QCD Resummation Techniques

Abstract

In this thesis, we develop resummation algorithms suitable for perturbative QCD. In the first part, we propose a resummation technique applicable to the Regge limit. We develop a new systematic procedure for this limit in perturbative QCD to arbitrary logarithmic order. The formalism relies on the IR structure and the gauge symmetry of the theory. Using a factorization procedure introduced by Sen, we derive a sum of convolutions in transverse momentum space over soft and jet functions, which approximate the amplitude up to power-suppressed corrections. A set of evolution equations generalizing the BFKL equation and controlling the high energy behavior of the amplitudes to arbitrary logarithmic accuracy is derived. The general method is illustrated in the case of leading and next-to-leading logarithmic gluon reggeization and BFKL equation. We confirm the standard results at LL accuracy. At NLL order, we find an agreement with the reggeization conjecture up to two loops. However, starting at three loop order, we identify contributions violating the Regge ansatz. In addition, we calculate the evolution kernel determining the high-energy behavior of the non-reggeized term in the scattering amplitude. In the second part, we focus our attention to another intriguing problem of high-energy QCD, the resummation associated with soft radiation in dijet events which is complicated by the presence of non-global logarithms. We introduce a set of correlations between energy flow and event shapes that are sensitive to the flow of color at short distances in jet events. The method is illustrated for electron-positron dijet events. We calculate the correlation at leading logarithm in the energy flow and at next-to-leading-logarithm in the event shape.