QCD String Tension & Quark Confinement

The Cornell potential V(r) = −α/r + κr models quark-antiquark interaction. The linear term κr arises from the color flux tube (QCD string), causing confinement at large distances. Energy density visualized as flux tube cross-section.

Cornell Potential

V(r) = −α/r + κr

α ≈ 0.3 (strong coupling)
κ ≈ 0.18 GeV² ≈ 0.9 GeV/fm
String breaks at ~1 fm
New q-q̄ pair created

Flux Tube

Color electric field E_z confined in tube of radius ~0.3 fm. Energy/length = κ = string tension. Analogous to superconductor vortex (dual Meissner effect).

Energetics

V(r) = ... GeV
Coulomb: ...
Linear: ...
Breaking threshold: ~1 GeV