Quark confinement lab

Choose αₛ, string tension σ and separation r using exact numeric fields or sliders. The diagram opens immediately and valid changes update live. Switch potential/force in the toolbar. Comparison contains set B and its parameters; enabling it adds a dashed total curve and probe values. Reset restores the default live view. Only raw input text and comparison/diagram choices are retained, including unfinished inputs; results are recomputed and menu state is not saved. Valid older numeric settings migrate.

For r in fm and energy in GeV, V(r)=−k/r+σr, where k=(4/3)αₛ ℏc and ℏc≈0.197326980459 GeV fm. σ is in GeV/fm; αₛ is dimensionless. The arbitrary additive potential constant is fixed to zero. Omitting ℏc would give inconsistent units.

The radial force is F(r)=−dV/dr=−k/r²−σ in GeV/fm. Negative means attraction. Both contributions point inward; they do not cancel. At large r, the model force tends to −σ. The potential increases monotonically for positive parameters and has no minimum.

r×=√(k/σ) is where the two force magnitudes are equal. It is not an equilibrium or a bound-state radius. With the chosen additive constant, the two potential terms cancel there, so V(r×)=0; this is not a special measured energy. If either parameter is zero there is no positive finite crossover. Zero σ gives the Coulomb limit; zero αₛ gives a purely linear potential.

The sketch uses a fixed 0–5 fm ruler, so the endpoint position follows r without saturation. Its width and colors are schematic; it does not compute a quantum field, quark size, wavefunction or QCD color state.

This effective static-potential model is useful for understanding heavy quark–antiquark interactions. αₛ is fixed, not running. In full QCD, dynamical light quarks allow string breaking, so indefinite linear growth at large distances is not a complete physical prediction. No string breaking, particle creation, masses or spectra are simulated here.

NIST CODATA 2022 · Cornell potential — Soni et al. (2018).

Click inside the graph to select r (eight significant digits); the r field is the exact, keyboard-accessible alternative. Moving r updates markers, values and the fixed-scale sketch without rebuilding curves. Typed input is not rounded or quantized to slider steps. Plot axes use the current language’s number format.