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

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 Λ 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≳Λ, 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 α_s^MS(M_Z)=0.110±0.001, with a theoretical uncertainty of ~5%.