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

Asymptotic freedom means that the QCD running coupling decreases at high momentum because its beta function 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 ${\Lambda }_{\mathrm{QCD}}$, defined schematically byAt energies of order ${\Lambda }_{\mathrm{QCD}}$ the coupling becomes strong, confinement and chiral symmetry breaking occur, and most visible hadron mass is generated dynamically.