Asymptotic Freedom: The Running Strong Coupling α_s(Q)

Probe Energy Scale

Q 10.0 GeV

Active Quark Flavors

n_f (light flavors felt at scale Q) 5

Live Readouts

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α_s(Q)

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Resolved distance r

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β₀ = 11 − 2n_f/3

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Cornell V(r)

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How it works

The strong force does the opposite of gravity or electromagnetism: it gets weaker at short distance / high energy, and gets stronger without bound as quarks are pulled apart. This is asymptotic freedom (Gross, Politzer, Wilczek — Nobel 2004), and it is computed from the QCD one-loop beta function:

β0 = 11 − (2/3) n_f
α_s(Q) = 4π / [ β0 · ln(Q² / Λ²) ]     (Λ_QCD ≈ 0.21 GeV)

As the probe energy Q rises, ln(Q²/Λ²) grows, so α_s(Q) falls — quarks inside a fast-moving proton barely feel each other, exactly as seen in deep-inelastic electron-proton scattering at SLAC and HERA. As Q drops toward Λ_QCD, the formula diverges (a "Landau pole") — perturbation theory breaks down and the true non-perturbative physics is confinement: quarks are bound by a flux tube whose potential energy grows linearly with separation,

V(r) = − (4/3) α_s ħc / r  +  σ·r      (σ ≈ 0.9 GeV/fm, string tension)

The resolved distance shown is r = ħc/Q with ħc = 0.1973 GeV·fm — the de Broglie wavelength of the virtual photon or gluon doing the probing. High Q ⇒ short r ⇒ you are "looking" deep inside the proton, where quarks act almost like free particles.

Q slider — probe energy in GeV, log-spaced from 0.35 to 500 GeV.
n_f slider — how many quark flavors are light enough to contribute virtual loops at this scale; changing it visibly steepens or flattens the running of α_s.
Auto-sweep — animates Q from low to high so you can watch the flux tube relax from a tight, turbulent, rigid bundle (confined, large α_s) into a loose cloud of nearly independent quarks (asymptotically free, small α_s).

The three colored spheres are a stylized proton (uud); the tube brightness, thickness and gluon-spark turbulence all scale directly with the computed α_s(Q) — this is an illustrative rendering of the mechanism, not a lattice-QCD wavefunction.

α_s vs ln(Q)

Quark (red) Quark (green) Quark (blue)

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Asymptotic Freedom: The Running Strong Coupling αs(Q)

Asymptotic Freedom: The Running Strong Coupling α_s(Q)