pith. machine review for the scientific record. sign in
theorem proved term proof

gut_above_ew

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

 221theorem gut_above_ew (gut : GUTUnification) :
 222    rs_anchor_scale < gut.μ_GUT → 0 < gut.μ_GUT :=

proof body

Term-mode proof.

 223  fun h => by unfold rs_anchor_scale at h; linarith
 224
 225/-! ## QCD Mass Running (Leading Order)
 226
 227The QCD mass anomalous dimension governs how quark masses change with
 228renormalization scale.  At one loop:
 229
 230    m(μ₂) = m(μ₁) × (α_s(μ₂)/α_s(μ₁))^(γ₀/(2b₀))
 231
 232where γ₀ = 8 is the universal one-loop anomalous dimension and b₀ depends
 233on the number of active flavors n_f.  Flavor thresholds (at m_c, m_b, m_t)
 234require matching the running across regions with different n_f.
 235
 236This infrastructure enables scheme-consistent quark residuals at a common
 237scale μ* = 182 GeV, removing the mixed-scheme artifacts that inflate
 238the sub-leading mass formula's eta parameter (Item 8). -/
 239
 240/-- One-loop QCD mass anomalous dimension: γ₀ = 8 (universal for all quarks). -/

depends on (29)

Lean names referenced from this declaration's body.