Soft and Collinear Radiation and Factorization in Perturbation Theory and Beyond

Abstract

Power corrections to differential cross sections near a kinematic threshold are analysed by Dressed Gluon Exponentiation. Exploiting the factorization property of soft and collinear radiation, the dominant radiative corrections in the threshold region are resummed, yielding a renormalization-scale-invariant expression for the Sudakov exponent. The interplay between Sudakov logs and renormalons is clarified, and the necessity to resum the latter whenever power corrections are non-negligible is emphasized. The presence of power-suppressed ambiguities in the exponentiation kernel suggests that power corrections exponentiate as well. This leads to a non-perturbative factorization formula with non-trivial predictions on the structure of power corrections, which can be contrasted with the OPE. Two examples are discussed. The first is event-shape distributions in the two-jet region, where a wealth of precise data provides a strong motivation for the improved perturbative technique and an ideal situation to study hadronization. The second example is deep inelastic structure functions. In contrast to event shapes, structure functions have an OPE. However, since the OPE breaks down at large x, it does not provide a practical framework for the parametrization of power corrections. Performing a detailed analysis of twist 4 it is shown precisely how the twist-2 renormalon ambiguity eventually cancels out. This analysis provides a physical picture which substantiates the non-perturbative factorization conjecture.