Renormalon resummation and exponentiation of soft and collinear gluon radiation in the thrust distribution

Abstract

The thrust distribution in e+e- annihilation is calculated exploiting its exponentiation property in the two-jet region t = 1-T << 1. We present a general method (DGE) to calculate a large class of logarithmically enhanced terms, using the dispersive approach in renormalon calculus. Dressed Gluon Exponentiation is based on the fact that the exponentiation kernel is associated primarily with a single gluon emission, and therefore the exponent is naturally represented as an integral over the running coupling. Fixing the definition of Lambda is enough to guarantee consistency with the exact exponent to next-to-leading logarithmic accuracy. Renormalization scale dependence is avoided by keeping all the logs. Sub-leading logs, that are usually neglected, are factorially enhanced and are therefore important. Renormalization-group invariance as well as infrared renormalon divergence are recovered in the sum of all the logs. The logarithmically enhanced cross-section is evaluated by Borel summation. Renormalon ambiguity is then used to study power corrections in the peak region Qt \gsim Lambda, where the hierarchy between the renormalon closest to the origin (~1/Qt) and others (~1/(Qt)^n) starts to break down. The exponentiated power-corrections can be described by a shape-function, as advocated by Korchemsky and Sterman. Our calculation suggests that the even central moments of the shape-function are suppressed. Good fits are obtained yielding alpha_s^{MSbar} (M_Z) = 0.110 \pm 0.001, with a theoretical uncertainty of ~5%.