>[!warning]
>This content has not been peer reviewed.
# Standard Model — Code documentation
## Purpose
`rst_standard_model.py` calibrates the RST fidelity function against running coupling constant data from the Particle Data Group (PDG 2024), testing the hypothesis that the transition sharpness $n$ equals the number of generators in each gauge group:
- U(1) → $n = 1$ (QED)
- SU(2) → $n = 3$ (Weak)
- SU(3) → $n = 8$ (QCD)
## Model
$\alpha(Q) = \alpha_0 + A \cdot \left[\frac{1}{\mu(Q/\Lambda,\, n)} - 1\right]$
For QED, the observable is $1/\alpha$ (which decreases with Q, maintaining structural consistency with the other sectors).
## Built-in data
- **QCD:** 11 $\alpha_s(Q)$ values from 1.78 GeV (tau mass) to 1 TeV (PDG world averages)
- **QED:** 5 $1/\alpha(Q)$ values from Thomson limit (0.000511 GeV) to Z pole (91.2 GeV)
- **Weak:** 5 $\sin^2\theta_W(Q)$ values from atomic parity violation (Q ≈ 0) to Z pole
## Modes
| Flag | Force | n | Parameters fitted | Benchmark |
|:---|:---|:---|:---|:---|
| `--qcd` | QCD (SU(3)) | 8 (fixed) | $\alpha_0$, A, $\Lambda$ | 1-loop pQCD |
| `--qed` | QED (U(1)) | 1 (fixed) | $C_0$, A, $\Lambda$ | 1-loop QED (e-only) |
| `--weak` | Weak (SU(2)) | 3 (fixed) | $s_0$, A, $\Lambda$ | — |
| `--discovery` | All | Free | $\alpha_0$, A, $\Lambda$, n | — |
Running without flags executes all modes.
## Dependencies
- Python 3.8+
- NumPy, SciPy, Matplotlib
- `rst_engine.core.mu_rst` (workspace-level shared module)
## Execution
```bash
cd "about systems"
python "expanded theory applied/further applications/Standard Model/rst_standard_model.py"
python "expanded theory applied/further applications/Standard Model/rst_standard_model.py" --qcd
python "expanded theory applied/further applications/Standard Model/rst_standard_model.py" --discovery
```
## Output
| File | Description |
|:---|:---|
| `standard_model_qcd.png` | QCD: RST vs 1-loop vs data |
| `standard_model_qed.png` | QED: RST vs 1-loop vs data (1/α) |
| `standard_model_weak.png` | Weak: RST vs data |
| `standard_model_discovery.png` | Discovery: free n for all three forces |
| `standard_model_qcd.csv` | QCD numerical output |
| `standard_model_qed.csv` | QED numerical output |
| `standard_model_weak.csv` | Weak numerical output |
## Links
- **Theory:** [[Standard Model (RST)]]
- **Results:** [[Standard Model Results]]