<Asymptotic freedom> means that the QCD <running coupling> decreases at high momentum because its <beta function (physics)> is negative near zero. Quarks and gluons therefore interact weakly in sufficiently hard processes, justifying perturbation theory and explaining approximate parton behavior. <Dimensional transmutation> replaces the dimensionless ultraviolet coupling by the <QCD scale> $\Lambda_{\rm QCD}$, defined schematically by
$$
\alpha_s(\mu)\simeq\frac1{b_0\log(\mu^2/\Lambda_{\rm QCD}^2)}.
$$
At energies of order $\Lambda_{\rm QCD}$ the coupling becomes strong, <confinement> and <chiral symmetry breaking> occur, and most visible hadron mass is generated dynamically.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 305 / 1 / ii / Solution

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{title2=$\Lambda_{\rm QCD}$}
{wiki=Lambda_QCD}

The QCD scale is the renormalization-group invariant energy at which the perturbative running coupling becomes strong. It sets the characteristic scale of confinement and most hadron masses.


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 Incoming links: QCD scale