alpha_s_Z
alpha_s_Z supplies the measured value of the strong coupling at the Z mass for use in unification arguments. Researchers comparing coupling strengths across scales in the Recognition Science framework cite this constant when verifying the position of the GUT coupling. The definition consists of a direct numerical assignment drawn from experiment.
claimThe strong coupling constant $α_s$ evaluated at the $Z$ boson mass equals $0.118$.
background
The module derives running couplings from φ-ladder scaling, where different rungs correspond to different energy scales and J-cost optimization adjusts accordingly. Upstream results include the definition of a constant scalar field as a uniform background. This setting connects to the broader Recognition Science approach of obtaining physics from φ-forcing chains.
proof idea
The declaration is a direct definition that assigns the numerical value 0.118 without further reduction or lemma application.
why it matters in Recognition Science
It supplies the input for the theorem establishing that the GUT coupling lies between the strong and electromagnetic values. This anchors the RS account of asymptotic freedom for the strong force within the φ-scaling mechanism. The placement is consistent with the eight-tick octave and D=3 dimensions in the forcing chain.
scope and limits
- Does not compute the coupling from the J-cost functional.
- Does not specify the renormalization scale in RS units.
- Does not address the beta function or running with scale.
- Does not connect to the phi-ladder rung explicitly.
Lean usage
theorem alpha_s_Z_positive : alpha_s_Z > 0 := by unfold alpha_s_Z; norm_numformal statement (Lean)
45noncomputable def alpha_s_Z : ℝ := 0.118
proof body
Definition body.
46
47/-- The weak coupling (related to Fermi constant). -/