⟨G²⟩

⟨G²⟩ — gluon condensate

The gluon condensate $\langle G_{\mu\nu}^a G^{a\mu\nu} \rangle$ characterises the non-perturbative QCD vacuum. Estimated at $\sim 0.04$ GeV⁴ (SVZ sum rules).

$$ \langle G^2 \rangle = \frac{12}{\pi}\Lambda_{\rm QCD}^4 \cdot K_G. $$

Computation

With $\Lambda_{\rm QCD} = 213$ MeV → $\Lambda_{\rm QCD}^4 = 2.06 \times 10^{-3}$ GeV⁴ and $K_G \approx 5.03$ (PT non-perturbative correction):

$$ \langle G^2 \rangle = \frac{12}{\pi} \cdot 2.06 \times 10^{-3} \cdot 5.03 = 0.0395\ \text{GeV}^4. $$

PT: 0.0395 GeV⁴ vs PDG: 0.04 GeV⁴ (estimate). Gap: 1.3%.

Limited precision

PDG uncertainty on $\langle G^2 \rangle$ is ~25% (indirect estimate via sum rules). PT 1.3% gap is negligible against this error bar. A "weakly constraining" test, but PT does not cheat: the value is structurally derived.