ABSTRACT
This Chapter illustrates the calculation to one loop order of QCD of the basic renormalisation constants relative to: gauge fields (gluon) propagator, quark propagator and vertex function, as functions of the running momentum https://www.w3.org/1998/Math/MathML" display="inline"> q 2 and renormalised at an arbitrary momentum scale https://www.w3.org/1998/Math/MathML" display="inline"> μ 2 . The results (obtained with dimensional regularisation, Appendix E), allow the determination of the high momentum behaviour of the colour coupling constant https://www.w3.org/1998/Math/MathML" display="inline"> α S ( q 2 ) , via the renormalisation group equation devised by Gell-Mann and Low for QED (Chapter 13). One finds the surprising result that the QCD coupling constant decreases for https://www.w3.org/1998/Math/MathML" display="inline"> q 2 → ∞ , for a not-too-large number of quark flavours ( https://www.w3.org/1998/Math/MathML" display="inline"> n f ≤ 16 ), a phenomenon called asymptotic freedom, discovered by D. Gross and F. Wilczek and, independently, by D. Politzer (1973). The running QCD coupling constant has been measured at the high energy colliders, LEP ( https://www.w3.org/1998/Math/MathML" display="inline"> e + e - collider ) and LHC (proton-proton~collider), up to momentum transfer of the order of the https://www.w3.org/1998/Math/MathML" display="inline"> Z 0 intermediate boson mass. The picture of the strong interaction that emerges is that strong interactions are indeed strong for exchanged momenta below a scale https://www.w3.org/1998/Math/MathML" display="inline"> Λ Q C D ≃ 100 MeV . Above https://www.w3.org/1998/Math/MathML" display="inline"> Λ Q C D , one enters into a region of increasingly weaker interactions, amenable to a perturbative treatment, which explains the quasi-free behaviour of quarks in reactions at large momentum transfer, observed in the so-called deep inelastic scattering processes.
