eta-meter
Compare the analytic and directly evaluated response of supported SU(4) multiplets to their boundary sign η.
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 to understand why changing a boundary sign sometimes moves a result and sometimes leaves it unchanged. Difference mode removes the common part of two calculations, making an otherwise hidden dependence easier to see.
First steps
- Choose a multiplet or load the AHMN content.
- Compare the predicted sign response with the directly evaluated Hessian.
- Draw the atlas and select η-difference mode to isolate the sign-dependent part.
- Filter sign-sensitive and insensitive multiplets, then compare individual tiles.
Controls and inputs
| Control | Meaning | Try this |
|---|---|---|
| Multiplet and content choices | Choose the contribution or combined content being studied. | Compare one sensitive multiplet with one labelled insensitive. |
| Flip every η | Changes the selected boundary signs together while retaining the content. | Read the predicted response before applying the flip. |
| Potential / η-difference | Switches between the full landscape and the difference under sign reversal. | Use both views for an insensitive multiplet. |
| Atlas filters and two-tile comparison | Select the displayed subset and compare two contributions at matching conventions. | Keep the display mode unchanged while switching tiles. |
Reading the results
| Result | Meaning |
|---|---|
| Predicted versus evaluated response | Compares the closed-form calculation with the direct numerical calculation of the stated quantity. |
| Difference landscape | A zero difference indicates sign insensitivity in that calculation, even if the full potential is nonzero. |
| Finite catalogue check | Tests the implemented rule across the 119 supported representations. |
Insensitivity to η concerns the specified difference or contribution. It does not mean that a representation contributes nothing to the potential or has no physical effects. The analytic statement and the finite numerical checks have their stated scope.
Worked example
See what a zero difference means
- Choose a multiplet labelled insensitive to η.
- Inspect its full potential.
- Switch to η-difference mode and read the zero response.
- Choose a sensitive multiplet and compare the same two views.
What to expect: A vanishing difference and a vanishing potential are visibly different statements.
Scope and limitations
- The result concerns the specified SU(4) sign dependence and projection.
- Numerical comparisons retain their cutoff and precision assumptions.
- Sign insensitivity alone does not determine the full spectrum or phenomenological viability.
If something is unclear
An atlas tile becomes blank in difference mode.
Check whether it is classified as sign-insensitive; a zero difference can be the expected result.
Terms used here
Sources and attribution
Current instrument guide. Archived editions retain their own scope.
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