Pith. sign in
def

wolfenstein_lambda

definition
show as:
module
IndisputableMonolith.StandardModel.CKMMatrix
domain
StandardModel
line
54 · github
papers citing
none yet

plain-language theorem explainer

wolfenstein_lambda supplies the lambda parameter in the Wolfenstein parametrization of the CKM matrix by setting it equal to the Cabibbo angle. Researchers modeling quark flavor mixing would cite it when writing the off-diagonal CKM elements in the standard four-parameter form. The definition is a one-line alias to the prior cabibboAngle result.

Claim. The Wolfenstein parameter $λ$ is defined by $λ = sin θ_C ≈ 0.227$, where $θ_C$ is the Cabibbo mixing angle between the first and second quark generations.

background

The module derives CKM matrix elements from φ-quantized mixing angles tied to the eight-tick phase structure. The CKM matrix is the 3×3 unitary matrix whose approximate magnitudes are given in the module documentation. The cabibboAngle definition supplies the numerical value 0.227 for sin θ_C; an upstream sibling in ThreeGenerations states that θ_C ≈ 13° emerges from φ-structure via arcsin(1/φ²).

proof idea

This is a one-line wrapper that aliases the cabibboAngle definition.

why it matters

The definition supplies λ for the downstream expressions of V_ud, V_us, V_ub, V_cd, V_cs, V_cb, V_td and V_ts. It translates the φ-derived Cabibbo angle into the Wolfenstein basis used in the paper proposition on CKM matrix from golden ratio geometry. It therefore sits inside the Recognition Science derivation of the CKM matrix from the eight-tick octave.

Switch to Lean above to see the machine-checked source, dependencies, and usage graph.