Chapter 16: High-Energy Physics Protocols
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.