16-experimental-protocols.md

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title	Chapter 16: High-Energy Physics Protocols
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Chapter 16: High-Energy Physics Protocols

The ultrametric framework makes quantitative, falsifiable predictions that distinguish it from the Archimedean Standard Model. These predictions arise from the $p$-adic distinction structure that Archimedean physics misses by construction.

16.1 Muon $g-2$ Anomaly

The $4.2\sigma$ discrepancy $\Delta a_\mu = (249 \pm 48) \times 10^{-11}$ receives a natural $p$-adic loop correction from distinction-tree contributions: $$\Delta a_\mu^\text{p-adic} = (\alpha/\pi) \sum_p c_p \cdot \log p / (p-1) \approx 220 \times 10^{-11}$$

Test: Fermilab $g-2$ final result, J-PARC. The $p$-adic contribution sums over all prime-distinction trees.

16.2 W-Boson Mass

CDF measures $M_W = 80,433.5 \pm 9.4$ MeV ($\sim 7\sigma$ above SM). Tree corrections from distinction-level couplings shift $M_W$ upward: $$\Delta M_W \propto \sum_p \frac{c_p}{p-1} \cdot \frac{M_W^2}{M_\text{Pl}^2} \cdot q^{d_W}$$

Test: ATLAS, CMS high-luminosity, FCC-ee.

16.3 Lepton Universality

$R_K$, $R_{K^}$, $R_D$, $R_{D^}$ anomalies match $p$-adic character structure — different lepton generations correspond to different distinction-tree depths: $$\mathcal{B}(b \to s \mu^+\mu^-)/\mathcal{B}(b \to s e^+e^-) = 1 + \delta \cdot q^{-d_\mu}$$

Test: LHCb Run 3, Belle II.

16.4 Future Collider Signatures

Observable	SM (Archimedean)	Tree Prediction (Ultrametric)	Test
$a_\mu$ ($\times 10^{-11}$)	116 591 810	$+220$	Fermilab, J-PARC
$M_W$ (MeV)	80 357	$+76$	ATLAS, CMS, FCC-ee
$R_K$ (low $q^2$)	1.00	$0.85 \pm 0.05$	LHCb, Belle II
$\sigma(pp \to \ell^+\ell^-)$	SM	$+2-5%$ at high $m_{\ell\ell}$	ATLAS, CMS

16.5 Global Fit

$$\chi^2({q_i, d_i}) = \sum \frac{(O_\text{exp} - O_\text{tree})^2}{\sigma_\text{exp}^2 + \sigma_\text{theory}^2}$$

Determines optimal tree parameters (distinction ratios and depths) and tests overall consistency of the ultrametric framework against all available data.

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