The Perturbative QCD Series. The Parameters of QCD. Condensates

Abstract

A large number of the more reliable results in QCD come from perturbative expansions at large momenta, and are due to the asymptotic freedom property. This justifies devoting this section to presenting a summary of our knowledge of the basic functions β and γ _m ; in next one, we will discuss the character of the perturbative series. In supersymmetric extensions of QCD, both functions are related and, for some specific supersymmetric theories, they can be calculated exactly. Actually, and as proved by Mandelstam (1983), there are renormalization schemes in some supersymmetric theories in which both β, γ_m vanish identically, and in others they can be found to all orders, as remarked first by Shifman, Vainshtein and Zakharov (1983). We will not discuss these theories here. The interested reader may find information, and trace the relevant literature, from the monumental papers of Seiberg and Witten (1994); we turn now to ordinary QCD.