mass_evo_exp_nf6
plain-language theorem explainer
The mass evolution exponent for QCD with six flavors equals exactly 8/14 under the RS renormalization scheme. Researchers deriving quark mass running from the phi-ladder to match one-loop QCD formulas would cite this explicit value. The proof is a one-line term wrapper that unfolds the exponent definition together with the anomalous dimension and b0 coefficient, then normalizes the arithmetic.
Claim. The mass evolution exponent satisfies $8/14 = 8/14$ for $n_f=6$ flavors, where the exponent is given by the ratio of the mass anomalous dimension to twice the QCD beta-function coefficient.
background
The module derives renormalization group flow from the RS phi-ladder, with the beta function structured as the ladder derivative scaled by $1/ ln phi$. The definitions of b0_qcd and mass_anomalous_dim encode the one-loop SU(3) contributions and flavor dependence that enter the mass running power. Upstream lemmas supply the phi^k scale factor and power spectrum conventions that anchor the ladder to cosmology and large-scale structure.
proof idea
The proof is a one-line term-mode wrapper. It unfolds mass_evolution_exp, mass_anomalous_dim, and b0_qcd, then applies norm_num to reduce the equality to arithmetic.
why it matters
This supplies the concrete exponent required by the LO QCD running mass formula in the module. It supports the asymptotic freedom criterion for nf <=16 and the running coupling formula by fixing the nf=6 case relevant to the top sector. The result follows from the phi-ladder derivative of the coupling and connects to the Recognition Composition Law that forces the beta-function sign.
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