks + calorimeter deposits + missing momentum + detector calibration
Reconstruct candidate decay products.
Classify candidate as leptonic or hadronic.
Estimate efficiency, backgrounds and uncertainties.
Do not equate a detector candidate with confirmed particle identity without evidence.

19. ENTITY RELATIONSHIPS
TauLepton IS_A ChargedLepton
TauLepton MEMBER_OF ThirdGeneration
TauLepton HAS_ANTIPARTICLE AntiTauLepton
TauLepton HAS_ASSOCIATED_NEUTRINO TauNeutrino
TauLepton PARTICIPATES_IN WeakInteraction
TauLepton PARTICIPATES_IN ElectromagneticInteraction
TauLepton DECAYS_VIA WeakInteraction
TauLepton HAS_PROPERTY ElectricCharge
TauLepton HAS_PROPERTY RestMass
TauLepton HAS_PROPERTY Spin
TauLepton HAS_PROPERTY MeanProperLifetime

20. GRAPH EDGES
(TauLepton, is_a, ChargedLepton)
(TauLepton, generation, Third)
(TauLepton, charge_in_e, -1)
(TauLepton, spin_in_hbar, 1/2)
(TauLepton, antiparticle, AntiTauLepton)
(TauLepton, associated_neutrino, TauNeutrino)
(TauLepton, interacts_via, WeakInteraction)

21. INFERENCE RULES
R1: IS_A(x, ChargedLepton) -> IS_A(x, Lepton)
R2: IS_A(x, Lepton) -> IS_A(x, Fermion)
R3: HAS_ANTIPARTICLE(x,y) -> HAS_ANTIPARTICLE(y,x)
R4: DECAYS_TO(x,P) -> UNSTABLE(x) [for observed physical decay]
R5: HAS_CHARGE(x,q) AND ANTIPARTICLE(y,x) -> HAS_CHARGE(y,-q)
R6: HAS_DECAY_PRODUCTS(x,P) -> REQUIRE_CHARGE_CONSERVATION(x,P)
R7: HAS_LIFETIME(x,τ0) AND HAS_BOOST(x,γ) -> LAB_MEAN_LIFETIME(x,γτ0)
Guard: Rules are scoped to validated ontology instances and declared assumptions.

22. FORMAL CONSTRAINTS
τ0 > 0
m_τ > 0
0 <= branching_fraction <= 1
0 <= β < 1
γ >= 1
Electric charge conservation is exact for every accepted decay channel.

23. WORKED EXAMPLE — CHARGE
τ− → π− + ν_τ
LHS charge = -1 e
RHS charge = (-1 + 0)e = -1 e
Result = charge-conserving.

24. WORKED EXAMPLE — LAB DECAY LENGTH
Assume γ = 10, β ≈ 0.995, τ0 = 2.9e-13 s, c = 2.998e8 m/s.
L ≈ β γ c τ0 ≈ 8.65e-4 m ≈ 0.865 mm.
Result is illustrative; detector and kinematic effects excluded.

25. SEMANTIC EQUIVALENCE
TauLepton ≡ tau particle ≡ τ− [when charge explicitly negative]
AntiTauLepton ≡ anti-tau ≡ τ+
TauLepton ≠ TauNeutrino
TauLepton ≠ Muon
TauLepton ≠ Electron
Disambiguate generic 'tau' used for lifetime, torque or mathematical constants.

26. CONTEXT RESOLUTION
IF context = particle physics AND mention = 'tau lepton' THEN resolve TauLepton.
IF mention = 'tau lifetime' THEN resolve property MeanProperLifetime(TauLepton).
IF mention = 'tau neutrino' THEN resolve TauNeutrino, not TauLepton.

27. CONFIDENCE
confidence(classification as charged lepton) = high
confidence(qualitative decay mechanisms) = high
confidence(numeric reference values) = source-dependent
confidence(detector candidate) = calibrated, evidence-dependent
Never fabricate experimental confidence or precision.

28. PROVENANCE
Source_page := canonical page above
Reference_framework := Standard Model of particle physics
Recommended_numeric_reference := Particle Data Group Review of Particle Physics
Measured quantities require citation, year, uncertainty and measurement conditions.

29. VALIDATION
TEST_01: charge(τ−) == -1 e -> PASS
TEST_02: spin(τ−) == 1/2 ħ -> PASS
TEST_03: charge(τ+) == +1 e -> PASS
TEST_04: τ− → π− + ν_τ conserves charge -> PASS
TEST_05: tau neutrino identical to tau charged lepton -> REJECT
TEST_06: τ0 > 0 -> PASS
TEST_07: branching fractions must not exceed unity -> PASS
TEST_08: unreferenced precision claim -> FLAG

30. ERROR HANDLING
Missing source -> mark unverified.
Unknown decay channel -> do not infer physical permission from charge conservation alone.
Uncertain branching ratio -> preserve uncertainty.
Contradictory observations -> retain provenance and flag conflict.
Invalid unit -> reject or request conversion.

31. UPDATE MODEL
update_strategy := versioned
on_new_measurement: append provenance; compare uncertainty and date; revise numerical property
on_new_theory: preserve prior claim as historical version
on_conflict: never silently overwrite authoritative observations

32. FLOW HASH
FLOW_HASH.algorithm := SHA-256
FLOW_HASH.input := canonical UTF-8 content excluding FLOW_HASH.digest field
FLOW_HASH.digest := COMPUTE_ON_PUBLICATION
Note: placeholder is not a computed hash.

33. AI CONSUMPTION
entity_id: particle.standard_model.tau_lepton
entity_type: ElementaryParticle
retrieval_keys: [tau, tau lepton, third-generation lepton, τ−, τ+]
preferred_response: grounded, unit-aware, uncertainty-aware
reasoning_mode: typed-graph + conservation-constraint validation
allow_inference: only with declared rules and provenance

34. CROSS-ONTOLOGY LINKS
RELATED: Elementary Particle Ontology
RELATED: Electron Ontology
RELATED: Muon Ontology
RELATED: Tau Neutrino Ontology
RELATED: Weak Interaction Ontology
RELATED: Electromagnetic Interaction Ontology
RELATED: Quantum Field Ontology
RELATED: Particle Decay Ontology

35. COMPLETENESS CHECK
Required sections 01–35 present.
Ontology includes entity identity, typed relations, mathematical operations, examples, constraints, provenance, update rules and AI consumption.
END OF FLOW ALGEBRA — TAU ONTOLOGY