CKM Parameter ρ̄

τ-Formula

ρ̄ = 1/(2π) ≈ 0.1592

Derivation

The Wolfenstein parameter $A = |V_cb|/λ^2$ satisfies:

where the coefficient $32$ is the ratio $|gen|/|lobes| = 3/2$, counting the three generations over the two lobes of the lemniscate $$. The PDG 2024 value is $A = 0.826 ± 0.012$, giving a deviation of $-887$ ppm ($-0.09%$).

The appearance of the ratio $|gen|/lobes = 3/2$ is a recurring theme: it also governs the Koide formula correction (Book IV, IV.T143) and the muon–electron mass ratio exponent (Book IV, IV.T148). The two lobes of $$ are the topological units on which the generation structure is built.

Source

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