Hierarchy
Calculate a compactification scale and Higgs mass for a chosen SU(7) bulk content, and compare the moment approximation with the implemented full Fourier potential.
Control names are kept as they appear in the application. Start with a reference, change one input at a time, and retain the assumptions with your result.
What this tool is for
Use this tool to see how changing bulk matter changes the scale associated with an extra dimension. A smaller nonzero Wilson phase can correspond to a larger compactification scale. The tool lets you compare an inexpensive small-angle approximation with calculations of the same implemented potential. Begin with the named examples; only interpret a changed model after checking which assumptions you changed.
First steps
- Start with a Table 1 row so the selected matter content has a named reference.
- Read the gauge-seed choice before comparing any numbers. Changing it changes the potential.
- Compare the approximate and full-potential minima, masses and scales. Then change one multiplicity and repeat.
- Open the approximation and uncertainty diagnostics; use their own coupling and W-mass conventions when reading their results.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Bulk multiplicities | Counts of the eight supported representation/parity types. These are discrete choices of matter content, not measured probabilities. | Load one published row, then change one count by one. |
| Gauge seed | Selects the printed gauge weights or the candidate split. The seed changes the Fourier coefficients and the arithmetic conditions. | Repeat the same content under both choices and retain the seed in any comparison. |
| Published rows and pre-registered sixth row | Load explicitly recorded contents. A row is a reproducible input, not a promise that its printed phase will be reproduced. | Read the printed value and the laboratory value side by side. |
| Robustness: g₄, model span and winding cutoff | Separate a coupling scenario from numerical convergence. Increasing the number of Fourier terms tests truncation; a coupling span is an assumed model range. | Change the cutoff while holding the physical inputs fixed, then vary the coupling separately. |
Reading the results
| Result | Meaning |
|---|---|
| Wilson phase, Higgs mass and compactification scale | Read which potential and convention produced each value. Compare the approximate and full-Fourier columns at matching inputs, with GeV and TeV kept distinct. |
| Distance to a ceiling | A conditional bound for the stated approximation. It is not automatically an attainable content or a bound for every full-potential vacuum. |
| Uncertainty budget and experimental references | Numerical bounds, recorded W-mass input uncertainty, coupling scenarios and unquantified physical effects have separate meanings. The ATLAS and CMS Higgs-mass entries are separate comparisons. |
A ceiling here belongs to its stated moment approximation, seed, coupling and mass window. A numerical result, an interval certificate for a fixed potential and agreement with a published physical model are different claims. The published-phase discrepancy remains open.
Worked example
Compare an approximation with its full potential
- Load a Table 1 row and leave the seed unchanged.
- Record the approximate phase, Higgs mass and scale.
- Open the moment/full-Fourier comparison and read the differences and available bounds.
- Increase the Fourier cutoff in the diagnostic and compare again without changing g₄.
What to expect: You can distinguish a truncation effect from an approximation error. Agreement between these calculations does not resolve the physical gauge-determinant question.
Formulas and conventions
1/R₅ = 2 m_W / α
The scale conversion in this SU(7) convention, for a nonzero phase. The factor belongs to this convention; do not transfer it unchanged to a different model's phase variable.
Scope and limitations
- The physical choice of gauge determinant still requires reconciliation with the literature. The eight reconstructed fermion tables do not settle that separate issue.
- The small-angle moment approximation has a domain of validity. Check its error against the full potential before using a derived mass or ceiling.
- Higher-loop and other physical theory uncertainties are not quantified by a Fourier-tail bound. The displayed uncertainty components are not a complete statistical confidence interval.
If something is unclear
The scale is absent or an output is declined.
Check for a symmetric or flat potential and for a zero phase. Read the stated reason rather than replacing a missing value with zero.
Two panels give different masses.
Compare their seed, potential, coupling, W-mass anchor and approximation labels before comparing their digits.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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