TFPT scientific source excerpt
Original repository path: documents/archive--paper-latex--tfpt-theory-fullv27-final/sections/003-subsection-the-cubic-fixed-point-equation-cfe.tex
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000025 | \begin{tcolorbox}[colback=yellow!3, colframe=yellow!60!black,
000026 |     title={\textbf{Quantization and scheme declaration}}, fonttitle=\bfseries\small]
000027 | \textbf{Scheme:} dimensional regularization, background-field gauge, $\overline{\mathrm{MS}}$.
000028 | \textbf{Coefficient policy:} we postulate the fixed coefficients in
000029 | $U(\alpha)=\frac{A}{4}\alpha^4-\frac{2}{3}A\cthree^3\alpha^3-8A\bone\cthree^6 L\,\alpha+\ldots$
000030 | within the declared scheme.
000031 | \textbf{Status:} postulated input, audited for internal consistency across suite implementations;
000032 | a full background-field derivation is deferred.
000033 | \end{tcolorbox}
000034 | 
000035 | \begin{tcolorbox}[colback=yellow!5, colframe=yellow!60!black,
000036 |     title={\textbf{Status of the $\alpha^2$ term and renorm condition}}, fonttitle=\bfseries\small]
000037 | \textbf{EFT framing:} $U(\alpha)$ is an EFT ansatz.
000038 | \textbf{Toy one-loop finding:} a quadratic term in $\alpha$ appears generically in the toy one-loop determinant.
000039 | \textbf{Renorm policy:} $\alpha^2$ term fixed by renormalization condition; we fix a counterterm $\delta c_2=-c_2$ at a declared reference point,
000040 | so the stationarity polynomial has no residual $\alpha^2$ term in the chosen scheme.
000041 | \textbf{Precision constraint:} the robustness scan requires $|\epsilon_2|\lesssim 1.58\times 10^{-10}$ to stay within 1 ppm.
000042 | \textbf{Toy scope:} toy model demonstration only; the toy $\beta$-prefactor mismatch is flagged and is not a Standard Model one-loop derivation.
000043 | \textbf{Evidence:} \texttt{alpha2\_renorm\_condition\_audit}, \texttt{alpha2\_term\_robustness\_scan}.
000044 | \textbf{Policy statement:} the absence of $\alpha^2$ is a renormalization condition, not a Ward-identity theorem.
000045 | \end{tcolorbox}