Infrared behaviour and renormalization scheme invariance of QCD observables

Abstract

In this thesis we study the infrared (IR) behaviour of QCD observables, and solutions to the problem of renormalization scheme dependence. We investigate the IR behaviour of all-orders leading-b renormalon resummations for certain Euclidean observables (the Adler-D function and the GLS and Björken sum rules) in the Borei representation. We find that these resummations are finite at the Landau pole (Q(^2) =Λ(^2)) and also 'freeze’ to zero in the Q(^2)→ 0 limit. We find this finite Landau pole behaviour has its origin in curious relations between IR and UV renormalons, which correspond to deeper conformal symmetries in QCD Green's functions. We consider these Borei resumed results in a skeleton expansion representation. This representation leads naturally to the standard Borei representation in the UV(Q(^2) ˃Λ(^2)) region and to a modified Borei representation in the IR (Q(^2) ˂Λ(^2)) region. We also consider the ambiguous part of the perturbative expansion in these representations. By demanding that such ambiguities cancel with similar ambiguities generated by the non-perturbative OPE, we are led to a new model for power corrections. We apply the complete renormalization group improved (CORGI) approach to all-orders renormalon resummations of the above-mentioned sum rules and compare the resultant predictions with experimental data. We also test our model for power corrections on these observables and find that the data favours power corrections of reasonably small magnitude. We also apply the CORGI approach, together with the physical scale and the effective charge approaches, to moments of F^^ and Բշ^. We use the Bernstein averages method in which any dependence of the analysis on regions of X and Q2 inaccessible to experiment is reduced.