Physics Ledger · Prediction Particle Physics τ-Effective 1–5%

CKM Parameter η̄

CKM Parameter η̄: τ-value 0.345, observed 0.348, deviation -2285~ppm.

Prediction

τ-Formula
ιτ⁻¹/⁴ κD⁵/⁴/sqrt5
τ-Value
0.345
Observed
0.348
Deviation
-2285~ppm

τ-Formula

η̄ = ιτ⁻¹ᐟ⁴ · κ_D⁵ᐟ⁴ / √5 ≈ 0.345

Derivation

where $κ_D = 1 - ιτ$. The PDG 2024 value is $η = 0.349^+0.012_-0.011$, giving a deviation of $-2\,285$ ppm ($-0.23%$, $0.7σ$).

The exponents in (eq:ch61-etabar) are not numerological accidents. They have a topological reading (IV.D363/IV.T173):

-14 &= -12 · |lobes| = -12 × 2 (holonomy factor), +54 &= |gen|2 · |lobes|

  • 1|lobes| = 34 + 12 (coupling factor), -12 &= -1|lobes| = |gen|^-1/2|_|gen|=4 (normalization factor).

η = ιτ^-1/(2·lobes)_holonomy \;·\; κ_D^|gen|/(2·lobes)+1/lobes_coupling \;·\; |generators|^-1/lobes_normalization.

Source

This prediction is derived in the Physics Ledger (Chapter 61 — mixing-baryogenesis), Books IV–V of Panta Rhei.

Registry

Canonical derivation in Book IV.

Metadata

DomainParticle Physics
Precision Tier1–5%
Scopeτ-Effective
Registry IDIV.T167
Canonical BookBook IV