Quark Confinement: Color Flux Tube

Separation

Quark–antiquark distance r 0.30 fm

QCD Parameters

String tension σ 0.90 GeV/fm

Coupling α_s 0.39

Pair-production threshold 0.60 GeV

Live Readouts

Confined — flux tube intact

Potential V(r)

0.00 GeV

String tension force

0.90 GeV/fm

Stored energy since start (ΔV)

0.00 GeV

How it works

Two color-charged quarks are joined by a gluon field that, unlike the electromagnetic field, does not spread out in space — it collapses into a narrow flux tube ("QCD string") because gluons themselves carry color charge and attract each other. The energy stored in that tube is described by the phenomenological Cornell potential:

V(r) = -(4/3)·(α_s·ħc)/r  +  σ·r
ħc ≈ 0.1973 GeV·fm
dV/dr = (4/3)·(α_s·ħc)/r²  +  σ   (restoring force / string tension)

At short range the first term dominates — a Coulomb-like attraction from one-gluon exchange. At long range the linear term σ·r dominates: pulling the quarks apart costs energy proportional to distance, exactly like stretching a string. That is color confinement — no free quark has ever been observed because it costs infinite energy to fully separate one.

Separation slider / Pull apart — increases r and stretches the flux tube; live readouts track V(r) and the tension force dV/dr.
σ, α_s — the two Cornell-potential parameters measured from lattice QCD and charmonium spectroscopy (real values ≈ 0.9 GeV/fm and ≈ 0.3–0.4).
Pair-production threshold — once the energy stored in the string since the start (ΔV) exceeds this value, it becomes energetically favorable for the vacuum to spontaneously create a new quark–antiquark pair rather than keep stretching. The tube snaps at its midpoint, the new pair fills the gap, and the system ends up as two color-neutral mesons flying apart — this is hadronization, the mechanism behind particle jets at colliders like the LHC.

Quark (color charge) Antiquark (anticolor) Gluon field flow

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