  In this PhD thesis, we analyze and generalize the renormalization group
approach to the resummation of large logarithms in the perturbative expansion
due to soft and collinear multiparton emissions. In particular, we present a
generalization of this approach to prompt photon production. It is interesting
to see that also with the more intricate two-scale kinematics that
characterizes prompt photon production in the soft limit, it remains true that
resummation simply follows from general kinematic properties of the phase
space. Also, this approach does not require a separate treatment of individual
colour structures when more than one colour structure contributes to fixed
order results. However, the resummation formulae obtained here turn out to be
less predictive than previous results: this depends on the fact that here
neither specific factorization properties of the cross section in the soft
limit is assumed, nor that soft emission satisfies eikonal-like relations. We
also derive resumation formulae to all logarithmic accuracy and valid for all
values of rapidity for the prompt photon production and the Drell-Yan rapidity
distributions. We show that for the fixed-target experiment E866/NuSea, the NLL
resummation corrections are comparable to NLO fixed-order corrections and are
crucial to obtain agreement with the data. Finally we outline also possible
future applications of the renormalization group approach.
