mass_evolution_exp
plain-language theorem explainer
This definition supplies the exponent γ₀/(2b₀) that governs the scale dependence of quark masses in one-loop QCD. Particle physicists working on renormalization-group evolution of masses cite it when evolving quark masses between different energy scales. The definition is a direct algebraic ratio of the universal mass anomalous dimension by twice the one-loop beta-function coefficient b₀(n_f).
Claim. The mass evolution exponent for $n_f$ active quark flavors is given by $8 / (2 b_0(n_f))$, where the one-loop mass anomalous dimension is the constant 8 and the one-loop QCD beta-function coefficient is $b_0(n_f) = 11 - (2 n_f)/3$.
background
In the Recognition Science treatment of renormalization group flow the one-loop QCD beta-function coefficient is defined as b₀ = 11 - 2n_f/3, which remains positive for n_f ≤ 16 and thereby enforces asymptotic freedom. The mass anomalous dimension is the universal constant γ₀ = 8 for all quarks. The mass evolution exponent is formed directly as their ratio divided by 2. The module sets the RS anchor scale μ* = 182.201 GeV as the stationarity point of the RG flow and derives the β-function sign from the φ-ladder derivative of the coupling.
proof idea
The definition is a one-line algebraic expression that divides the constant mass anomalous dimension by twice the value of b0_qcd applied to the number of flavors.
why it matters
This exponent is used to prove that mass ratios within a sector remain RG-invariant at leading order and to obtain the concrete numerical values for n_f = 3 to 6. It feeds the running-mass formula and the positivity theorem that holds whenever the asymptotic-freedom criterion is satisfied. In the RS framework it links the φ-ladder structure to the observable scale dependence of quark masses at the RS anchor scale.
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