TauLib · API Book IV

TauLib.BookIV.Particles.HadronsNuclei

TauLib.BookIV.Particles.HadronsNuclei

Hadron structure (baryons, mesons), quark confinement in hadrons, nucleon mass decomposition, nuclear binding from strong+EM balance, nuclear shell model, magic numbers, iron peak, and decay channels from sector admissibility.

Registry Cross-References

  • [IV.D200] Meson Classification — MesonClassification

  • [IV.D201] Glueball — GlueballDef

  • [IV.D202] Nuclear Force — NuclearForce

  • [IV.P128] Nucleon Mass Decomposition — nucleon_mass_decomposition

  • [IV.P129] Nuclear Force Saturation — nuclear_force_saturation

  • [IV.P130] Nuclear Shell Structure — nuclear_shell_structure

  • [IV.P131] Iron Peak from Competing Sectors — iron_peak

  • [IV.P132] Decay Channels from Sector Admissibility — decay_channels

  • [IV.R128] Eta-eta’ Splitting — eta_eta_prime (conjectural)

  • [IV.R129] Glueballs and the Mass Gap — glueballs_mass_gap

  • [IV.R130] Mass from Nothing — comment-only (not_applicable)

  • [IV.R131] Isospin Splitting from Polarity — isospin_splitting

  • [IV.R132] Proton Lighter but Ontologically Later — comment-only (not_applicable)

  • [IV.R133] Deuteron Binding in tau-language — deuteron_binding

  • [IV.R134] Spin-orbit from omega-sector — comment-only (not_applicable)

  • [IV.R135] Why He-4 is Tightly Bound — helium4_tightly_bound

  • [IV.R136] Nucleosynthesis Forward to Book V — nucleosynthesis_forward

  • [IV.R137] Alpha-decay as Mode Cluster Ejection — alpha_decay_mode

  • [IV.R138] Neutron Stability inside Nuclei — neutron_stability_nuclear

  • [IV.R139] Gamma-decay as Mode Transition — gamma_decay_mode

Mathematical Content

Hadrons are color-neutral composites: mesons (qq̄, B = 0) and baryons (qqq, B = 1). The nucleon mass is 99% vacuum + kinetic energy from confinement, only 1% from quark rest masses. Nuclear binding comes from residual C-sector interaction, with shell structure producing magic numbers (2, 8, 20, 28, 50, 82, 126). The iron peak (A ≈ 56) results from optimal C-sector binding vs B-sector Coulomb repulsion balance.

Ground Truth Sources

  • Chapter 48 of Book IV (2nd Edition)

Tau.BookIV.Particles.BaryonNumber

source inductive Tau.BookIV.Particles.BaryonNumber :Type

Hadron baryon number.

  • zero : BaryonNumber Meson: B = 0 (quark-antiquark).

  • one : BaryonNumber Baryon: B = 1 (three quarks).

Instances For

Tau.BookIV.Particles.instReprBaryonNumber.repr

source def Tau.BookIV.Particles.instReprBaryonNumber.repr :BaryonNumber → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.instReprBaryonNumber

source instance Tau.BookIV.Particles.instReprBaryonNumber :Repr BaryonNumber

Equations

  • Tau.BookIV.Particles.instReprBaryonNumber = { reprPrec := Tau.BookIV.Particles.instReprBaryonNumber.repr }

Tau.BookIV.Particles.instDecidableEqBaryonNumber

source instance Tau.BookIV.Particles.instDecidableEqBaryonNumber :DecidableEq BaryonNumber

Equations

  • Tau.BookIV.Particles.instDecidableEqBaryonNumber x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

Tau.BookIV.Particles.instBEqBaryonNumber

source instance Tau.BookIV.Particles.instBEqBaryonNumber :BEq BaryonNumber

Equations

  • Tau.BookIV.Particles.instBEqBaryonNumber = { beq := Tau.BookIV.Particles.instBEqBaryonNumber.beq }

Tau.BookIV.Particles.instBEqBaryonNumber.beq

source def Tau.BookIV.Particles.instBEqBaryonNumber.beq :BaryonNumber → BaryonNumber → Bool

Equations

  • Tau.BookIV.Particles.instBEqBaryonNumber.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx) Instances For

Tau.BookIV.Particles.MesonClassification

source structure Tau.BookIV.Particles.MesonClassification :Type

[IV.D200] A meson q_i q̄_j⟩ classified by:

  • Flavor content (quark flavors from {u,d,s,c,b,t})

  • Spin-parity J^PC (angular momentum + spin)

  • Generation class (lemniscate mode classes of constituents)

Pseudoscalar (J=0): anti-aligned spins. Vector (J=1): aligned spins.

  • name : String Name.

  • quark : String Quark content.

  • antiquark : String Antiquark content.

  • spin : ℕ Spin J.

  • mass_mev : ℕ Approximate mass (MeV).

Instances For

Tau.BookIV.Particles.instReprMesonClassification.repr

source def Tau.BookIV.Particles.instReprMesonClassification.repr :MesonClassification → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.instReprMesonClassification

source instance Tau.BookIV.Particles.instReprMesonClassification :Repr MesonClassification

Equations

  • Tau.BookIV.Particles.instReprMesonClassification = { reprPrec := Tau.BookIV.Particles.instReprMesonClassification.repr }

Tau.BookIV.Particles.pion_plus

source def Tau.BookIV.Particles.pion_plus :MesonClassification

Canonical mesons. Equations

  • Tau.BookIV.Particles.pion_plus = { name := “pi+”, quark := “u”, antiquark := “d_bar”, spin := 0, mass_mev := 140 } Instances For

Tau.BookIV.Particles.kaon_plus

source def Tau.BookIV.Particles.kaon_plus :MesonClassification

Equations

  • Tau.BookIV.Particles.kaon_plus = { name := “K+”, quark := “u”, antiquark := “s_bar”, spin := 0, mass_mev := 494 } Instances For

Tau.BookIV.Particles.rho_meson

source def Tau.BookIV.Particles.rho_meson :MesonClassification

Equations

  • Tau.BookIV.Particles.rho_meson = { name := “rho”, quark := “u”, antiquark := “d_bar”, spin := 1, mass_mev := 775 } Instances For

Tau.BookIV.Particles.EtaEtaPrime

source structure Tau.BookIV.Particles.EtaEtaPrime :Type

[IV.R128] The η-η’ mass splitting (~410 MeV) exceeds quark mass predictions alone: the resolution is the axial anomaly breaking U(1)_A symmetry via quantum effects. Conjectural scope.

  • splitting_mev : ℕ Splitting in MeV.

  • mechanism : String Mechanism.

  • scope : String Scope.

Instances For

Tau.BookIV.Particles.instReprEtaEtaPrime

source instance Tau.BookIV.Particles.instReprEtaEtaPrime :Repr EtaEtaPrime

Equations

  • Tau.BookIV.Particles.instReprEtaEtaPrime = { reprPrec := Tau.BookIV.Particles.instReprEtaEtaPrime.repr }

Tau.BookIV.Particles.instReprEtaEtaPrime.repr

source def Tau.BookIV.Particles.instReprEtaEtaPrime.repr :EtaEtaPrime → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.eta_eta_prime

source def Tau.BookIV.Particles.eta_eta_prime :EtaEtaPrime

Equations

  • Tau.BookIV.Particles.eta_eta_prime = { } Instances For

Tau.BookIV.Particles.GlueballDef

source structure Tau.BookIV.Particles.GlueballDef :Type

[IV.D201] A glueball is a bound state of the strong vacuum field Γ_s* with no quark content: a color-neutral excitation of the su(3) connection field above the vacuum minimum.

Predicted by lattice QCD at ~1.5-1.7 GeV for J^PC = 0^++.

  • quark_content : ℕ Quark content: none.

  • mass_low_mev : ℕ Predicted mass range low (MeV).

  • mass_high_mev : ℕ Predicted mass range high (MeV).

  • jpc : String Quantum numbers J^PC.

Instances For

Tau.BookIV.Particles.instReprGlueballDef

source instance Tau.BookIV.Particles.instReprGlueballDef :Repr GlueballDef

Equations

  • Tau.BookIV.Particles.instReprGlueballDef = { reprPrec := Tau.BookIV.Particles.instReprGlueballDef.repr }

Tau.BookIV.Particles.instReprGlueballDef.repr

source def Tau.BookIV.Particles.instReprGlueballDef.repr :GlueballDef → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.glueball_def

source def Tau.BookIV.Particles.glueball_def :GlueballDef

Equations

  • Tau.BookIV.Particles.glueball_def = { } Instances For

Tau.BookIV.Particles.glueball_no_quarks

source theorem Tau.BookIV.Particles.glueball_no_quarks :glueball_def.quark_content = 0

Tau.BookIV.Particles.glueballs_mass_gap

source def Tau.BookIV.Particles.glueballs_mass_gap :String

[IV.R129] Glueball existence is a direct consequence of the mass gap: confinement ensures every excitation above vacuum carries positive mass. m_gb ≈ 2π/σ_τ^(1/2) ≈ 1.5 GeV. Equations

  • Tau.BookIV.Particles.glueballs_mass_gap = “Glueball existence: structural consequence of mass gap (confinement)” Instances For

Tau.BookIV.Particles.NucleonMassDecomp

source structure Tau.BookIV.Particles.NucleonMassDecomp :Type

[IV.P128] m_N = E_vac + E_kin + Σm_qi

  • C-sector vacuum energy: ~400 MeV (42%)

  • Quark kinetic energy: ~500 MeV (53%)

  • Bare quark rest masses: ~12 MeV (1%)

  • Trace anomaly + sigma terms: ~27 MeV (3%)

Vacuum + kinetic ≈ 99% of nucleon mass. All energies in MeV.

  • e_vac_mev : ℕ Vacuum energy (MeV).

  • e_kin_mev : ℕ Kinetic energy (MeV).

  • e_quark_mev : ℕ Quark rest masses (MeV).

  • e_other_mev : ℕ Other (trace anomaly, sigma).

  • total_mev : ℕ Total nucleon mass (MeV, approximate).

  • nonquark_pct : ℕ Percentage from non-quark-mass sources.

Instances For

Tau.BookIV.Particles.instReprNucleonMassDecomp

source instance Tau.BookIV.Particles.instReprNucleonMassDecomp :Repr NucleonMassDecomp

Equations

  • Tau.BookIV.Particles.instReprNucleonMassDecomp = { reprPrec := Tau.BookIV.Particles.instReprNucleonMassDecomp.repr }

Tau.BookIV.Particles.instReprNucleonMassDecomp.repr

source def Tau.BookIV.Particles.instReprNucleonMassDecomp.repr :NucleonMassDecomp → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.nucleon_mass_decomposition

source def Tau.BookIV.Particles.nucleon_mass_decomposition :NucleonMassDecomp

Equations

  • Tau.BookIV.Particles.nucleon_mass_decomposition = { } Instances For

Tau.BookIV.Particles.nucleon_99pct_nonquark

source theorem Tau.BookIV.Particles.nucleon_99pct_nonquark :nucleon_mass_decomposition.nonquark_pct = 99

Tau.BookIV.Particles.nucleon_decomp_sums

source theorem Tau.BookIV.Particles.nucleon_decomp_sums :nucleon_mass_decomposition.e_vac_mev + nucleon_mass_decomposition.e_kin_mev + nucleon_mass_decomposition.e_quark_mev + nucleon_mass_decomposition.e_other_mev = nucleon_mass_decomposition.total_mev

Decomposition sums to approximately the nucleon mass.

Tau.BookIV.Particles.IsospinSplitting

source structure Tau.BookIV.Particles.IsospinSplitting :Type

[IV.R131] m_d > m_u has structural origin: the d-quark has η-winding n ≡ 1 mod 3 (χ₋-dominant), while u-quark has n ≡ 2 mod 3 (complement class). δ_A ≈ 1.293 MeV.

  • d_winding_mod3 : ℕ d-quark winding class mod 3.

  • u_winding_mod3 : ℕ u-quark winding class mod 3.

  • delta_A_keV : ℕ Mass splitting (keV).

  • d_heavier : Bool d heavier than u.

Instances For

Tau.BookIV.Particles.instReprIsospinSplitting.repr

source def Tau.BookIV.Particles.instReprIsospinSplitting.repr :IsospinSplitting → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.instReprIsospinSplitting

source instance Tau.BookIV.Particles.instReprIsospinSplitting :Repr IsospinSplitting

Equations

  • Tau.BookIV.Particles.instReprIsospinSplitting = { reprPrec := Tau.BookIV.Particles.instReprIsospinSplitting.repr }

Tau.BookIV.Particles.isospin_splitting

source def Tau.BookIV.Particles.isospin_splitting :IsospinSplitting

Equations

  • Tau.BookIV.Particles.isospin_splitting = { } Instances For

Tau.BookIV.Particles.NuclearForce

source structure Tau.BookIV.Particles.NuclearForce :Type

[IV.D202] The nuclear force is the residual C-sector interaction from partial overlap of nucleon color fields at ~1 fm. Mediated by virtual meson exchange, principally the pion (range ≈ ℏ/m_π c ≈ 1.4 fm).

  • range_fm_x10 : ℕ Range (fm ×10).

  • mediator : String Mediator.

  • mechanism : String Mechanism.

Instances For

Tau.BookIV.Particles.instReprNuclearForce

source instance Tau.BookIV.Particles.instReprNuclearForce :Repr NuclearForce

Equations

  • Tau.BookIV.Particles.instReprNuclearForce = { reprPrec := Tau.BookIV.Particles.instReprNuclearForce.repr }

Tau.BookIV.Particles.instReprNuclearForce.repr

source def Tau.BookIV.Particles.instReprNuclearForce.repr :NuclearForce → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.nuclear_force

source def Tau.BookIV.Particles.nuclear_force :NuclearForce

Equations

  • Tau.BookIV.Particles.nuclear_force = { } Instances For

Tau.BookIV.Particles.DeuteronBinding

source structure Tau.BookIV.Particles.DeuteronBinding :Type

[IV.R133] The deuteron is the minimal two-nucleon winding configuration on T². Binding energy B_d ≈ 2.224 MeV from η-holonomy field overlap.

  • nucleon_count : ℕ Number of nucleons.

  • binding_keV : ℕ Binding energy (keV).

  • minimal : Bool Minimal configuration.

Instances For

Tau.BookIV.Particles.instReprDeuteronBinding

source instance Tau.BookIV.Particles.instReprDeuteronBinding :Repr DeuteronBinding

Equations

  • Tau.BookIV.Particles.instReprDeuteronBinding = { reprPrec := Tau.BookIV.Particles.instReprDeuteronBinding.repr }

Tau.BookIV.Particles.instReprDeuteronBinding.repr

source def Tau.BookIV.Particles.instReprDeuteronBinding.repr :DeuteronBinding → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.deuteron_binding

source def Tau.BookIV.Particles.deuteron_binding :DeuteronBinding

Equations

  • Tau.BookIV.Particles.deuteron_binding = { } Instances For

Tau.BookIV.Particles.NuclearSaturation

source structure Tau.BookIV.Particles.NuclearSaturation :Type

[IV.P129] Each nucleon’s defect bundle has finite angular extent Δθ ≈ ι_τ on the η-circle, so only ~12 nearest neighbors interact. Binding energy per nucleon B/A plateaus near 8.8 MeV for large A.

  • max_neighbors : ℕ Max neighbors interacting.

  • ba_plateau_mev_x10 : ℕ B/A plateau (MeV ×10).

  • angular_extent : Bool Angular extent determines saturation.

Instances For

Tau.BookIV.Particles.instReprNuclearSaturation.repr

source def Tau.BookIV.Particles.instReprNuclearSaturation.repr :NuclearSaturation → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.instReprNuclearSaturation

source instance Tau.BookIV.Particles.instReprNuclearSaturation :Repr NuclearSaturation

Equations

  • Tau.BookIV.Particles.instReprNuclearSaturation = { reprPrec := Tau.BookIV.Particles.instReprNuclearSaturation.repr }

Tau.BookIV.Particles.nuclear_force_saturation

source def Tau.BookIV.Particles.nuclear_force_saturation :NuclearSaturation

Equations

  • Tau.BookIV.Particles.nuclear_force_saturation = { } Instances For

Tau.BookIV.Particles.NuclearShellStructure

source structure Tau.BookIV.Particles.NuclearShellStructure :Type

[IV.P130] T²-winding modes for nucleons organize into shells. Cumulative counts at shell closures produce the magic numbers: 2, 8, 20, 28, 50, 82, 126.

  • magic_numbers : List ℕ Magic numbers.

  • origin : String Origin: T²-winding shell closures.

Instances For

Tau.BookIV.Particles.instReprNuclearShellStructure.repr

source def Tau.BookIV.Particles.instReprNuclearShellStructure.repr :NuclearShellStructure → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.instReprNuclearShellStructure

source instance Tau.BookIV.Particles.instReprNuclearShellStructure :Repr NuclearShellStructure

Equations

  • Tau.BookIV.Particles.instReprNuclearShellStructure = { reprPrec := Tau.BookIV.Particles.instReprNuclearShellStructure.repr }

Tau.BookIV.Particles.nuclear_shell_structure

source def Tau.BookIV.Particles.nuclear_shell_structure :NuclearShellStructure

Equations

  • Tau.BookIV.Particles.nuclear_shell_structure = { } Instances For

Tau.BookIV.Particles.seven_magic_numbers

source theorem Tau.BookIV.Particles.seven_magic_numbers :nuclear_shell_structure.magic_numbers.length = 7

Tau.BookIV.Particles.Helium4Bound

source structure Tau.BookIV.Particles.Helium4Bound :Type

[IV.R135] He-4 (Z=N=2) is the first doubly magic nucleus. B/A ≈ 7.1 MeV, preferred alpha-decay product. Completely fills lowest winding mode (0,0) with all four slots.

  • z : ℕ Atomic number Z.

  • n : ℕ Neutron number N.

  • ba_mev_x10 : ℕ Binding per nucleon (MeV ×10).

  • doubly_magic : Bool Doubly magic.

  • slots_filled : ℕ Number of nucleon slots filled.

Instances For

Tau.BookIV.Particles.instReprHelium4Bound.repr

source def Tau.BookIV.Particles.instReprHelium4Bound.repr :Helium4Bound → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.instReprHelium4Bound

source instance Tau.BookIV.Particles.instReprHelium4Bound :Repr Helium4Bound

Equations

  • Tau.BookIV.Particles.instReprHelium4Bound = { reprPrec := Tau.BookIV.Particles.instReprHelium4Bound.repr }

Tau.BookIV.Particles.helium4_tightly_bound

source def Tau.BookIV.Particles.helium4_tightly_bound :Helium4Bound

Equations

  • Tau.BookIV.Particles.helium4_tightly_bound = { } Instances For

Tau.BookIV.Particles.helium4_doubly_magic

source theorem Tau.BookIV.Particles.helium4_doubly_magic :helium4_tightly_bound.doubly_magic = true

Tau.BookIV.Particles.IronPeak

source structure Tau.BookIV.Particles.IronPeak :Type

[IV.P131] The binding energy maximum at A ≈ 56 (iron peak) results from optimal balance between:

  • C-sector (strong) binding per nucleon (saturating)

  • B-sector (EM) repulsion per nucleon (growing as Z²/A^(1/3))

Crossover near iron-56 where Coulomb cost exceeds marginal binding.

  • peak_A : ℕ Peak mass number.

  • binding_sector : BookIII.Sectors.Sector Binding sector.

  • repulsion_sector : BookIII.Sectors.Sector Repulsion sector.

  • ba_peak_mev_x100 : ℕ B/A at peak (MeV ×100).

Instances For

Tau.BookIV.Particles.instReprIronPeak.repr

source def Tau.BookIV.Particles.instReprIronPeak.repr :IronPeak → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.instReprIronPeak

source instance Tau.BookIV.Particles.instReprIronPeak :Repr IronPeak

Equations

  • Tau.BookIV.Particles.instReprIronPeak = { reprPrec := Tau.BookIV.Particles.instReprIronPeak.repr }

Tau.BookIV.Particles.iron_peak

source def Tau.BookIV.Particles.iron_peak :IronPeak

Equations

  • Tau.BookIV.Particles.iron_peak = { } Instances For

Tau.BookIV.Particles.iron_at_56

source theorem Tau.BookIV.Particles.iron_at_56 :iron_peak.peak_A = 56

Tau.BookIV.Particles.nucleosynthesis_forward

source def Tau.BookIV.Particles.nucleosynthesis_forward :String

[IV.R136] Fusion releases energy below iron peak (A < 56), fission above it (A > 56). Astrophysical consequences deferred to Book V. Equations

  • Tau.BookIV.Particles.nucleosynthesis_forward = “Fusion (A<56) and fission (A>56) consequences deferred to Book V” Instances For

Tau.BookIV.Particles.alpha_decay_mode

source def Tau.BookIV.Particles.alpha_decay_mode :String

[IV.R137] Alpha-decay: ejection of a completely filled lowest-winding-mode cluster (4 nucleons) from the parent nucleus, tunneling through the Coulomb barrier. Equations

  • Tau.BookIV.Particles.alpha_decay_mode = “Alpha-decay: 4-nucleon cluster ejection, lowest winding mode, Coulomb tunneling” Instances For

Tau.BookIV.Particles.NeutronStabilityNuclear

source structure Tau.BookIV.Particles.NeutronStabilityNuclear :Type

[IV.R138] Free neutrons decay in ~10 min, but bound neutrons are stable because nuclear binding makes Q_β < 0 (energetically forbidden). This is a readout-level phenomenon; the ontic neutron is unchanged.

  • free_lifetime_min : ℕ Free lifetime (minutes, approx).

  • stable_in_nuclei : Bool Stable in nuclei.

  • mechanism : String Mechanism: Q_β < 0.

Instances For

Tau.BookIV.Particles.instReprNeutronStabilityNuclear.repr

source def Tau.BookIV.Particles.instReprNeutronStabilityNuclear.repr :NeutronStabilityNuclear → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.instReprNeutronStabilityNuclear

source instance Tau.BookIV.Particles.instReprNeutronStabilityNuclear :Repr NeutronStabilityNuclear

Equations

  • Tau.BookIV.Particles.instReprNeutronStabilityNuclear = { reprPrec := Tau.BookIV.Particles.instReprNeutronStabilityNuclear.repr }

Tau.BookIV.Particles.neutron_stability_nuclear

source def Tau.BookIV.Particles.neutron_stability_nuclear :NeutronStabilityNuclear

Equations

  • Tau.BookIV.Particles.neutron_stability_nuclear = { } Instances For

Tau.BookIV.Particles.gamma_decay_mode

source def Tau.BookIV.Particles.gamma_decay_mode :String

[IV.R139] Gamma-decay is the same mechanism as atomic spectral lines: a T²-winding mode transition with energy carried by a B-sector photon. Only difference: scale (MeV nuclear vs eV atomic). Equations

  • Tau.BookIV.Particles.gamma_decay_mode = “Gamma-decay: T^2 mode transition at MeV scale (same mechanism as atomic lines)” Instances For

Tau.BookIV.Particles.DecayChannels

source structure Tau.BookIV.Particles.DecayChannels :Type

[IV.P132] Every radioactive decay satisfies sector admissibility:

  • Color neutrality (η-holonomy trivial mod 3)

  • Baryon number conserved

  • Electric charge conserved (γ-holonomy)

  • Energy-momentum conserved

Each decay type corresponds to a specific sector-transition pattern.

  • conservation_laws : ℕ Number of conservation laws.

  • types : List String Decay types.

  • all_admissible : Bool All satisfy sector admissibility.

Instances For

Tau.BookIV.Particles.instReprDecayChannels.repr

source def Tau.BookIV.Particles.instReprDecayChannels.repr :DecayChannels → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.Particles.instReprDecayChannels

source instance Tau.BookIV.Particles.instReprDecayChannels :Repr DecayChannels

Equations

  • Tau.BookIV.Particles.instReprDecayChannels = { reprPrec := Tau.BookIV.Particles.instReprDecayChannels.repr }

Tau.BookIV.Particles.decay_channels

source def Tau.BookIV.Particles.decay_channels :DecayChannels

Equations

  • Tau.BookIV.Particles.decay_channels = { } Instances For

Tau.BookIV.Particles.three_decay_types

source theorem Tau.BookIV.Particles.three_decay_types :decay_channels.types.length = 3

Tau.BookIV.Particles.four_conservation_laws

source theorem Tau.BookIV.Particles.four_conservation_laws :decay_channels.conservation_laws = 4