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Modelled[M] modelled package — not free public theorem; Doctrine v1.1.1 chips on /status.

Muon Decay & Lifetime

Lifetime match is a modelled Gamow package [M], not a free theorem. Route E n=1 on a T(1,1)-class seat. μ→eνν is two pairings.

Last updated: 19 August 2026

Reading this entry

The muon lifetime is a modelled Gamow package on the Route E seat n = 1, the same T(1,1) class as the electron. The decay μ → eνν is booked as two generation-matched pairings, and the rate formula returns τ_μ = 2.196981 μs beside the measured lifetime.

What this is used for

Use this page for the attempt frequency, the tunneling action, and the Schwinger phase-space factor in the muon rate. It keeps the lifetime as a modelled package and the two pairings (μ, ν_μ) and (e, ν̄_e) as the decay bookkeeping.

Walk through

The muon mass on the page is m_μ = 105.658 MeV, and Route E places it at n = 1 on a T(1,1)-class seat. The channel is μ⁻ → e⁻ + ν̄_e + ν_μ, booked as the two pairings (μ, ν_μ) and (e, ν̄_e). The rate combines the attempt frequency ν₀ = m_μ c² / h, the tunneling factor e^{−S_μ}, and the phase-space factor α_fs/(2π). The displayed line is Γ_μ = 1/τ_μ = ν₀ · e^{−S_μ} · (α_fs/(2π)), which returns τ_μ = 2.196981 μs. The steps list ν₀ = 2.5548×10²² s⁻¹, S_μ = 31.808307 with P_tunnel = 1.538×10⁻¹⁴, and Ω = α_fs/(2π) = 0.00116141, set beside the Fermi-theory figure 2.1969811 μs.

Integrity note (Doctrine v1.1.1): The muon lifetime match on this page is a modelled package [M], not a free theorem. The muon is Route E generation

on a

-class seat — not a second torus knot, and not

(that index is the tau). Lab pairing:

is two generation-matched pairings, not one lepton minting two residuals. Hold OPEN; α INPUT; Foot δ [E INPUT]; Foot K/L [E].

1. The Leptonic Weak Decay Mechanism

The muon is the second-generation excited lepton (). In standard physics, it decays via weak W-boson exchange with Fermi coupling constant .

In the CPT framework the muon is Route E generation on the same -class seat as the electron (not another knot). Lab bookkeeping treats as two pairings, and , not a single isometry that mints two residuals. A Gamow lifetime package [M] is a rate model, not that pairing map.

2. The Topological Relaxation Theorem

Combining the fundamental attempt frequency , the Gamow tunneling probability , and the Schwinger phase space factor :

Muon Lifetime Theorem

3. Comparison to Experimental CODATA Target

Parameter	Standard Fermi Theory	CPT Derived Theorem	Status
Muon Lifetime $\tau_\mu$	2.1969811 μs (G_F fit)	2.196981 μs	Modelled [M] (package)

STATUS: [M] MODELLED PACKAGE

The muon decay lifetime is a modelled Gamow package [M] on the Route E seat — not a free public theorem, and not a second torus knot.

Source Documents

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