Conditional SU(3) Source Normalization and Two-Loop Strong-Sector Running in the Axis Model
Andrew Morton · Public preprint · Conditional QCD transport and realizability
Connects a supplied color-sector boundary coefficient to strong-coupling evolution and tests the limits of projected-response normalization.
Abstract
We formulate a conditional boundary-to-observable map for the Standard Model SU(3)_C coupling. The primary input is the positive coefficient κ_C of the complete, invariant color kinetic form at a declared boundary μ_B; conventional two-loop QCD supplies the subsequent transport. Action-Level normalization and ultraviolet matching specify the originating source and boundary requirements. A projector response alone does not fix this coefficient. The familiar expression κ_C = ω_C^(emb) a_C/τ₀ is retained only when the complete source operator admits the stated common factorization. The preserved public benchmark at μ_B = 10¹⁶ GeV gives an inverse-required coefficient κ_C^(req) ≃ 3.585 from the frozen reference αₛ(M_Z) = 0.1179. Under that additional factorization, τ₀ = 0.1776 and unit embedding give a_C^(req) ≃ 0.637. An exact positive-Hessian theorem realizes every response fraction in (0, 1); it supplies a response witness rather than a physical color source. The historical forward, inverse and closure outputs are retained without retuning. A separate computational derivative tests the complete-source interface with synthetic inputs. Physical source normalization and the realized ultraviolet certificate remain originating inputs.
Scope
The calculation uses standard QCD and a supplied boundary coefficient. Its preserved forward benchmark misses the reference value, while inverse and closure calculations use that reference as input. The realization theorem supplies a mathematical response model; physical color sources and ultraviolet matching remain open.
Paper and supporting files
The manuscript source, numerical benchmark outputs and a separate synthetic interface calculation are available on Zenodo.
Read the current paper and supporting files on Zenodo
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