Calculator Inputs
The page is single-column overall, while the calculator fields use a responsive three-column, two-column, and one-column grid.
Formula used
Characteristic momentum: p ≈ k × ℏc / r
Kinetic corrections: Ti = √(p2 + mi2) - mi
Coulomb-like strong term: VC = - (4/3) × αs × (ℏc / r)
Linear confinement term: Vconf = σ × r
Total model energy: E = m1 + m2 + T1 + T2 + VC + Vconf + E0
Here, ℏc is taken as 0.1973269804 GeV·fm. The model combines a short-range attractive term with a long-range linear confinement term.
This gives an intuitive phenomenological estimate for bound quark systems. It does not replace full QCD, lattice calculations, or precision spectroscopy fits.
How to use this calculator
- Enter the quark separation radius in femtometers.
- Choose a strong coupling value for the Coulomb-like term.
- Enter the string tension that controls linear confinement growth.
- Provide effective masses for the two quarks in GeV.
- Adjust the uncertainty factor if you want a stronger or weaker momentum estimate.
- Use the energy offset to calibrate the model to a chosen state.
- Set the graph range to inspect how the model energy changes with radius.
- Press Calculate Energy to show results above the form, then download the CSV or PDF if needed.
Example data table
| Scenario | r (fm) | αs | σ (GeV/fm) | m1 (GeV) | m2 (GeV) | k | E0 (GeV) | Approx. total energy (GeV) |
|---|---|---|---|---|---|---|---|---|
| Light meson trial | 0.80 | 0.45 | 0.90 | 0.33 | 0.33 | 1.00 | 0.25 | 1.6460 |
| Strange pair trial | 0.70 | 0.40 | 0.90 | 0.50 | 0.50 | 1.00 | 0.25 | 1.8776 |
| Charmonium trial | 0.60 | 0.35 | 0.90 | 1.27 | 1.27 | 1.00 | 0.20 | 3.2103 |
| Bottomonium trial | 0.45 | 0.28 | 0.90 | 4.18 | 4.18 | 1.00 | 0.18 | 8.8272 |
FAQs
1) What does this calculator estimate?
It estimates an approximate quark-pair energy using a Cornell-style interaction, uncertainty-based momentum, and user-selected effective masses. It is best for intuition and comparative analysis.
2) Is this a full QCD calculation?
No. This is a phenomenological model, not a first-principles QCD or lattice-QCD solver. It simplifies confinement into useful analytic terms for fast exploration.
3) Why is there a Coulomb-like term?
At short distances, one-gluon exchange motivates an attractive term that behaves roughly like 1/r. It helps model near-origin behavior before linear confinement dominates.
4) Why can the energy curve first dip and then rise?
Short-range attraction can lower the energy at small or moderate radii, while the linear confinement term increases steadily with distance. Their competition can create a local minimum.
5) What does the uncertainty factor k change?
It scales the characteristic momentum estimate. Larger k increases kinetic corrections, which usually raises the total model energy at a fixed radius.
6) What string tension values are commonly explored?
Many simple models use values near 0.9 GeV/fm, though calibration choices vary. The best input depends on whether you are making illustrative or fitted comparisons.
7) Can this model heavy quarkonia like charmonium?
Yes. Heavy quarkonium systems are common test cases because effective-potential descriptions often work reasonably well for qualitative behavior and parameter studies.
8) Do the CSV and PDF downloads use current inputs?
Yes. They export the currently calculated result set shown on the page, including the active inputs and core output values.
Practical notes
This tool is designed for educational physics pages, quick comparisons, and parameter sensitivity checks. Because it is a single-file implementation, the CSV export is server-side and the PDF export is generated in the browser.