Quark Confinement: Color Flux Tube & String Breaking

Pull the Pair Apart

Separation r 0.20 fm

QCD Parameters

String tension σ 0.90 GeV/fm

Coupling α_s 0.30

Flux-Tube Energy

ΔE = 0.00 GeVthreshold 0.66 GeV

Potential V(r)

0.00 GeV

Confining force

0.00 GeV/fm

String breaks

Regime

Coulomb-like

How it works

The quark–antiquark potential is well modelled by the Cornell potential, a short-range one-gluon-exchange term plus a linear confining term:

V(r) = -(4/3) · α_s·ħc / r  +  σ·r
F(r) = dV/dr = (4/3) · α_s·ħc / r²  +  σ

At short r the Coulomb-like term dominates (asymptotic freedom: quarks move almost freely inside a hadron). Past about 0.5 fm the linear term takes over — unlike a photon's field lines, gluon field lines self-attract (gluons carry color charge themselves) and get squeezed into a narrow flux tube of roughly constant cross-section. That gives a force that stays ~constant with distance instead of falling off, so pulling the pair apart costs an ever-growing, unbounded amount of energy.

Once the stored energy ΔE = V(r) − V(r₀) exceeds the pair-production threshold (≈2 × the ~0.33 GeV light-quark constituent mass), it becomes energetically cheaper for the vacuum to create a fresh quark–antiquark pair than to keep stretching the string. The tube snaps at a point along its length, and each half immediately re-pairs into a new color-singlet meson. This is why free quarks have never been observed — confinement always ends in hadronization, not isolation.

Separation slider / Auto-Pull — sets or animates the quark–antiquark distance r.
σ, α_s — adjust the confinement strength and the short-range coupling; both shift where the snap happens.
Energy bar — stored string energy vs. the pair-production threshold; hits 100% and the string breaks.

Quark (color charge) Antiquark (anti-color) Gluon flux tube

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