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I have a question about $\Lambda_{QCD}$, the energy scale at which there is a transition from the regime of perturbative QCD to quark confinement. How it is measured experimentally?

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$Λ_{QCD}$ is measured in processes where the strong coupling constant and other measurables vary with momentum scale $Q$. For instance, evolution of nucleon structure functions measured in lepton-nucleon deep-inelastic scattering, heavy quarkonia decays, collider jet physics, electroweak physics at the Z, ...

Most results are in the 200 to 300 MeV range.

A good place to find definitive answers is always the Particle Data Book: http://pdg.lbl.gov/

In the review of QCD therein at http://pdg.lbl.gov/2014/reviews/rpp2014-rev-qcd.pdf they point out on page 3 that "... it has become standard practice to quote the value of $\alpha_S$ at a given scale (typically $M_Z$) rather than to quote a value for $\Lambda$."

Nevertheless, they give values of $Λ_{QCD}$ on page 30 (as equations 9.24 a-c). They also show the running of $\alpha_S$ as a function of $Q^2$ as the last plot (Fig. 9.4).

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